From 3d7a6e35edb6ab05442f4f0d2e61abf5fd1469de Mon Sep 17 00:00:00 2001
From: Chuan Zhang <engineerchuan@gmail.com>
Date: Mon, 9 Sep 2019 20:09:06 -0400
Subject: [PATCH 01/28] Add basic low pass filtering

---
 examples/filter_file.py            |  14 +++++
 test/assets/whitenoise.mp3         | Bin 0 -> 57136 bytes
 test/test_functional_filtering.py  |  44 +++++++++++++++
 torchaudio/functional.py           |   4 ++
 torchaudio/functional_filtering.py |  86 +++++++++++++++++++++++++++++
 5 files changed, 148 insertions(+)
 create mode 100644 examples/filter_file.py
 create mode 100644 test/assets/whitenoise.mp3
 create mode 100644 test/test_functional_filtering.py
 create mode 100644 torchaudio/functional_filtering.py

diff --git a/examples/filter_file.py b/examples/filter_file.py
new file mode 100644
index 0000000000..eb829551b4
--- /dev/null
+++ b/examples/filter_file.py
@@ -0,0 +1,14 @@
+import os
+import sys
+import torchaudio
+
+if __name__ == '__main__':
+
+    AUDIO_PATH = sys.argv[1]
+    OUTPUT_PATH = sys.argv[2]
+    N_FFT = 512
+    THRESHOLD_HZ = 3000
+
+    audio, sample_rate = torchaudio.load(AUDIO_PATH, normalization=False)
+    lowpassed_audio = torchaudio.functional.lowpass(audio, sample_rate, N_FFT, THRESHOLD_HZ)
+    torchaudio.save(OUTPUT_PATH, lowpassed_audio, sample_rate)
\ No newline at end of file
diff --git a/test/assets/whitenoise.mp3 b/test/assets/whitenoise.mp3
new file mode 100644
index 0000000000000000000000000000000000000000..d6fe9f44b90bb0e03d7b3ebfb8f46858f888bc3a
GIT binary patch
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diff --git a/test/test_functional_filtering.py b/test/test_functional_filtering.py
new file mode 100644
index 0000000000..89cb76a0f2
--- /dev/null
+++ b/test/test_functional_filtering.py
@@ -0,0 +1,44 @@
+from __future__ import absolute_import, division, print_function, unicode_literals
+import math
+import os
+import torch
+import torchaudio
+import torchaudio.functional as F
+import unittest
+import common_utils
+
+
+class TestFunctionalFiltering(unittest.TestCase):
+    test_dirpath, test_dir = common_utils.create_temp_assets_dir()
+
+    """
+    Open up a file of white noise.
+    Compute ratio of power in high band vs low bands, should be approximately equal
+    Perform a low pass filter at half Nyquist
+    Recompute ratio, should be very skewed
+    """
+    def test_band_energy_reduction(self):
+
+        def compute_ratio_high_vs_low(signal, n_fft):
+            dft = torch.stft(signal, n_fft)
+            psd = torch.sqrt(dft[:,:,:,0] * dft[:,:,:,0] + dft[:,:,:,1] * dft[:,:,:,1])
+            upper_indices = [slice(None), torch.arange(n_fft//4, n_fft//2+1).long(), slice(None)]
+            lower_indices = [slice(None), torch.arange(0, n_fft//4).long(), slice(None)]
+
+            higher_bands_avg_energy = torch.mean(psd[upper_indices]).item()
+            lower_bands_avg_energy = torch.mean(psd[lower_indices]).item()
+            return (higher_bands_avg_energy / lower_bands_avg_energy)
+
+        white_noise_path = os.path.join(os.path.join(self.test_dirpath, "assets"), 'whitenoise.mp3')
+        audio, sample_rate = torchaudio.load(white_noise_path, normalization=False)
+        high_to_low_pre_lowpass = compute_ratio_high_vs_low(audio, 512)
+        self.assertTrue(0.25 < high_to_low_pre_lowpass < 4)
+        CUTOFF_FREQ = sample_rate // 4 # half of nyquist
+        lowpassed_audio = torchaudio.functional.lowpass(audio, sample_rate, 512, CUTOFF_FREQ)
+        high_to_low_post_lowpass = compute_ratio_high_vs_low(lowpassed_audio, 512)
+        
+        print(high_to_low_pre_lowpass, high_to_low_post_lowpass)
+        self.assertTrue( high_to_low_post_lowpass * 10 < high_to_low_pre_lowpass )
+
+if __name__ == '__main__':
+    unittest.main()
diff --git a/torchaudio/functional.py b/torchaudio/functional.py
index e33cc702c7..0b2e7122ff 100644
--- a/torchaudio/functional.py
+++ b/torchaudio/functional.py
@@ -15,6 +15,7 @@
     'angle',
     'magphase',
     'phase_vocoder',
+    'lowpass',
 ]
 
 
@@ -466,3 +467,6 @@ def phase_vocoder(complex_specgrams, rate, phase_advance):
     complex_specgrams_stretch = torch.stack([real_stretch, imag_stretch], dim=-1)
 
     return complex_specgrams_stretch
+
+
+from torchaudio.functional_filtering import lowpass1 as lowpass
\ No newline at end of file
diff --git a/torchaudio/functional_filtering.py b/torchaudio/functional_filtering.py
new file mode 100644
index 0000000000..a925b1a154
--- /dev/null
+++ b/torchaudio/functional_filtering.py
@@ -0,0 +1,86 @@
+from __future__ import absolute_import, division, print_function, unicode_literals
+import math
+import torch
+import torchaudio
+
+
+__all__ = [
+    'lowpass1',
+]
+
+# Should we name this low pass filter?
+def lowpass1(waveform,           # type: Tensor
+             sample_rate,        # type: int
+             n_fft,              # type: int
+             f_thresh,           # type: int
+             hop_length=None,    # type: Optional[int]
+             win_length=None,    # type: Optional[int]
+             window=None,        # type: Optional[Tensor]
+             center=True,        # type: Optional[bool]
+             pad_mode='reflect', # type: Optional[str]
+             normalized=False,   # type: Optional[bool]
+             onesided=True,      # type: Optional[bool]
+            ):
+    # type: (...) -> Tensor
+    r"""Simple low pass filter.  Performs Short Time Fourier Transform, zeros out elements
+        above a threshold requency, and inverts Fourier Transform.
+        
+    Args:
+        waveform (torch.Tensor): Audio waveform that has a size of (channel, n_frames)
+        sample_rate (int): Audio waveform sampling rate in frames / sec (Hz)
+        n_fft (int): Size of Fourier transform in frames
+        f_thresh (int): Threshold above which signal will be filtered out (Hz)
+        hop_length (Optional[int]): See STFT documentation
+        win_length (Optional[int]): See STFT documentation
+        window (Optional[torch.Tensor]): See STFT documentation
+        center (Optional[bool]): See STFT documentation
+        pad_mode (Optional[str]): See STFT documentation
+        normalized (Optional[bool]): See STFT documentation
+        onesided (Optional[bool]): See STFT documentation
+
+    Returns:
+        torch.Tensor: Audio waveform that has been denoised of size (channel, n_frames)
+    """    
+
+    assert(f_thresh < sample_rate // 2)
+    assert(f_thresh >= 0)
+
+    # Convert threshold frequency cutoff to index
+    # Depends on the sampling rate
+    i_thresh = math.ceil(f_thresh * n_fft / sample_rate)
+
+    assert(i_thresh < n_fft // 2)
+
+    waveform_stft = torch.stft( waveform,
+                                n_fft,
+                                hop_length,
+                                win_length,
+                                window,
+                                center,
+                                pad_mode,
+                                normalized,
+                                onesided
+                               )
+
+
+    # Zero out elements above the CUTOFF
+    (n_channels, fft_size, n_windows, n_real_complex) = waveform_stft.size()
+    assert(2 == n_real_complex)
+    assert(1 == n_channels or 2 == n_channels)  # audio is mono or stereo
+    
+    # Set all components above threshold to zero
+    i_thresh_end = fft_size if onesided else fft_size - i_thresh - 1
+    waveform_stft[[slice(None), torch.arange(i_thresh, i_thresh_end).long(), slice(None), slice(None)]] = 0
+
+    denoised_audio = torchaudio.functional.istft(waveform_stft,
+                                                 n_fft,
+                                                 hop_length,
+                                                 win_length,
+                                                 window,
+                                                 center,
+                                                 pad_mode,
+                                                 normalized,
+                                                 onesided,
+                                                 waveform.size()[1])
+
+    return denoised_audio

From 5202837510598726069148320162c3d4939410a3 Mon Sep 17 00:00:00 2001
From: Chuan Zhang <engineerchuan@gmail.com>
Date: Mon, 9 Sep 2019 21:03:49 -0400
Subject: [PATCH 02/28] Naive first implementation of biquad per SoX
 implementation

---
 test/test_functional_filtering.py  | 26 ++++++++++++++++++++
 torchaudio/functional.py           |  4 +++-
 torchaudio/functional_filtering.py | 38 +++++++++++++++++++++++++++++-
 3 files changed, 66 insertions(+), 2 deletions(-)

diff --git a/test/test_functional_filtering.py b/test/test_functional_filtering.py
index 89cb76a0f2..a90b920903 100644
--- a/test/test_functional_filtering.py
+++ b/test/test_functional_filtering.py
@@ -40,5 +40,31 @@ def compute_ratio_high_vs_low(signal, n_fft):
         print(high_to_low_pre_lowpass, high_to_low_post_lowpass)
         self.assertTrue( high_to_low_post_lowpass * 10 < high_to_low_pre_lowpass )
 
+    def test_biquad_sox_compliance(self):
+
+        """
+        Run a file through SoX biquad with randomly chosen coefficients
+        Then run a file through our biquad method. 
+        Should match
+        """
+        b0 = 0.4
+        b1 = 0.2
+        b2 = 0.9
+        a0 = 0.7
+        a1 = 0.2
+        a2 = 0.6
+
+        fn_sine = os.path.join(self.test_dirpath, "assets", "sinewave.wav")
+        
+        E = torchaudio.sox_effects.SoxEffectsChain()
+        E.set_input_file(fn_sine)
+        E.append_effect_to_chain("biquad", [b0, b1, b2, a0, a1, a2])
+        sox_signal_out, sr = E.sox_build_flow_effects()
+        
+        audio, sample_rate = torchaudio.load(fn_sine, normalization=True)
+        signal_out = torchaudio.functional.biquad(audio, b0, b1, b2, a0, a1, a2)
+
+        assert(torch.allclose(sox_signal_out, signal_out, atol=1e-4))
+
 if __name__ == '__main__':
     unittest.main()
diff --git a/torchaudio/functional.py b/torchaudio/functional.py
index 0b2e7122ff..a8924025da 100644
--- a/torchaudio/functional.py
+++ b/torchaudio/functional.py
@@ -16,6 +16,7 @@
     'magphase',
     'phase_vocoder',
     'lowpass',
+    'biquad',
 ]
 
 
@@ -469,4 +470,5 @@ def phase_vocoder(complex_specgrams, rate, phase_advance):
     return complex_specgrams_stretch
 
 
-from torchaudio.functional_filtering import lowpass1 as lowpass
\ No newline at end of file
+from torchaudio.functional_filtering import lowpass1 as lowpass
+from torchaudio.functional_filtering import biquad
\ No newline at end of file
diff --git a/torchaudio/functional_filtering.py b/torchaudio/functional_filtering.py
index a925b1a154..83b96321cc 100644
--- a/torchaudio/functional_filtering.py
+++ b/torchaudio/functional_filtering.py
@@ -6,9 +6,45 @@
 
 __all__ = [
     'lowpass1',
+    'biquad',
 ]
 
-# Should we name this low pass filter?
+
+"""
+Biquad filtering approach based on SoX
+
+Given coefficients of a biquad filter, return the output
+
+TBD Need to do performance profile, very slow
+"""
+def biquad(input, b0, b1, b2, a0, a1, a2):
+
+    n_channels, n_samples = input.size()
+    output = torch.zeros_like(input)
+
+    # Normalize the coefficients
+    b2 = b2 / a0
+    b1 = b1 / a0
+    b0 = b0 / a0
+    a2 = a2 / a0
+    a1 = a1 / a0
+
+    # Initial Conditions set to zero
+    pi1 = torch.zeros(n_channels, 1)
+    pi2 = torch.zeros(n_channels, 1)
+    po1 = torch.zeros(n_channels, 1)
+    po2 = torch.zeros(n_channels, 1)
+
+    for i in range(input.size()[1]):
+        o0 = input[:, i] * b0 + pi1 * b1 + pi2 * b2 - po1 * a1 - po2 * a2
+        pi2 = pi1
+        pi1 = input[:, i]
+        po2 = po1
+        po1 = o0
+        output[:, i] = o0
+
+    return output
+
 def lowpass1(waveform,           # type: Tensor
              sample_rate,        # type: int
              n_fft,              # type: int

From b98522ea34dbe99e561a9a8bd589f36d19470ff0 Mon Sep 17 00:00:00 2001
From: Chuan Zhang <engineerchuan@gmail.com>
Date: Mon, 9 Sep 2019 21:50:21 -0400
Subject: [PATCH 03/28] Add highpass filtering

---
 test/test_functional_filtering.py  | 53 ++++++++++++++++++++++++++++--
 torchaudio/functional.py           |  4 +++
 torchaudio/functional_filtering.py | 48 ++++++++++++++++++++++++---
 3 files changed, 97 insertions(+), 8 deletions(-)

diff --git a/test/test_functional_filtering.py b/test/test_functional_filtering.py
index a90b920903..49f7e8893a 100644
--- a/test/test_functional_filtering.py
+++ b/test/test_functional_filtering.py
@@ -34,7 +34,7 @@ def compute_ratio_high_vs_low(signal, n_fft):
         high_to_low_pre_lowpass = compute_ratio_high_vs_low(audio, 512)
         self.assertTrue(0.25 < high_to_low_pre_lowpass < 4)
         CUTOFF_FREQ = sample_rate // 4 # half of nyquist
-        lowpassed_audio = torchaudio.functional.lowpass(audio, sample_rate, 512, CUTOFF_FREQ)
+        lowpassed_audio = F.lowpass(audio, sample_rate, 512, CUTOFF_FREQ)
         high_to_low_post_lowpass = compute_ratio_high_vs_low(lowpassed_audio, 512)
         
         print(high_to_low_pre_lowpass, high_to_low_post_lowpass)
@@ -55,16 +55,63 @@ def test_biquad_sox_compliance(self):
         a2 = 0.6
 
         fn_sine = os.path.join(self.test_dirpath, "assets", "sinewave.wav")
-        
         E = torchaudio.sox_effects.SoxEffectsChain()
         E.set_input_file(fn_sine)
         E.append_effect_to_chain("biquad", [b0, b1, b2, a0, a1, a2])
         sox_signal_out, sr = E.sox_build_flow_effects()
         
         audio, sample_rate = torchaudio.load(fn_sine, normalization=True)
-        signal_out = torchaudio.functional.biquad(audio, b0, b1, b2, a0, a1, a2)
+        signal_out = F.biquad(audio, b0, b1, b2, a0, a1, a2)
 
         assert(torch.allclose(sox_signal_out, signal_out, atol=1e-4))
 
+    def test_lowpass_sox_compliance(self):
+
+        """
+        Run a file through SoX lowpass filter
+        Then run through our lowpass filter
+        Should match
+        """
+
+        CUTOFF_FREQ = 3000
+
+        noise_filepath = os.path.join(self.test_dirpath, "assets", "whitenoise.mp3")
+        E = torchaudio.sox_effects.SoxEffectsChain()
+        E.set_input_file(noise_filepath)
+        E.append_effect_to_chain("lowpass", [CUTOFF_FREQ])
+        sox_signal_out, sr = E.sox_build_flow_effects()
+
+        noise, sample_rate = torchaudio.load(noise_filepath, normalization=True)
+        signal_out = F.lowpass_biquad(noise, sample_rate, CUTOFF_FREQ)
+
+        print(sox_signal_out, signal_out)
+
+        assert(torch.allclose(sox_signal_out, signal_out, atol=1e-4))
+
+    def test_highpass_sox_compliance(self):
+
+        """
+        Run a file through SoX highpass filter
+        Then run through our highpass filter
+        Should match
+        """
+
+        CUTOFF_FREQ = 1000
+
+        noise_filepath = os.path.join(self.test_dirpath, "assets", "whitenoise.mp3")
+        E = torchaudio.sox_effects.SoxEffectsChain()
+        E.set_input_file(noise_filepath)
+        E.append_effect_to_chain("highpass", [CUTOFF_FREQ])
+        sox_signal_out, sr = E.sox_build_flow_effects()
+
+        noise, sample_rate = torchaudio.load(noise_filepath, normalization=True)
+        signal_out = F.highpass_biquad(noise, sample_rate, CUTOFF_FREQ)
+
+        print(sox_signal_out, signal_out)
+
+        assert(torch.allclose(sox_signal_out, signal_out, atol=1e-4))
+
+
+
 if __name__ == '__main__':
     unittest.main()
diff --git a/torchaudio/functional.py b/torchaudio/functional.py
index a8924025da..f19371d5b4 100644
--- a/torchaudio/functional.py
+++ b/torchaudio/functional.py
@@ -16,6 +16,8 @@
     'magphase',
     'phase_vocoder',
     'lowpass',
+    'lowpass_biquad',
+    'highpass_biquad',
     'biquad',
 ]
 
@@ -471,4 +473,6 @@ def phase_vocoder(complex_specgrams, rate, phase_advance):
 
 
 from torchaudio.functional_filtering import lowpass1 as lowpass
+from torchaudio.functional_filtering import lowpass_biquad
+from torchaudio.functional_filtering import highpass_biquad
 from torchaudio.functional_filtering import biquad
\ No newline at end of file
diff --git a/torchaudio/functional_filtering.py b/torchaudio/functional_filtering.py
index 83b96321cc..1ca01c79b7 100644
--- a/torchaudio/functional_filtering.py
+++ b/torchaudio/functional_filtering.py
@@ -1,22 +1,60 @@
 from __future__ import absolute_import, division, print_function, unicode_literals
 import math
 import torch
+import math
 import torchaudio
 
+"""
+Biquad filtering approach based on SoX implementation 14.4.2
+
+Performance is currently very slow
+"""
 
 __all__ = [
     'lowpass1',
     'biquad',
+    'lowpass_biquad',
+    'highpass_biquad',
 ]
 
 
-"""
-Biquad filtering approach based on SoX
+def _dB2Linear(x):
+    return math.exp(x * math.log(10) / 20.0)
+
+def highpass_biquad(input, sr, cutoff_freq, Q = 0.707):
+
+    GAIN = 1
+    w0 = 2 * math.pi * cutoff_freq / sr
+    A = math.exp(GAIN / 40.0 * math.log(10))
+    alpha = math.sin(w0) / 2 / Q
+    mult = _dB2Linear(max(GAIN, 0))
+
+    b0 = (1 + math.cos(w0))/2
+    b1 = -1 - math.cos(w0)
+    b2 = b0
+    a0 = 1 + alpha
+    a1 = -2 * math.cos(w0)
+    a2 = 1 - alpha
+    return biquad(input, b0, b1, b2, a0, a1, a2)
+
+
+def lowpass_biquad(input, sr, cutoff_freq, Q = 0.707):
+    
+    GAIN = 1
+    w0 = 2 * math.pi * cutoff_freq / sr
+    A = math.exp(GAIN / 40.0 * math.log(10))
+    alpha = math.sin(w0) / 2 / Q
+    mult = _dB2Linear(max(GAIN, 0))
+
+    b0 = (1 - math.cos(w0))/2
+    b1 = 1 - math.cos(w0)
+    b2 = b0
+    a0 = 1 + alpha
+    a1 = -2 * math.cos(w0)
+    a2 = 1 - alpha
+    return biquad(input, b0, b1, b2, a0, a1, a2)
 
-Given coefficients of a biquad filter, return the output
 
-TBD Need to do performance profile, very slow
-"""
 def biquad(input, b0, b1, b2, a0, a1, a2):
 
     n_channels, n_samples = input.size()

From 55a904c1e1209dde219ca37e7971570f3f2b2e41 Mon Sep 17 00:00:00 2001
From: Chuan Zhang <engineerchuan@gmail.com>
Date: Sat, 14 Sep 2019 20:39:37 -0400
Subject: [PATCH 04/28] added cpp implementation of filtering

---
 setup.py                           |   8 ++
 test/test_functional_filtering.py  | 117 ++++++++++------
 torchaudio/filtering.cpp           |  73 ++++++++++
 torchaudio/filtering.h             |  21 +++
 torchaudio/functional_filtering.py | 216 +++++++++++++++++++++--------
 5 files changed, 334 insertions(+), 101 deletions(-)
 create mode 100644 torchaudio/filtering.cpp
 create mode 100644 torchaudio/filtering.h

diff --git a/setup.py b/setup.py
index 9ed91f2468..4822a6e9d0 100644
--- a/setup.py
+++ b/setup.py
@@ -113,6 +113,14 @@ def check_env_flag(name, default=''):
             extra_compile_args=eca,
             extra_objects=extra_objects,
             extra_link_args=ela),
+        CppExtension(
+            '_torch_filtering',
+            ['torchaudio/filtering.cpp'],
+            libraries=libraries,
+            include_dirs=include_dirs,
+            extra_compile_args=eca,
+            extra_objects=extra_objects,
+            extra_link_args=ela),
     ],
     cmdclass={'build_ext': BuildExtension},
     install_requires=[pytorch_package_dep]
diff --git a/test/test_functional_filtering.py b/test/test_functional_filtering.py
index 49f7e8893a..0102bf5dd4 100644
--- a/test/test_functional_filtering.py
+++ b/test/test_functional_filtering.py
@@ -17,54 +17,43 @@ class TestFunctionalFiltering(unittest.TestCase):
     Perform a low pass filter at half Nyquist
     Recompute ratio, should be very skewed
     """
-    def test_band_energy_reduction(self):
 
+    @unittest.skip
+    def test_band_energy_reduction(self):
         def compute_ratio_high_vs_low(signal, n_fft):
             dft = torch.stft(signal, n_fft)
-            psd = torch.sqrt(dft[:,:,:,0] * dft[:,:,:,0] + dft[:,:,:,1] * dft[:,:,:,1])
-            upper_indices = [slice(None), torch.arange(n_fft//4, n_fft//2+1).long(), slice(None)]
-            lower_indices = [slice(None), torch.arange(0, n_fft//4).long(), slice(None)]
+            psd = torch.sqrt(
+                dft[:, :, :, 0] * dft[:, :, :, 0] + dft[:, :, :, 1] * dft[:, :, :, 1]
+            )
+            upper_indices = [
+                slice(None),
+                torch.arange(n_fft // 4, n_fft // 2 + 1).long(),
+                slice(None),
+            ]
+            lower_indices = [
+                slice(None),
+                torch.arange(0, n_fft // 4).long(),
+                slice(None),
+            ]
 
             higher_bands_avg_energy = torch.mean(psd[upper_indices]).item()
             lower_bands_avg_energy = torch.mean(psd[lower_indices]).item()
-            return (higher_bands_avg_energy / lower_bands_avg_energy)
+            return higher_bands_avg_energy / lower_bands_avg_energy
 
-        white_noise_path = os.path.join(os.path.join(self.test_dirpath, "assets"), 'whitenoise.mp3')
+        white_noise_path = os.path.join(
+            os.path.join(self.test_dirpath, "assets"), "whitenoise.mp3"
+        )
         audio, sample_rate = torchaudio.load(white_noise_path, normalization=False)
         high_to_low_pre_lowpass = compute_ratio_high_vs_low(audio, 512)
         self.assertTrue(0.25 < high_to_low_pre_lowpass < 4)
-        CUTOFF_FREQ = sample_rate // 4 # half of nyquist
+        CUTOFF_FREQ = sample_rate // 4  # half of nyquist
         lowpassed_audio = F.lowpass(audio, sample_rate, 512, CUTOFF_FREQ)
         high_to_low_post_lowpass = compute_ratio_high_vs_low(lowpassed_audio, 512)
-        
-        print(high_to_low_pre_lowpass, high_to_low_post_lowpass)
-        self.assertTrue( high_to_low_post_lowpass * 10 < high_to_low_pre_lowpass )
-
-    def test_biquad_sox_compliance(self):
-
-        """
-        Run a file through SoX biquad with randomly chosen coefficients
-        Then run a file through our biquad method. 
-        Should match
-        """
-        b0 = 0.4
-        b1 = 0.2
-        b2 = 0.9
-        a0 = 0.7
-        a1 = 0.2
-        a2 = 0.6
-
-        fn_sine = os.path.join(self.test_dirpath, "assets", "sinewave.wav")
-        E = torchaudio.sox_effects.SoxEffectsChain()
-        E.set_input_file(fn_sine)
-        E.append_effect_to_chain("biquad", [b0, b1, b2, a0, a1, a2])
-        sox_signal_out, sr = E.sox_build_flow_effects()
-        
-        audio, sample_rate = torchaudio.load(fn_sine, normalization=True)
-        signal_out = F.biquad(audio, b0, b1, b2, a0, a1, a2)
 
-        assert(torch.allclose(sox_signal_out, signal_out, atol=1e-4))
+        print(high_to_low_pre_lowpass, high_to_low_post_lowpass)
+        self.assertTrue(high_to_low_post_lowpass * 10 < high_to_low_pre_lowpass)
 
+    @unittest.skip        
     def test_lowpass_sox_compliance(self):
 
         """
@@ -84,10 +73,59 @@ def test_lowpass_sox_compliance(self):
         noise, sample_rate = torchaudio.load(noise_filepath, normalization=True)
         signal_out = F.lowpass_biquad(noise, sample_rate, CUTOFF_FREQ)
 
-        print(sox_signal_out, signal_out)
+        assert torch.allclose(sox_signal_out, signal_out, atol=1e-4)
 
-        assert(torch.allclose(sox_signal_out, signal_out, atol=1e-4))
+    def test_biquad_filtering(self):
+        """
+        Try three implementations of biquad filtering and test speed
+        - 1.) Call to SoX
+        - 2.) Call to cpp biquad function
+        - 3.) Call to Python biquad function
+
+        Current results: 1 ~20x faster than 2 ~ 15x faster than 3
+        """
+
+        import time, _torch_filtering
+
+        b0 = 0.4
+        b1 = 0.2
+        b2 = 0.9
+        a0 = 0.7
+        a1 = 0.2
+        a2 = 0.6
+
+        # SoX method
+        fn_sine = os.path.join(self.test_dirpath, "assets", "sinewave.wav")
+        E = torchaudio.sox_effects.SoxEffectsChain()
+        E.set_input_file(fn_sine)
+        _timing_sox = time.time()
+        E.append_effect_to_chain("biquad", [b0, b1, b2, a0, a1, a2])
+        waveform_sox_out, sr = E.sox_build_flow_effects()
+        _timing_sox_run_time = time.time() - _timing_sox
+        
+        # CPP Filtering with Biquad
+        audio, sample_rate = torchaudio.load(fn_sine, normalization=True)
+        waveform_cpp_out = torch.zeros_like(audio)
+        _timing_cpp_filtering = time.time()
+        _torch_filtering.biquad(audio, waveform_cpp_out, b0, b1, b2, a0, a1, a2)
+        _timing_cpp_run_time = time.time() - _timing_cpp_filtering
+
+        # Native Python Implementation
+        _timing_python = time.time()
+        waveform_python_out = F.biquad(audio, b0, b1, b2, a0, a1, a2)
+        _timing_python_run_time = time.time() - _timing_python        
+        
+        assert torch.allclose(waveform_sox_out, waveform_python_out, atol=1e-5)
+        assert torch.allclose(waveform_sox_out, waveform_cpp_out, atol=1e-5)
+
+        print("SoX Run Time   : ", round(_timing_sox_run_time, 3))
+        print("CPP Run Time   : ", round(_timing_cpp_run_time, 3))
+        print("Python Run Time: ", round(_timing_python_run_time, 3))
+
+        assert( 1== 0)
 
+
+    @unittest.skip
     def test_highpass_sox_compliance(self):
 
         """
@@ -107,11 +145,8 @@ def test_highpass_sox_compliance(self):
         noise, sample_rate = torchaudio.load(noise_filepath, normalization=True)
         signal_out = F.highpass_biquad(noise, sample_rate, CUTOFF_FREQ)
 
-        print(sox_signal_out, signal_out)
-
-        assert(torch.allclose(sox_signal_out, signal_out, atol=1e-4))
-
+        assert torch.allclose(sox_signal_out, signal_out, atol=1e-4)
 
 
-if __name__ == '__main__':
+if __name__ == "__main__":
     unittest.main()
diff --git a/torchaudio/filtering.cpp b/torchaudio/filtering.cpp
new file mode 100644
index 0000000000..6ed701db82
--- /dev/null
+++ b/torchaudio/filtering.cpp
@@ -0,0 +1,73 @@
+#include <torch/extension.h>
+
+#include <sox.h>
+
+#include <algorithm>
+#include <cstdint>
+#include <stdexcept>
+#include <vector>
+
+namespace torch {
+namespace audio {
+
+  void biquad(
+    at::Tensor& input_waveform,
+    at::Tensor& output_waveform,
+    double b0,
+    double b1,
+    double b2,
+    double a0,
+    double a1,
+    double a2
+  ) {
+
+    int64_t n_channels = input_waveform.size(0);
+    int64_t n_frames = input_waveform.size(1);
+
+    //assert(output_waveform.size(0) == n_channels);
+    //assert(output_waveform.size(1) == n_frames);
+
+    b0 = b0 / a0;
+    b1 = b1 / a0;
+    b2 = b2 / a0;
+    a1 = a1 / a0;
+    a2 = a2 / a0;
+
+    for (int64_t i_channel = 0; i_channel < n_channels; ++i_channel) {
+
+      double pi1 = 0;
+      double pi2 = 0;
+      double po1 = 0;
+      double po2 = 0;
+      double o0, i0;
+    
+      for (int64_t i_frame = 0; i_frame < n_frames; ++i_frame) {
+        i0 = input_waveform[i_channel][i_frame].item<double>();
+        o0 = (i0 * b0 + pi1 * b1 + pi2 * b2 - po1 * a1 - po2 * a2);
+        
+        // increment time forward
+        pi2 = pi1;
+        pi1 = i0;
+        po2 = po1;
+        po1 = o0;
+        if (o0 > 1) {
+          o0 = 1;
+        } else if (o0 < -1) {
+          o0 = -1;
+        }
+        output_waveform[i_channel][i_frame] = o0;
+      }
+    }
+  }
+
+
+}}
+
+
+PYBIND11_MODULE(_torch_filtering, m) {
+  m.def(
+      "biquad",
+      &torch::audio::biquad,
+      "Executes biquad");
+
+}
diff --git a/torchaudio/filtering.h b/torchaudio/filtering.h
new file mode 100644
index 0000000000..908cf691ff
--- /dev/null
+++ b/torchaudio/filtering.h
@@ -0,0 +1,21 @@
+#include <string>
+
+namespace at {
+struct Tensor;
+} // namespace at
+
+namespace torch { namespace audio {
+
+/// Takes a tensor and performs a biquad difference function
+
+int biquad(
+    at::Tensor& input_waveform,
+    at::Tensor output_waveform,
+    float a0,
+    float a1,
+    float a2,
+    float b0,
+    float b1,
+    float b2
+);
+}} // namespace torch::audio
diff --git a/torchaudio/functional_filtering.py b/torchaudio/functional_filtering.py
index 1ca01c79b7..00a20076bf 100644
--- a/torchaudio/functional_filtering.py
+++ b/torchaudio/functional_filtering.py
@@ -7,21 +7,18 @@
 """
 Biquad filtering approach based on SoX implementation 14.4.2
 
-Performance is currently very slow
+Performance needs to be evaluated against SoX
+
 """
 
-__all__ = [
-    'lowpass1',
-    'biquad',
-    'lowpass_biquad',
-    'highpass_biquad',
-]
+__all__ = ["lowpass1", "biquad", "lowpass_biquad", "highpass_biquad"]
 
 
 def _dB2Linear(x):
     return math.exp(x * math.log(10) / 20.0)
 
-def highpass_biquad(input, sr, cutoff_freq, Q = 0.707):
+
+def highpass_biquad(input, sr, cutoff_freq, Q=0.707):
 
     GAIN = 1
     w0 = 2 * math.pi * cutoff_freq / sr
@@ -29,7 +26,7 @@ def highpass_biquad(input, sr, cutoff_freq, Q = 0.707):
     alpha = math.sin(w0) / 2 / Q
     mult = _dB2Linear(max(GAIN, 0))
 
-    b0 = (1 + math.cos(w0))/2
+    b0 = (1 + math.cos(w0)) / 2
     b1 = -1 - math.cos(w0)
     b2 = b0
     a0 = 1 + alpha
@@ -38,15 +35,15 @@ def highpass_biquad(input, sr, cutoff_freq, Q = 0.707):
     return biquad(input, b0, b1, b2, a0, a1, a2)
 
 
-def lowpass_biquad(input, sr, cutoff_freq, Q = 0.707):
-    
+def lowpass_biquad(input, sr, cutoff_freq, Q=0.707):
+
     GAIN = 1
     w0 = 2 * math.pi * cutoff_freq / sr
     A = math.exp(GAIN / 40.0 * math.log(10))
     alpha = math.sin(w0) / 2 / Q
     mult = _dB2Linear(max(GAIN, 0))
 
-    b0 = (1 - math.cos(w0))/2
+    b0 = (1 - math.cos(w0)) / 2
     b1 = 1 - math.cos(w0)
     b2 = b0
     a0 = 1 + alpha
@@ -55,17 +52,79 @@ def lowpass_biquad(input, sr, cutoff_freq, Q = 0.707):
     return biquad(input, b0, b1, b2, a0, a1, a2)
 
 
+
+
+def diff_eq_calculate(waveform, a_coeffs, b_coeffs):
+    """
+    waveform is the input audio tensor of size [n_channels, n_frames]
+
+    expresses general difference equation of the form:
+
+    a0 * o[n] + a1 * o[n-1] + a2 * o[n-2] + ... =
+    b0 * i[n] + b1 * i[n-1] + b2 * i[n-2] + ...
+
+    a_coeffs input list of length and [a0, a1, a2, ...]
+    b_coeffs input list length and [b0, b1, b2, ...]
+
+    """
+
+    def clip(v):
+        return max(-1.0, min(1.0, v))
+
+    [n_channels, n_frames] = waveform.size()    
+    n_a_coeffs = len(a_coeffs)
+    n_b_coeffs = len(b_coeffs)
+    n_order = max([n_a_coeffs, n_b_coeffs])
+    assert(n_order > 0 and n_a_coeffs > 0)
+    a0 = a_coeffs[0]
+
+    coeff_matrix = torch.zeros(2, n_order, dtype=torch.float)
+    # fill in the output coefficients
+    for i_a, a in enumerate(a_coeffs):
+        if i_a > 0:
+            coeff_matrix[0, n_order - i_a - 1] = -1.0 * a / a0
+    # fill in the input coefficients
+    for i_b, b in enumerate(b_coeffs):
+        coeff_matrix[1, n_order - i_b - 1] = float(b) / a0
+
+    print("Coefficients matrix", coeff_matrix)
+
+    # pad waveform by the order of the filter
+    pad = torch.zeros(n_channels, n_order - 1)
+    
+    padded_waveform = torch.cat([pad, waveform], dim = 1)
+    print("padded waveform", padded_waveform, padded_waveform.size())
+
+    dat = torch.stack([torch.zeros_like(padded_waveform), padded_waveform])
+    #print("padded data", dat.size(), dat)
+    coeff_flattened = coeff_matrix.view(-1)
+    for i in range(n_frames):
+        for i_channel in range(n_channels):
+            sub = dat[
+                [
+                    slice(None),
+                    i_channel,
+                    torch.arange(i, i + n_order).long(),
+                ]
+            ]
+            dat[0, i_channel, i + n_order - 1] = clip(torch.dot(sub.view(-1), coeff_flattened))
+    
+    return dat[[0, slice(None), torch.arange(n_order - 1, n_frames + n_order-1)]]
+
 def biquad(input, b0, b1, b2, a0, a1, a2):
 
+    def clip(v):
+        return max(-1.0, min(1.0, v))
+
     n_channels, n_samples = input.size()
     output = torch.zeros_like(input)
 
     # Normalize the coefficients
-    b2 = b2 / a0
-    b1 = b1 / a0
-    b0 = b0 / a0
-    a2 = a2 / a0
-    a1 = a1 / a0
+    b2 = float(b2) / a0
+    b1 = float(b1) / a0
+    b0 = float(b0) / a0
+    a2 = float(a2) / a0
+    a1 = float(a1) / a0
 
     # Initial Conditions set to zero
     pi1 = torch.zeros(n_channels, 1)
@@ -74,7 +133,7 @@ def biquad(input, b0, b1, b2, a0, a1, a2):
     po2 = torch.zeros(n_channels, 1)
 
     for i in range(input.size()[1]):
-        o0 = input[:, i] * b0 + pi1 * b1 + pi2 * b2 - po1 * a1 - po2 * a2
+        o0 = clip(input[:, i] * b0 + pi1 * b1 + pi2 * b2 - po1 * a1 - po2 * a2)
         pi2 = pi1
         pi1 = input[:, i]
         po2 = po1
@@ -83,18 +142,19 @@ def biquad(input, b0, b1, b2, a0, a1, a2):
 
     return output
 
-def lowpass1(waveform,           # type: Tensor
-             sample_rate,        # type: int
-             n_fft,              # type: int
-             f_thresh,           # type: int
-             hop_length=None,    # type: Optional[int]
-             win_length=None,    # type: Optional[int]
-             window=None,        # type: Optional[Tensor]
-             center=True,        # type: Optional[bool]
-             pad_mode='reflect', # type: Optional[str]
-             normalized=False,   # type: Optional[bool]
-             onesided=True,      # type: Optional[bool]
-            ):
+def lowpass1(
+    waveform,  # type: Tensor
+    sample_rate,  # type: int
+    n_fft,  # type: int
+    f_thresh,  # type: int
+    hop_length=None,  # type: Optional[int]
+    win_length=None,  # type: Optional[int]
+    window=None,  # type: Optional[Tensor]
+    center=True,  # type: Optional[bool]
+    pad_mode="reflect",  # type: Optional[str]
+    normalized=False,  # type: Optional[bool]
+    onesided=True,  # type: Optional[bool]
+):
     # type: (...) -> Tensor
     r"""Simple low pass filter.  Performs Short Time Fourier Transform, zeros out elements
         above a threshold requency, and inverts Fourier Transform.
@@ -114,47 +174,83 @@ def lowpass1(waveform,           # type: Tensor
 
     Returns:
         torch.Tensor: Audio waveform that has been denoised of size (channel, n_frames)
-    """    
+    """
 
-    assert(f_thresh < sample_rate // 2)
-    assert(f_thresh >= 0)
+    assert f_thresh < sample_rate // 2
+    assert f_thresh >= 0
 
     # Convert threshold frequency cutoff to index
     # Depends on the sampling rate
     i_thresh = math.ceil(f_thresh * n_fft / sample_rate)
 
-    assert(i_thresh < n_fft // 2)
-
-    waveform_stft = torch.stft( waveform,
-                                n_fft,
-                                hop_length,
-                                win_length,
-                                window,
-                                center,
-                                pad_mode,
-                                normalized,
-                                onesided
-                               )
+    assert i_thresh < n_fft // 2
 
+    waveform_stft = torch.stft(
+        waveform,
+        n_fft,
+        hop_length,
+        win_length,
+        window,
+        center,
+        pad_mode,
+        normalized,
+        onesided,
+    )
 
     # Zero out elements above the CUTOFF
     (n_channels, fft_size, n_windows, n_real_complex) = waveform_stft.size()
-    assert(2 == n_real_complex)
-    assert(1 == n_channels or 2 == n_channels)  # audio is mono or stereo
-    
+    assert 2 == n_real_complex
+    assert 1 == n_channels or 2 == n_channels  # audio is mono or stereo
+
     # Set all components above threshold to zero
     i_thresh_end = fft_size if onesided else fft_size - i_thresh - 1
-    waveform_stft[[slice(None), torch.arange(i_thresh, i_thresh_end).long(), slice(None), slice(None)]] = 0
-
-    denoised_audio = torchaudio.functional.istft(waveform_stft,
-                                                 n_fft,
-                                                 hop_length,
-                                                 win_length,
-                                                 window,
-                                                 center,
-                                                 pad_mode,
-                                                 normalized,
-                                                 onesided,
-                                                 waveform.size()[1])
+    waveform_stft[
+        [
+            slice(None),
+            torch.arange(i_thresh, i_thresh_end).long(),
+            slice(None),
+            slice(None),
+        ]
+    ] = 0
+
+    denoised_audio = torchaudio.functional.istft(
+        waveform_stft,
+        n_fft,
+        hop_length,
+        win_length,
+        window,
+        center,
+        pad_mode,
+        normalized,
+        onesided,
+        waveform.size()[1],
+    )
 
     return denoised_audio
+
+
+if __name__ == '__main__':
+
+    import _torch_filtering
+    x = torch.rand(1, 8000 * 10, dtype=torch.float)
+
+    
+    b0 = 0.3
+    b1 = 0.2
+    b2 = 0.4
+    a0 = 1.0
+    a1 = 0.2
+    a2 = 0.4
+    print(_torch_filtering.biquad(x, x, a0, a1, a2, b0,b1, b2))
+    
+
+    """startdiff = time.time()
+    v = diff_eq_calculate(x, [a0, a1, a2], [b0, b1, b2])
+    enddiff = time.time()
+    y = biquad(x, b0, b1, b2, a0, a1, a2)
+    end2 = time.time()
+    print(y.size())
+    print(v.size())
+    print(v, y)
+    print("time1", enddiff - startdiff)
+    print("time2", end2 - enddiff)"""
\ No newline at end of file

From 575339b50457b4fe10659cde707a14ac0351501f Mon Sep 17 00:00:00 2001
From: Chuan Zhang <engineerchuan@gmail.com>
Date: Sat, 14 Sep 2019 22:48:33 -0400
Subject: [PATCH 05/28] More tests of IIR vs FIR

---
 test/test_functional_filtering.py  | 246 +++++++++++++++++++----------
 torchaudio/filtering.cpp           |  66 +++++++-
 torchaudio/functional.py           |  21 +--
 torchaudio/functional_filtering.py | 119 +++-----------
 4 files changed, 254 insertions(+), 198 deletions(-)

diff --git a/test/test_functional_filtering.py b/test/test_functional_filtering.py
index 0102bf5dd4..4d658dec7b 100644
--- a/test/test_functional_filtering.py
+++ b/test/test_functional_filtering.py
@@ -6,54 +6,12 @@
 import torchaudio.functional as F
 import unittest
 import common_utils
+import time
 
 
 class TestFunctionalFiltering(unittest.TestCase):
     test_dirpath, test_dir = common_utils.create_temp_assets_dir()
 
-    """
-    Open up a file of white noise.
-    Compute ratio of power in high band vs low bands, should be approximately equal
-    Perform a low pass filter at half Nyquist
-    Recompute ratio, should be very skewed
-    """
-
-    @unittest.skip
-    def test_band_energy_reduction(self):
-        def compute_ratio_high_vs_low(signal, n_fft):
-            dft = torch.stft(signal, n_fft)
-            psd = torch.sqrt(
-                dft[:, :, :, 0] * dft[:, :, :, 0] + dft[:, :, :, 1] * dft[:, :, :, 1]
-            )
-            upper_indices = [
-                slice(None),
-                torch.arange(n_fft // 4, n_fft // 2 + 1).long(),
-                slice(None),
-            ]
-            lower_indices = [
-                slice(None),
-                torch.arange(0, n_fft // 4).long(),
-                slice(None),
-            ]
-
-            higher_bands_avg_energy = torch.mean(psd[upper_indices]).item()
-            lower_bands_avg_energy = torch.mean(psd[lower_indices]).item()
-            return higher_bands_avg_energy / lower_bands_avg_energy
-
-        white_noise_path = os.path.join(
-            os.path.join(self.test_dirpath, "assets"), "whitenoise.mp3"
-        )
-        audio, sample_rate = torchaudio.load(white_noise_path, normalization=False)
-        high_to_low_pre_lowpass = compute_ratio_high_vs_low(audio, 512)
-        self.assertTrue(0.25 < high_to_low_pre_lowpass < 4)
-        CUTOFF_FREQ = sample_rate // 4  # half of nyquist
-        lowpassed_audio = F.lowpass(audio, sample_rate, 512, CUTOFF_FREQ)
-        high_to_low_post_lowpass = compute_ratio_high_vs_low(lowpassed_audio, 512)
-
-        print(high_to_low_pre_lowpass, high_to_low_post_lowpass)
-        self.assertTrue(high_to_low_post_lowpass * 10 < high_to_low_pre_lowpass)
-
-    @unittest.skip        
     def test_lowpass_sox_compliance(self):
 
         """
@@ -71,21 +29,155 @@ def test_lowpass_sox_compliance(self):
         sox_signal_out, sr = E.sox_build_flow_effects()
 
         noise, sample_rate = torchaudio.load(noise_filepath, normalization=True)
-        signal_out = F.lowpass_biquad(noise, sample_rate, CUTOFF_FREQ)
+        signal_out = F.lowpass_biquad_python(noise, sample_rate, CUTOFF_FREQ)
 
         assert torch.allclose(sox_signal_out, signal_out, atol=1e-4)
 
-    def test_biquad_filtering(self):
+    def test_diff_eq(self):
+        """
+        Design a lowpass filter using scipy.signal filter design
+        https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.iirdesign.html#scipy.signal.iirdesign
+
+        from scipy.signal import iirdesign
+        b, a = iirdesign(0.2, 0.3, 1, 60)
+
+        Test is that this runs
+        """
+
+        b_coeffs = torch.tensor(
+            [
+                0.00299893,
+                -0.0051152,
+                0.00841964,
+                -0.00747802,
+                0.00841964,
+                -0.0051152,
+                0.00299893,
+            ]
+        )
+        a_coeffs = torch.tensor(
+            [
+                1.0,
+                -4.8155751,
+                10.2217618,
+                -12.14481273,
+                8.49018171,
+                -3.3066882,
+                0.56088705,
+            ]
+        )
+
+        noise_filepath = os.path.join(self.test_dirpath, "assets", "whitenoise.mp3")
+        audio, sample_rate = torchaudio.load(noise_filepath, normalization=True)
+
+        waveform_diff_eq_out = torch.zeros_like(audio)
+        F.diffeq_cpp(audio, waveform_diff_eq_out, a_coeffs, b_coeffs)
+
+    def test_low_pass_perf_iir_vs_fir(self):
+        """
+        Try two low pass filters to compare performance
+        - 10th order IIR 
+        - 40th order FIR
+        """
+
+        fir_impulse_response = [
+            -0.00040463742194593165,
+            -0.0011997613323707066,
+            -0.0018908492870125047,
+            -0.00207654308585229,
+            -0.001096110046662624,
+            0.0015056218536868779,
+            0.005330573111949219,
+            0.008753080180802494,
+            0.009251376850303583,
+            0.004551586188930009,
+            -0.00579865949432587,
+            -0.01919960191734472,
+            -0.029922330203954777,
+            -0.03058886187399114,
+            -0.014900805267782886,
+            0.019382291456268037,
+            0.06852266400807679,
+            0.12297037769851049,
+            0.16984408705548223,
+            0.19696650152723372,
+            0.19696650152723374,
+            0.16984408705548223,
+            0.12297037769851049,
+            0.06852266400807679,
+            0.01938229145626804,
+            -0.014900805267782887,
+            -0.03058886187399115,
+            -0.029922330203954784,
+            -0.01919960191734472,
+            -0.00579865949432587,
+            0.004551586188930011,
+            0.009251376850303588,
+            0.008753080180802494,
+            0.005330573111949219,
+            0.0015056218536868779,
+            -0.001096110046662626,
+            -0.0020765430858522907,
+            -0.0018908492870125056,
+            -0.0011997613323707066,
+            -0.00040463742194593165,
+        ]
+
+        iir_b_coeffs = torch.tensor(
+            [
+                4.14176942e-05,
+                -6.74168865e-05,
+                1.28894969e-04,
+                -7.60724730e-05,
+                6.18923831e-05,
+                6.18923831e-05,
+                -7.60724730e-05,
+                1.28894969e-04,
+                -6.74168865e-05,
+                4.14176942e-05,
+            ]
+        )
+        iir_a_coeffs = torch.tensor(
+            [
+                1.0,
+                -7.51701965,
+                25.93753044,
+                -53.79433042,
+                73.79210968,
+                -69.36257588,
+                44.65306696,
+                -18.98130961,
+                4.83553413,
+                -0.56282822,
+            ]
+        )
+
+        noise_filepath = os.path.join(self.test_dirpath, "assets", "whitenoise.mp3")
+        noise, sample_rate = torchaudio.load(noise_filepath, normalization=True)
+
+        waveform_diff_eq_out = torch.zeros_like(noise)
+        _diffeq_start_time = time.time()
+        F.diffeq_cpp(noise, waveform_diff_eq_out, iir_a_coeffs, iir_b_coeffs)
+        _diffeq_run_time = time.time() - _diffeq_start_time
+
+        # TBD
+
+        print("Diff Eq Low Pass Run Time:", _diffeq_run_time)
+        # print("FIR Low Pass Run Time    :", _fir_run_time)
+
+    def test_perf_biquad_filtering(self):
         """
-        Try three implementations of biquad filtering and test speed
+        Try implementations of biquad filtering and test speed
         - 1.) Call to SoX
         - 2.) Call to cpp biquad function
-        - 3.) Call to Python biquad function
+        - 3.) Call to cpp general difference equation function
+        - 4.) Call to Python biquad function
 
-        Current results: 1 ~20x faster than 2 ~ 15x faster than 3
+        Current results: 1 ~20x faster than 2, 2 ~ 2x faster than 3, 3 ~8x faster than 4
         """
 
-        import time, _torch_filtering
+        fn_sine = os.path.join(self.test_dirpath, "assets", "sinewave.wav")
+        audio, sample_rate = torchaudio.load(fn_sine, normalization=True)
 
         b0 = 0.4
         b1 = 0.2
@@ -95,57 +187,43 @@ def test_biquad_filtering(self):
         a2 = 0.6
 
         # SoX method
-        fn_sine = os.path.join(self.test_dirpath, "assets", "sinewave.wav")
         E = torchaudio.sox_effects.SoxEffectsChain()
         E.set_input_file(fn_sine)
         _timing_sox = time.time()
         E.append_effect_to_chain("biquad", [b0, b1, b2, a0, a1, a2])
         waveform_sox_out, sr = E.sox_build_flow_effects()
         _timing_sox_run_time = time.time() - _timing_sox
-        
+
         # CPP Filtering with Biquad
-        audio, sample_rate = torchaudio.load(fn_sine, normalization=True)
         waveform_cpp_out = torch.zeros_like(audio)
         _timing_cpp_filtering = time.time()
-        _torch_filtering.biquad(audio, waveform_cpp_out, b0, b1, b2, a0, a1, a2)
+        F.biquad_cpp(audio, waveform_cpp_out, b0, b1, b2, a0, a1, a2)
         _timing_cpp_run_time = time.time() - _timing_cpp_filtering
 
+        # Diff Eq Filter
+        waveform_diff_eq_out = torch.zeros_like(audio)
+        _timing_cpp_filtering = time.time()
+        F.diffeq_cpp(
+            audio,
+            waveform_diff_eq_out,
+            torch.tensor([a0, a1, a2]),
+            torch.tensor([b0, b1, b2]),
+        )
+        _timing_diff_eq_run_time = time.time() - _timing_cpp_filtering
+
         # Native Python Implementation
         _timing_python = time.time()
-        waveform_python_out = F.biquad(audio, b0, b1, b2, a0, a1, a2)
-        _timing_python_run_time = time.time() - _timing_python        
-        
+        waveform_python_out = F.biquad_python(audio, b0, b1, b2, a0, a1, a2)
+        _timing_python_run_time = time.time() - _timing_python
+
         assert torch.allclose(waveform_sox_out, waveform_python_out, atol=1e-5)
         assert torch.allclose(waveform_sox_out, waveform_cpp_out, atol=1e-5)
+        assert torch.allclose(waveform_sox_out, waveform_diff_eq_out, atol=1e-5)
 
-        print("SoX Run Time   : ", round(_timing_sox_run_time, 3))
-        print("CPP Run Time   : ", round(_timing_cpp_run_time, 3))
-        print("Python Run Time: ", round(_timing_python_run_time, 3))
-
-        assert( 1== 0)
-
-
-    @unittest.skip
-    def test_highpass_sox_compliance(self):
-
-        """
-        Run a file through SoX highpass filter
-        Then run through our highpass filter
-        Should match
-        """
-
-        CUTOFF_FREQ = 1000
-
-        noise_filepath = os.path.join(self.test_dirpath, "assets", "whitenoise.mp3")
-        E = torchaudio.sox_effects.SoxEffectsChain()
-        E.set_input_file(noise_filepath)
-        E.append_effect_to_chain("highpass", [CUTOFF_FREQ])
-        sox_signal_out, sr = E.sox_build_flow_effects()
-
-        noise, sample_rate = torchaudio.load(noise_filepath, normalization=True)
-        signal_out = F.highpass_biquad(noise, sample_rate, CUTOFF_FREQ)
-
-        assert torch.allclose(sox_signal_out, signal_out, atol=1e-4)
+        print("SoX Run Time          : ", round(_timing_sox_run_time, 3))
+        print("CPP Biquad Run Time   : ", round(_timing_cpp_run_time, 3))
+        print("CPP Diff Eq Run Time  : ", round(_timing_diff_eq_run_time, 3))
+        print("Python Run Time       : ", round(_timing_python_run_time, 3))
 
 
 if __name__ == "__main__":
diff --git a/torchaudio/filtering.cpp b/torchaudio/filtering.cpp
index 6ed701db82..c527f9b8db 100644
--- a/torchaudio/filtering.cpp
+++ b/torchaudio/filtering.cpp
@@ -1,15 +1,64 @@
 #include <torch/extension.h>
 
-#include <sox.h>
-
-#include <algorithm>
-#include <cstdint>
-#include <stdexcept>
-#include <vector>
+//#include <algorithm>
+//#include <cstdint>
+//#include <stdexcept>
+//#include <vector>
 
 namespace torch {
 namespace audio {
 
+
+  void diff_eq(
+    at::Tensor& input_waveform,
+    at::Tensor& output_waveform,
+    at::Tensor& a_coeffs,
+    at::Tensor& b_coeffs
+  ) {
+
+    int64_t n_channels = input_waveform.size(0);
+    int64_t n_frames = input_waveform.size(1);
+
+    assert(output_waveform.size(0) == n_channels);
+    assert(output_waveform.size(1) == n_frames);
+
+    int n_order = a_coeffs.size(0); // n'th order filter
+    assert(a_coeffs.size(0) == b_coeffs.size(0));
+
+    for (int64_t i_channel = 0; i_channel < n_channels; ++i_channel) {
+
+      // allocate a temporary data structure of size 2 x n_order
+      double i_s[n_order]= { };
+      double o_s[n_order]= { };
+    
+      for (int64_t i_frame = 0; i_frame < n_frames; ++i_frame) {
+
+        // populate the output
+        i_s[n_order-1] = input_waveform[i_channel][i_frame].item<double>();
+        double o0 = 0;
+        for (int i = 0; i < n_order; ++i) {
+          o0 += i_s[i] * b_coeffs[n_order - i - 1].item<double>();
+          if (i != n_order - 1) {
+            o0 -= o_s[i] * a_coeffs[n_order - i - 1].item<double>();
+          }
+        }
+        o0 = o0 / a_coeffs[0].item<double>();
+        if (o0 > 1) o0 = 1;
+        if (o0 < -1) o0 = -1;
+        o_s[n_order-1] = o0;
+        output_waveform[i_channel][i_frame] = o0;
+        
+        // shift everything over
+        for (int i = 0; i < (n_order - 1); ++i) {
+          i_s[i] = i_s[i+1];
+          o_s[i] = o_s[i+1];
+        }
+      }
+    }
+  }
+
+
+
   void biquad(
     at::Tensor& input_waveform,
     at::Tensor& output_waveform,
@@ -69,5 +118,8 @@ PYBIND11_MODULE(_torch_filtering, m) {
       "biquad",
       &torch::audio::biquad,
       "Executes biquad");
-
+  m.def(
+      "diff_eq",
+      &torch::audio::diff_eq,
+      "Executes difference equation");
 }
diff --git a/torchaudio/functional.py b/torchaudio/functional.py
index f19371d5b4..98a13fab23 100644
--- a/torchaudio/functional.py
+++ b/torchaudio/functional.py
@@ -15,13 +15,14 @@
     'angle',
     'magphase',
     'phase_vocoder',
-    'lowpass',
-    'lowpass_biquad',
-    'highpass_biquad',
-    'biquad',
+    'lowpass_depr',
+    'lowpass_biquad_python',
+    'highpass_biquad_python',
+    'biquad_python',
+    'biquad_cpp',
+    'diffeq_cpp',
 ]
 
-
 # TODO: remove this once https://github.com/pytorch/pytorch/issues/21478 gets solved
 @torch.jit.ignore
 def _stft(waveform, n_fft, hop_length, win_length, window, center, pad_mode, normalized, onesided):
@@ -472,7 +473,9 @@ def phase_vocoder(complex_specgrams, rate, phase_advance):
     return complex_specgrams_stretch
 
 
-from torchaudio.functional_filtering import lowpass1 as lowpass
-from torchaudio.functional_filtering import lowpass_biquad
-from torchaudio.functional_filtering import highpass_biquad
-from torchaudio.functional_filtering import biquad
\ No newline at end of file
+from torchaudio.functional_filtering import lowpass_depr
+from torchaudio.functional_filtering import lowpass_biquad_python
+from torchaudio.functional_filtering import highpass_biquad_python
+from torchaudio.functional_filtering import biquad_python
+from torchaudio.functional_filtering import biquad_cpp
+from torchaudio.functional_filtering import diffeq_cpp
diff --git a/torchaudio/functional_filtering.py b/torchaudio/functional_filtering.py
index 00a20076bf..07a4dc3fe5 100644
--- a/torchaudio/functional_filtering.py
+++ b/torchaudio/functional_filtering.py
@@ -1,24 +1,27 @@
 from __future__ import absolute_import, division, print_function, unicode_literals
 import math
 import torch
-import math
 import torchaudio
 
-"""
-Biquad filtering approach based on SoX implementation 14.4.2
-
-Performance needs to be evaluated against SoX
-
-"""
+__all__ = [
+    "lowpass_depr",
+    "biquad_python",
+    "lowpass_biquad_python",
+    "highpass_biquad_python",
+    "biquad_cpp",
+    "diffeq_cpp",
+]
 
-__all__ = ["lowpass1", "biquad", "lowpass_biquad", "highpass_biquad"]
+from _torch_filtering import biquad as biquad_cpp
+from _torch_filtering import diff_eq as diffeq_cpp
 
 
 def _dB2Linear(x):
+
     return math.exp(x * math.log(10) / 20.0)
 
 
-def highpass_biquad(input, sr, cutoff_freq, Q=0.707):
+def highpass_biquad_python(input, sr, cutoff_freq, Q=0.707):
 
     GAIN = 1
     w0 = 2 * math.pi * cutoff_freq / sr
@@ -32,10 +35,10 @@ def highpass_biquad(input, sr, cutoff_freq, Q=0.707):
     a0 = 1 + alpha
     a1 = -2 * math.cos(w0)
     a2 = 1 - alpha
-    return biquad(input, b0, b1, b2, a0, a1, a2)
+    return biquad_python(input, b0, b1, b2, a0, a1, a2)
 
 
-def lowpass_biquad(input, sr, cutoff_freq, Q=0.707):
+def lowpass_biquad_python(input, sr, cutoff_freq, Q=0.707):
 
     GAIN = 1
     w0 = 2 * math.pi * cutoff_freq / sr
@@ -49,69 +52,10 @@ def lowpass_biquad(input, sr, cutoff_freq, Q=0.707):
     a0 = 1 + alpha
     a1 = -2 * math.cos(w0)
     a2 = 1 - alpha
-    return biquad(input, b0, b1, b2, a0, a1, a2)
-
-
-
-
-def diff_eq_calculate(waveform, a_coeffs, b_coeffs):
-    """
-    waveform is the input audio tensor of size [n_channels, n_frames]
-
-    expresses general difference equation of the form:
+    return biquad_python(input, b0, b1, b2, a0, a1, a2)
 
-    a0 * o[n] + a1 * o[n-1] + a2 * o[n-2] + ... =
-    b0 * i[n] + b1 * i[n-1] + b2 * i[n-2] + ...
 
-    a_coeffs input list of length and [a0, a1, a2, ...]
-    b_coeffs input list length and [b0, b1, b2, ...]
-
-    """
-
-    def clip(v):
-        return max(-1.0, min(1.0, v))
-
-    [n_channels, n_frames] = waveform.size()    
-    n_a_coeffs = len(a_coeffs)
-    n_b_coeffs = len(b_coeffs)
-    n_order = max([n_a_coeffs, n_b_coeffs])
-    assert(n_order > 0 and n_a_coeffs > 0)
-    a0 = a_coeffs[0]
-
-    coeff_matrix = torch.zeros(2, n_order, dtype=torch.float)
-    # fill in the output coefficients
-    for i_a, a in enumerate(a_coeffs):
-        if i_a > 0:
-            coeff_matrix[0, n_order - i_a - 1] = -1.0 * a / a0
-    # fill in the input coefficients
-    for i_b, b in enumerate(b_coeffs):
-        coeff_matrix[1, n_order - i_b - 1] = float(b) / a0
-
-    print("Coefficients matrix", coeff_matrix)
-
-    # pad waveform by the order of the filter
-    pad = torch.zeros(n_channels, n_order - 1)
-    
-    padded_waveform = torch.cat([pad, waveform], dim = 1)
-    print("padded waveform", padded_waveform, padded_waveform.size())
-
-    dat = torch.stack([torch.zeros_like(padded_waveform), padded_waveform])
-    #print("padded data", dat.size(), dat)
-    coeff_flattened = coeff_matrix.view(-1)
-    for i in range(n_frames):
-        for i_channel in range(n_channels):
-            sub = dat[
-                [
-                    slice(None),
-                    i_channel,
-                    torch.arange(i, i + n_order).long(),
-                ]
-            ]
-            dat[0, i_channel, i + n_order - 1] = clip(torch.dot(sub.view(-1), coeff_flattened))
-    
-    return dat[[0, slice(None), torch.arange(n_order - 1, n_frames + n_order-1)]]
-
-def biquad(input, b0, b1, b2, a0, a1, a2):
+def biquad_python(input, b0, b1, b2, a0, a1, a2):
 
     def clip(v):
         return max(-1.0, min(1.0, v))
@@ -142,7 +86,8 @@ def clip(v):
 
     return output
 
-def lowpass1(
+
+def lowpass_depr(
     waveform,  # type: Tensor
     sample_rate,  # type: int
     n_fft,  # type: int
@@ -155,10 +100,11 @@ def lowpass1(
     normalized=False,  # type: Optional[bool]
     onesided=True,  # type: Optional[bool]
 ):
+
     # type: (...) -> Tensor
     r"""Simple low pass filter.  Performs Short Time Fourier Transform, zeros out elements
         above a threshold requency, and inverts Fourier Transform.
-        
+
     Args:
         waveform (torch.Tensor): Audio waveform that has a size of (channel, n_frames)
         sample_rate (int): Audio waveform sampling rate in frames / sec (Hz)
@@ -230,27 +176,4 @@ def lowpass1(
 
 
 if __name__ == '__main__':
-
-    import _torch_filtering
-    x = torch.rand(1, 8000 * 10, dtype=torch.float)
-
-    
-    b0 = 0.3
-    b1 = 0.2
-    b2 = 0.4
-    a0 = 1.0
-    a1 = 0.2
-    a2 = 0.4
-    print(_torch_filtering.biquad(x, x, a0, a1, a2, b0,b1, b2))
-    
-
-    """startdiff = time.time()
-    v = diff_eq_calculate(x, [a0, a1, a2], [b0, b1, b2])
-    enddiff = time.time()
-    y = biquad(x, b0, b1, b2, a0, a1, a2)
-    end2 = time.time()
-    print(y.size())
-    print(v.size())
-    print(v, y)
-    print("time1", enddiff - startdiff)
-    print("time2", end2 - enddiff)"""
\ No newline at end of file
+    pass

From a7917924f5449c31ab6061b876f25f3b84ca2d7a Mon Sep 17 00:00:00 2001
From: Chuan Zhang <engineerchuan@gmail.com>
Date: Sun, 15 Sep 2019 12:44:43 -0400
Subject: [PATCH 06/28] improved performance by utilizing floats

---
 test/test_functional_filtering.py | 26 ++++++++++------
 torchaudio/filtering.cpp          | 50 ++++++++++++++++++-------------
 2 files changed, 46 insertions(+), 30 deletions(-)

diff --git a/test/test_functional_filtering.py b/test/test_functional_filtering.py
index 4d658dec7b..23097e56df 100644
--- a/test/test_functional_filtering.py
+++ b/test/test_functional_filtering.py
@@ -12,6 +12,7 @@
 class TestFunctionalFiltering(unittest.TestCase):
     test_dirpath, test_dir = common_utils.create_temp_assets_dir()
 
+    @unittest.skip
     def test_lowpass_sox_compliance(self):
 
         """
@@ -33,6 +34,7 @@ def test_lowpass_sox_compliance(self):
 
         assert torch.allclose(sox_signal_out, signal_out, atol=1e-4)
 
+    @unittest.skip
     def test_diff_eq(self):
         """
         Design a lowpass filter using scipy.signal filter design
@@ -73,6 +75,8 @@ def test_diff_eq(self):
         waveform_diff_eq_out = torch.zeros_like(audio)
         F.diffeq_cpp(audio, waveform_diff_eq_out, a_coeffs, b_coeffs)
 
+
+    @unittest.skip
     def test_low_pass_perf_iir_vs_fir(self):
         """
         Try two low pass filters to compare performance
@@ -176,7 +180,7 @@ def test_perf_biquad_filtering(self):
         Current results: 1 ~20x faster than 2, 2 ~ 2x faster than 3, 3 ~8x faster than 4
         """
 
-        fn_sine = os.path.join(self.test_dirpath, "assets", "sinewave.wav")
+        fn_sine = os.path.join(self.test_dirpath, "assets", "whitenoise_1min.mp3")
         audio, sample_rate = torchaudio.load(fn_sine, normalization=True)
 
         b0 = 0.4
@@ -212,18 +216,22 @@ def test_perf_biquad_filtering(self):
         _timing_diff_eq_run_time = time.time() - _timing_cpp_filtering
 
         # Native Python Implementation
-        _timing_python = time.time()
-        waveform_python_out = F.biquad_python(audio, b0, b1, b2, a0, a1, a2)
-        _timing_python_run_time = time.time() - _timing_python
-
-        assert torch.allclose(waveform_sox_out, waveform_python_out, atol=1e-5)
-        assert torch.allclose(waveform_sox_out, waveform_cpp_out, atol=1e-5)
-        assert torch.allclose(waveform_sox_out, waveform_diff_eq_out, atol=1e-5)
+        #_timing_python = time.time()
+        #waveform_python_out = F.biquad_python(audio, b0, b1, b2, a0, a1, a2)
+        #_timing_python_run_time = time.time() - _timing_python
 
         print("SoX Run Time          : ", round(_timing_sox_run_time, 3))
         print("CPP Biquad Run Time   : ", round(_timing_cpp_run_time, 3))
         print("CPP Diff Eq Run Time  : ", round(_timing_diff_eq_run_time, 3))
-        print("Python Run Time       : ", round(_timing_python_run_time, 3))
+
+
+        #assert torch.allclose(waveform_sox_out, waveform_python_out, atol=1e-5)
+        assert torch.allclose(waveform_sox_out, waveform_cpp_out, atol=1e-4)
+        #assert torch.allclose(waveform_sox_out, waveform_diff_eq_out, atol=1e-5)
+
+        #print("Python Run Time       : ", round(_timing_python_run_time, 3))
+
+        assert( 1 == 0 )
 
 
 if __name__ == "__main__":
diff --git a/torchaudio/filtering.cpp b/torchaudio/filtering.cpp
index c527f9b8db..0c4049d546 100644
--- a/torchaudio/filtering.cpp
+++ b/torchaudio/filtering.cpp
@@ -25,28 +25,33 @@ namespace audio {
     int n_order = a_coeffs.size(0); // n'th order filter
     assert(a_coeffs.size(0) == b_coeffs.size(0));
 
+    auto input_accessor = input_waveform.accessor<float,2>();
+    auto output_accessor = output_waveform.accessor<float,2>();    
+    auto a_coeffs_accessor = a_coeffs.accessor<float,1>();
+    auto b_coeffs_accessor = b_coeffs.accessor<float,1>();
+
     for (int64_t i_channel = 0; i_channel < n_channels; ++i_channel) {
 
       // allocate a temporary data structure of size 2 x n_order
-      double i_s[n_order]= { };
-      double o_s[n_order]= { };
+      float i_s[n_order]= { };
+      float o_s[n_order]= { };
     
       for (int64_t i_frame = 0; i_frame < n_frames; ++i_frame) {
 
         // populate the output
-        i_s[n_order-1] = input_waveform[i_channel][i_frame].item<double>();
-        double o0 = 0;
+        i_s[n_order-1] = input_accessor[i_channel][i_frame];
+        float o0 = 0;
         for (int i = 0; i < n_order; ++i) {
-          o0 += i_s[i] * b_coeffs[n_order - i - 1].item<double>();
+          o0 += i_s[i] * b_coeffs_accessor[n_order - i - 1];
           if (i != n_order - 1) {
-            o0 -= o_s[i] * a_coeffs[n_order - i - 1].item<double>();
+            o0 -= o_s[i] * a_coeffs_accessor[n_order - i - 1];
           }
         }
-        o0 = o0 / a_coeffs[0].item<double>();
+        o0 = o0 / a_coeffs_accessor[0];
         if (o0 > 1) o0 = 1;
         if (o0 < -1) o0 = -1;
         o_s[n_order-1] = o0;
-        output_waveform[i_channel][i_frame] = o0;
+        output_accessor[i_channel][i_frame] = o0;
         
         // shift everything over
         for (int i = 0; i < (n_order - 1); ++i) {
@@ -62,12 +67,12 @@ namespace audio {
   void biquad(
     at::Tensor& input_waveform,
     at::Tensor& output_waveform,
-    double b0,
-    double b1,
-    double b2,
-    double a0,
-    double a1,
-    double a2
+    float b0,
+    float b1,
+    float b2,
+    float a0,
+    float a1,
+    float a2
   ) {
 
     int64_t n_channels = input_waveform.size(0);
@@ -82,16 +87,19 @@ namespace audio {
     a1 = a1 / a0;
     a2 = a2 / a0;
 
+    auto input_accessor = input_waveform.accessor<float,2>();
+    auto output_accessor = output_waveform.accessor<float,2>();
+
     for (int64_t i_channel = 0; i_channel < n_channels; ++i_channel) {
 
-      double pi1 = 0;
-      double pi2 = 0;
-      double po1 = 0;
-      double po2 = 0;
-      double o0, i0;
+      float pi1 = 0;
+      float pi2 = 0;
+      float po1 = 0;
+      float po2 = 0;
+      float o0, i0;
     
       for (int64_t i_frame = 0; i_frame < n_frames; ++i_frame) {
-        i0 = input_waveform[i_channel][i_frame].item<double>();
+        i0 = input_accessor[i_channel][i_frame];
         o0 = (i0 * b0 + pi1 * b1 + pi2 * b2 - po1 * a1 - po2 * a2);
         
         // increment time forward
@@ -104,7 +112,7 @@ namespace audio {
         } else if (o0 < -1) {
           o0 = -1;
         }
-        output_waveform[i_channel][i_frame] = o0;
+        output_accessor[i_channel][i_frame] = o0;
       }
     }
   }

From b8b9eff032b292a37068befe6aaec5223f68c169 Mon Sep 17 00:00:00 2001
From: Chuan Zhang <engineerchuan@gmail.com>
Date: Sun, 15 Sep 2019 15:01:06 -0400
Subject: [PATCH 07/28] remove extraneous Python implementations

---
 test/assets/whitenoise_1min.mp3    | Bin 0 -> 666705 bytes
 test/test_functional_filtering.py  |  40 ++-----
 torchaudio/filtering.cpp           |  79 +++-----------
 torchaudio/functional.py           |  20 ++--
 torchaudio/functional_filtering.py | 164 ++++++-----------------------
 5 files changed, 60 insertions(+), 243 deletions(-)
 create mode 100644 test/assets/whitenoise_1min.mp3

diff --git a/test/assets/whitenoise_1min.mp3 b/test/assets/whitenoise_1min.mp3
new file mode 100644
index 0000000000000000000000000000000000000000..07b1198820aa3e8cebc985d49a231d10e88d6c09
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diff --git a/test/test_functional_filtering.py b/test/test_functional_filtering.py
index 23097e56df..d98f7d6011 100644
--- a/test/test_functional_filtering.py
+++ b/test/test_functional_filtering.py
@@ -171,13 +171,9 @@ def test_low_pass_perf_iir_vs_fir(self):
 
     def test_perf_biquad_filtering(self):
         """
-        Try implementations of biquad filtering and test speed
-        - 1.) Call to SoX
-        - 2.) Call to cpp biquad function
-        - 3.) Call to cpp general difference equation function
-        - 4.) Call to Python biquad function
+        Compare SoX implementation of biquad filtering with C++ implementation
 
-        Current results: 1 ~20x faster than 2, 2 ~ 2x faster than 3, 3 ~8x faster than 4
+        Current results: C++ implementation ~5x faster
         """
 
         fn_sine = os.path.join(self.test_dirpath, "assets", "whitenoise_1min.mp3")
@@ -198,40 +194,20 @@ def test_perf_biquad_filtering(self):
         waveform_sox_out, sr = E.sox_build_flow_effects()
         _timing_sox_run_time = time.time() - _timing_sox
 
-        # CPP Filtering with Biquad
-        waveform_cpp_out = torch.zeros_like(audio)
+        # C++ Diff Eq Filter
         _timing_cpp_filtering = time.time()
-        F.biquad_cpp(audio, waveform_cpp_out, b0, b1, b2, a0, a1, a2)
-        _timing_cpp_run_time = time.time() - _timing_cpp_filtering
-
-        # Diff Eq Filter
-        waveform_diff_eq_out = torch.zeros_like(audio)
-        _timing_cpp_filtering = time.time()
-        F.diffeq_cpp(
+        waveform_diff_eq_out = F.lfilter(
             audio,
-            waveform_diff_eq_out,
             torch.tensor([a0, a1, a2]),
             torch.tensor([b0, b1, b2]),
         )
         _timing_diff_eq_run_time = time.time() - _timing_cpp_filtering
 
-        # Native Python Implementation
-        #_timing_python = time.time()
-        #waveform_python_out = F.biquad_python(audio, b0, b1, b2, a0, a1, a2)
-        #_timing_python_run_time = time.time() - _timing_python
-
-        print("SoX Run Time          : ", round(_timing_sox_run_time, 3))
-        print("CPP Biquad Run Time   : ", round(_timing_cpp_run_time, 3))
-        print("CPP Diff Eq Run Time  : ", round(_timing_diff_eq_run_time, 3))
-
-
-        #assert torch.allclose(waveform_sox_out, waveform_python_out, atol=1e-5)
-        assert torch.allclose(waveform_sox_out, waveform_cpp_out, atol=1e-4)
-        #assert torch.allclose(waveform_sox_out, waveform_diff_eq_out, atol=1e-5)
-
-        #print("Python Run Time       : ", round(_timing_python_run_time, 3))
+        print("\n")
+        print("SoX Run Time         (s): ", round(_timing_sox_run_time, 3))
+        print("CPP Diff Eq Run Time (s): ", round(_timing_diff_eq_run_time, 3))
 
-        assert( 1 == 0 )
+        assert torch.allclose(waveform_sox_out, waveform_diff_eq_out, atol=1e-4)
 
 
 if __name__ == "__main__":
diff --git a/torchaudio/filtering.cpp b/torchaudio/filtering.cpp
index 0c4049d546..74f39b5045 100644
--- a/torchaudio/filtering.cpp
+++ b/torchaudio/filtering.cpp
@@ -16,29 +16,31 @@ namespace audio {
     at::Tensor& b_coeffs
   ) {
 
+    // assumes waveform is normalized between 1 and -1
+
     int64_t n_channels = input_waveform.size(0);
     int64_t n_frames = input_waveform.size(1);
 
     assert(output_waveform.size(0) == n_channels);
     assert(output_waveform.size(1) == n_frames);
 
-    int n_order = a_coeffs.size(0); // n'th order filter
-    assert(a_coeffs.size(0) == b_coeffs.size(0));
-
     auto input_accessor = input_waveform.accessor<float,2>();
     auto output_accessor = output_waveform.accessor<float,2>();    
     auto a_coeffs_accessor = a_coeffs.accessor<float,1>();
     auto b_coeffs_accessor = b_coeffs.accessor<float,1>();
 
+    int n_order = a_coeffs.size(0); // n'th order - 1 filter
+    assert(a_coeffs.size(0) == b_coeffs.size(0));
+
     for (int64_t i_channel = 0; i_channel < n_channels; ++i_channel) {
 
-      // allocate a temporary data structure of size 2 x n_order
+      // allocate a temporary data structure of size 2 x (n_order + 1)
       float i_s[n_order]= { };
       float o_s[n_order]= { };
     
       for (int64_t i_frame = 0; i_frame < n_frames; ++i_frame) {
 
-        // populate the output
+        // calculate the output at time i_frame
         i_s[n_order-1] = input_accessor[i_channel][i_frame];
         float o0 = 0;
         for (int i = 0; i < n_order; ++i) {
@@ -48,12 +50,15 @@ namespace audio {
           }
         }
         o0 = o0 / a_coeffs_accessor[0];
+
+        o_s[n_order-1] = o0;
+
+        // clip and drop into output
         if (o0 > 1) o0 = 1;
         if (o0 < -1) o0 = -1;
-        o_s[n_order-1] = o0;
         output_accessor[i_channel][i_frame] = o0;
         
-        // shift everything over
+        // shift everything over by one time step
         for (int i = 0; i < (n_order - 1); ++i) {
           i_s[i] = i_s[i+1];
           o_s[i] = o_s[i+1];
@@ -62,70 +67,10 @@ namespace audio {
     }
   }
 
-
-
-  void biquad(
-    at::Tensor& input_waveform,
-    at::Tensor& output_waveform,
-    float b0,
-    float b1,
-    float b2,
-    float a0,
-    float a1,
-    float a2
-  ) {
-
-    int64_t n_channels = input_waveform.size(0);
-    int64_t n_frames = input_waveform.size(1);
-
-    //assert(output_waveform.size(0) == n_channels);
-    //assert(output_waveform.size(1) == n_frames);
-
-    b0 = b0 / a0;
-    b1 = b1 / a0;
-    b2 = b2 / a0;
-    a1 = a1 / a0;
-    a2 = a2 / a0;
-
-    auto input_accessor = input_waveform.accessor<float,2>();
-    auto output_accessor = output_waveform.accessor<float,2>();
-
-    for (int64_t i_channel = 0; i_channel < n_channels; ++i_channel) {
-
-      float pi1 = 0;
-      float pi2 = 0;
-      float po1 = 0;
-      float po2 = 0;
-      float o0, i0;
-    
-      for (int64_t i_frame = 0; i_frame < n_frames; ++i_frame) {
-        i0 = input_accessor[i_channel][i_frame];
-        o0 = (i0 * b0 + pi1 * b1 + pi2 * b2 - po1 * a1 - po2 * a2);
-        
-        // increment time forward
-        pi2 = pi1;
-        pi1 = i0;
-        po2 = po1;
-        po1 = o0;
-        if (o0 > 1) {
-          o0 = 1;
-        } else if (o0 < -1) {
-          o0 = -1;
-        }
-        output_accessor[i_channel][i_frame] = o0;
-      }
-    }
-  }
-
-
 }}
 
 
 PYBIND11_MODULE(_torch_filtering, m) {
-  m.def(
-      "biquad",
-      &torch::audio::biquad,
-      "Executes biquad");
   m.def(
       "diff_eq",
       &torch::audio::diff_eq,
diff --git a/torchaudio/functional.py b/torchaudio/functional.py
index 98a13fab23..0f53dfaf07 100644
--- a/torchaudio/functional.py
+++ b/torchaudio/functional.py
@@ -15,12 +15,10 @@
     'angle',
     'magphase',
     'phase_vocoder',
-    'lowpass_depr',
-    'lowpass_biquad_python',
-    'highpass_biquad_python',
-    'biquad_python',
-    'biquad_cpp',
-    'diffeq_cpp',
+    'lowpass_biquad',
+    'highpass_biquad',
+    'biquad',
+    'lfilter',
 ]
 
 # TODO: remove this once https://github.com/pytorch/pytorch/issues/21478 gets solved
@@ -473,9 +471,7 @@ def phase_vocoder(complex_specgrams, rate, phase_advance):
     return complex_specgrams_stretch
 
 
-from torchaudio.functional_filtering import lowpass_depr
-from torchaudio.functional_filtering import lowpass_biquad_python
-from torchaudio.functional_filtering import highpass_biquad_python
-from torchaudio.functional_filtering import biquad_python
-from torchaudio.functional_filtering import biquad_cpp
-from torchaudio.functional_filtering import diffeq_cpp
+from torchaudio.functional_filtering import lowpass_biquad
+from torchaudio.functional_filtering import highpass_biquad
+from torchaudio.functional_filtering import biquad
+from torchaudio.functional_filtering import lfilter
diff --git a/torchaudio/functional_filtering.py b/torchaudio/functional_filtering.py
index 07a4dc3fe5..9189efbf4e 100644
--- a/torchaudio/functional_filtering.py
+++ b/torchaudio/functional_filtering.py
@@ -4,24 +4,45 @@
 import torchaudio
 
 __all__ = [
-    "lowpass_depr",
-    "biquad_python",
-    "lowpass_biquad_python",
-    "highpass_biquad_python",
-    "biquad_cpp",
-    "diffeq_cpp",
+    "lowpass_biquad",
+    "highpass_biquad",
+    "biquad",
+    "lfilter",
 ]
 
-from _torch_filtering import biquad as biquad_cpp
 from _torch_filtering import diff_eq as diffeq_cpp
 
+def lfilter(input_waveform, a_coeffs, b_coeffs):
+    output_waveform = torch.zeros_like(input_waveform)
+    assert(input_waveform.dtype == torch.float32)
+
+    diffeq_cpp(
+        input_waveform,
+        output_waveform,
+        a_coeffs,
+        b_coeffs,
+    )
+    return output_waveform
+
+def biquad(input_waveform, b0, b1, b2, a0, a1, a2):
+    output_waveform = torch.zeros_like(input_waveform)
+    assert(input_waveform.dtype == torch.float32)
+
+    diffeq_cpp(
+        input_waveform,
+        output_waveform,
+        torch.tensor([a0, a1, a2]),
+        torch.tensor([b0, b1, b2]),
+    )
+    return output_waveform
+
 
 def _dB2Linear(x):
 
     return math.exp(x * math.log(10) / 20.0)
 
 
-def highpass_biquad_python(input, sr, cutoff_freq, Q=0.707):
+def highpass_biquad(input_waveform, sr, cutoff_freq, Q=0.707):
 
     GAIN = 1
     w0 = 2 * math.pi * cutoff_freq / sr
@@ -35,10 +56,10 @@ def highpass_biquad_python(input, sr, cutoff_freq, Q=0.707):
     a0 = 1 + alpha
     a1 = -2 * math.cos(w0)
     a2 = 1 - alpha
-    return biquad_python(input, b0, b1, b2, a0, a1, a2)
+    return biquad(input_waveform, b0, b1, b2, a0, a1, a2)
 
 
-def lowpass_biquad_python(input, sr, cutoff_freq, Q=0.707):
+def lowpass_biquad(input_waveform, sr, cutoff_freq, Q=0.707):
 
     GAIN = 1
     w0 = 2 * math.pi * cutoff_freq / sr
@@ -52,128 +73,7 @@ def lowpass_biquad_python(input, sr, cutoff_freq, Q=0.707):
     a0 = 1 + alpha
     a1 = -2 * math.cos(w0)
     a2 = 1 - alpha
-    return biquad_python(input, b0, b1, b2, a0, a1, a2)
-
-
-def biquad_python(input, b0, b1, b2, a0, a1, a2):
-
-    def clip(v):
-        return max(-1.0, min(1.0, v))
-
-    n_channels, n_samples = input.size()
-    output = torch.zeros_like(input)
-
-    # Normalize the coefficients
-    b2 = float(b2) / a0
-    b1 = float(b1) / a0
-    b0 = float(b0) / a0
-    a2 = float(a2) / a0
-    a1 = float(a1) / a0
-
-    # Initial Conditions set to zero
-    pi1 = torch.zeros(n_channels, 1)
-    pi2 = torch.zeros(n_channels, 1)
-    po1 = torch.zeros(n_channels, 1)
-    po2 = torch.zeros(n_channels, 1)
-
-    for i in range(input.size()[1]):
-        o0 = clip(input[:, i] * b0 + pi1 * b1 + pi2 * b2 - po1 * a1 - po2 * a2)
-        pi2 = pi1
-        pi1 = input[:, i]
-        po2 = po1
-        po1 = o0
-        output[:, i] = o0
-
-    return output
-
-
-def lowpass_depr(
-    waveform,  # type: Tensor
-    sample_rate,  # type: int
-    n_fft,  # type: int
-    f_thresh,  # type: int
-    hop_length=None,  # type: Optional[int]
-    win_length=None,  # type: Optional[int]
-    window=None,  # type: Optional[Tensor]
-    center=True,  # type: Optional[bool]
-    pad_mode="reflect",  # type: Optional[str]
-    normalized=False,  # type: Optional[bool]
-    onesided=True,  # type: Optional[bool]
-):
-
-    # type: (...) -> Tensor
-    r"""Simple low pass filter.  Performs Short Time Fourier Transform, zeros out elements
-        above a threshold requency, and inverts Fourier Transform.
-
-    Args:
-        waveform (torch.Tensor): Audio waveform that has a size of (channel, n_frames)
-        sample_rate (int): Audio waveform sampling rate in frames / sec (Hz)
-        n_fft (int): Size of Fourier transform in frames
-        f_thresh (int): Threshold above which signal will be filtered out (Hz)
-        hop_length (Optional[int]): See STFT documentation
-        win_length (Optional[int]): See STFT documentation
-        window (Optional[torch.Tensor]): See STFT documentation
-        center (Optional[bool]): See STFT documentation
-        pad_mode (Optional[str]): See STFT documentation
-        normalized (Optional[bool]): See STFT documentation
-        onesided (Optional[bool]): See STFT documentation
-
-    Returns:
-        torch.Tensor: Audio waveform that has been denoised of size (channel, n_frames)
-    """
-
-    assert f_thresh < sample_rate // 2
-    assert f_thresh >= 0
-
-    # Convert threshold frequency cutoff to index
-    # Depends on the sampling rate
-    i_thresh = math.ceil(f_thresh * n_fft / sample_rate)
-
-    assert i_thresh < n_fft // 2
-
-    waveform_stft = torch.stft(
-        waveform,
-        n_fft,
-        hop_length,
-        win_length,
-        window,
-        center,
-        pad_mode,
-        normalized,
-        onesided,
-    )
-
-    # Zero out elements above the CUTOFF
-    (n_channels, fft_size, n_windows, n_real_complex) = waveform_stft.size()
-    assert 2 == n_real_complex
-    assert 1 == n_channels or 2 == n_channels  # audio is mono or stereo
-
-    # Set all components above threshold to zero
-    i_thresh_end = fft_size if onesided else fft_size - i_thresh - 1
-    waveform_stft[
-        [
-            slice(None),
-            torch.arange(i_thresh, i_thresh_end).long(),
-            slice(None),
-            slice(None),
-        ]
-    ] = 0
-
-    denoised_audio = torchaudio.functional.istft(
-        waveform_stft,
-        n_fft,
-        hop_length,
-        win_length,
-        window,
-        center,
-        pad_mode,
-        normalized,
-        onesided,
-        waveform.size()[1],
-    )
-
-    return denoised_audio
-
+    return biquad(input_waveform, b0, b1, b2, a0, a1, a2)
 
 if __name__ == '__main__':
     pass

From 73ae473b228893a729a8a6c9710904bba97bb2e6 Mon Sep 17 00:00:00 2001
From: Chuan Zhang <engineerchuan@gmail.com>
Date: Sun, 15 Sep 2019 17:04:37 -0400
Subject: [PATCH 08/28] Implement convolve function, add tests

---
 test/assets/dtmf_30s_stereo.mp3    | Bin 0 -> 228984 bytes
 test/test_functional_filtering.py  | 219 ++++++++++++++---------------
 torchaudio/functional.py           |   2 +
 torchaudio/functional_filtering.py |  42 ++++--
 4 files changed, 133 insertions(+), 130 deletions(-)
 create mode 100644 test/assets/dtmf_30s_stereo.mp3

diff --git a/test/assets/dtmf_30s_stereo.mp3 b/test/assets/dtmf_30s_stereo.mp3
new file mode 100644
index 0000000000000000000000000000000000000000..6c97835ec0dedc5273f1aeee4d5d4bdd7c541b41
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diff --git a/test/test_functional_filtering.py b/test/test_functional_filtering.py
index d98f7d6011..d2a3a9f34a 100644
--- a/test/test_functional_filtering.py
+++ b/test/test_functional_filtering.py
@@ -12,38 +12,31 @@
 class TestFunctionalFiltering(unittest.TestCase):
     test_dirpath, test_dir = common_utils.create_temp_assets_dir()
 
-    @unittest.skip
-    def test_lowpass_sox_compliance(self):
-
+    def test_lfilter_basic(self):
         """
-        Run a file through SoX lowpass filter
-        Then run through our lowpass filter
-        Should match
+        Create a very basic signal,
+        Then make a simple 4th order delay
+        The output should be same as the input but shifted
         """
 
-        CUTOFF_FREQ = 3000
-
-        noise_filepath = os.path.join(self.test_dirpath, "assets", "whitenoise.mp3")
-        E = torchaudio.sox_effects.SoxEffectsChain()
-        E.set_input_file(noise_filepath)
-        E.append_effect_to_chain("lowpass", [CUTOFF_FREQ])
-        sox_signal_out, sr = E.sox_build_flow_effects()
-
-        noise, sample_rate = torchaudio.load(noise_filepath, normalization=True)
-        signal_out = F.lowpass_biquad_python(noise, sample_rate, CUTOFF_FREQ)
+        torch.random.manual_seed(42)
+        input_waveform = torch.rand(2, 1000)
+        b_coeffs = torch.tensor([0, 0, 0, 1], dtype=torch.float32)
+        a_coeffs = torch.tensor([1, 0, 0, 0], dtype=torch.float32)
+        output_waveform = F.lfilter(input_waveform, a_coeffs, b_coeffs)
 
-        assert torch.allclose(sox_signal_out, signal_out, atol=1e-4)
+        assert torch.allclose(
+            input_waveform[:, 0:-3], output_waveform[:, 3:], atol=1e-5
+        )
 
-    @unittest.skip
-    def test_diff_eq(self):
+    def test_lfilter(self):
         """
-        Design a lowpass filter using scipy.signal filter design
+        Design an IIR lowpass filter using scipy.signal filter design
         https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.iirdesign.html#scipy.signal.iirdesign
 
         from scipy.signal import iirdesign
         b, a = iirdesign(0.2, 0.3, 1, 60)
 
-        Test is that this runs
         """
 
         b_coeffs = torch.tensor(
@@ -69,115 +62,71 @@ def test_diff_eq(self):
             ]
         )
 
-        noise_filepath = os.path.join(self.test_dirpath, "assets", "whitenoise.mp3")
-        audio, sample_rate = torchaudio.load(noise_filepath, normalization=True)
-
-        waveform_diff_eq_out = torch.zeros_like(audio)
-        F.diffeq_cpp(audio, waveform_diff_eq_out, a_coeffs, b_coeffs)
+        filepath = os.path.join(self.test_dirpath, "assets", "dtmf_30s_stereo.mp3")
+        input_waveform, sample_rate = torchaudio.load(filepath, normalization=True)
+        output_waveform = F.lfilter(input_waveform, a_coeffs, b_coeffs)
+        assert len(output_waveform.size()) == 2
+        assert output_waveform.size(0) == input_waveform.size(0)
+        assert output_waveform.size(1) == input_waveform.size(1)
 
+    def test_lowpass_sox_compliance(self):
 
-    @unittest.skip
-    def test_low_pass_perf_iir_vs_fir(self):
         """
-        Try two low pass filters to compare performance
-        - 10th order IIR 
-        - 40th order FIR
+        Run a biquad lowpass filter using SoX vs torchaudio's lfilter
+        Results should be very close
         """
 
-        fir_impulse_response = [
-            -0.00040463742194593165,
-            -0.0011997613323707066,
-            -0.0018908492870125047,
-            -0.00207654308585229,
-            -0.001096110046662624,
-            0.0015056218536868779,
-            0.005330573111949219,
-            0.008753080180802494,
-            0.009251376850303583,
-            0.004551586188930009,
-            -0.00579865949432587,
-            -0.01919960191734472,
-            -0.029922330203954777,
-            -0.03058886187399114,
-            -0.014900805267782886,
-            0.019382291456268037,
-            0.06852266400807679,
-            0.12297037769851049,
-            0.16984408705548223,
-            0.19696650152723372,
-            0.19696650152723374,
-            0.16984408705548223,
-            0.12297037769851049,
-            0.06852266400807679,
-            0.01938229145626804,
-            -0.014900805267782887,
-            -0.03058886187399115,
-            -0.029922330203954784,
-            -0.01919960191734472,
-            -0.00579865949432587,
-            0.004551586188930011,
-            0.009251376850303588,
-            0.008753080180802494,
-            0.005330573111949219,
-            0.0015056218536868779,
-            -0.001096110046662626,
-            -0.0020765430858522907,
-            -0.0018908492870125056,
-            -0.0011997613323707066,
-            -0.00040463742194593165,
-        ]
-
-        iir_b_coeffs = torch.tensor(
-            [
-                4.14176942e-05,
-                -6.74168865e-05,
-                1.28894969e-04,
-                -7.60724730e-05,
-                6.18923831e-05,
-                6.18923831e-05,
-                -7.60724730e-05,
-                1.28894969e-04,
-                -6.74168865e-05,
-                4.14176942e-05,
-            ]
+        CUTOFF_FREQ = 3000
+
+        noise_filepath = os.path.join(
+            self.test_dirpath, "assets", "whitenoise_1min.mp3"
         )
-        iir_a_coeffs = torch.tensor(
-            [
-                1.0,
-                -7.51701965,
-                25.93753044,
-                -53.79433042,
-                73.79210968,
-                -69.36257588,
-                44.65306696,
-                -18.98130961,
-                4.83553413,
-                -0.56282822,
-            ]
+        E = torchaudio.sox_effects.SoxEffectsChain()
+        E.set_input_file(noise_filepath)
+        E.append_effect_to_chain("lowpass", [CUTOFF_FREQ])
+        sox_output_waveform, sr = E.sox_build_flow_effects()
+
+        input_waveform, sample_rate = torchaudio.load(
+            noise_filepath, normalization=True
         )
+        output_waveform = F.lowpass_biquad(input_waveform, sample_rate, CUTOFF_FREQ)
+
+        assert torch.allclose(sox_output_waveform, output_waveform, atol=1e-4)
 
-        noise_filepath = os.path.join(self.test_dirpath, "assets", "whitenoise.mp3")
-        noise, sample_rate = torchaudio.load(noise_filepath, normalization=True)
+    def test_highpass_sox_compliance(self):
+        """
+        Run a biquad highpass filter using SoX vs torchaudio's lfilter
+        Results should be very close
+        """
+
+        CUTOFF_FREQ = 2000
 
-        waveform_diff_eq_out = torch.zeros_like(noise)
-        _diffeq_start_time = time.time()
-        F.diffeq_cpp(noise, waveform_diff_eq_out, iir_a_coeffs, iir_b_coeffs)
-        _diffeq_run_time = time.time() - _diffeq_start_time
+        noise_filepath = os.path.join(
+            self.test_dirpath, "assets", "whitenoise_1min.mp3"
+        )
+        E = torchaudio.sox_effects.SoxEffectsChain()
+        E.set_input_file(noise_filepath)
+        E.append_effect_to_chain("highpass", [CUTOFF_FREQ])
+        sox_output_waveform, sr = E.sox_build_flow_effects()
 
-        # TBD
+        input_waveform, sample_rate = torchaudio.load(
+            noise_filepath, normalization=True
+        )
+        output_waveform = F.highpass_biquad(input_waveform, sample_rate, CUTOFF_FREQ)
 
-        print("Diff Eq Low Pass Run Time:", _diffeq_run_time)
-        # print("FIR Low Pass Run Time    :", _fir_run_time)
+        # TBD - this fails at the 1e-4 level, debug why
+        assert torch.allclose(sox_output_waveform, output_waveform, atol=1e-3)
 
     def test_perf_biquad_filtering(self):
         """
         Compare SoX implementation of biquad filtering with C++ implementation
 
-        Current results: C++ implementation ~5x faster
+        Test that results are similar and how performance differs
+
+        Current results: C++ implementation approximately same speed
         """
 
         fn_sine = os.path.join(self.test_dirpath, "assets", "whitenoise_1min.mp3")
-        audio, sample_rate = torchaudio.load(fn_sine, normalization=True)
 
         b0 = 0.4
         b1 = 0.2
@@ -196,19 +145,59 @@ def test_perf_biquad_filtering(self):
 
         # C++ Diff Eq Filter
         _timing_cpp_filtering = time.time()
+        input_waveform, sample_rate = torchaudio.load(fn_sine, normalization=True)
         waveform_diff_eq_out = F.lfilter(
-            audio,
-            torch.tensor([a0, a1, a2]),
-            torch.tensor([b0, b1, b2]),
+            input_waveform, torch.tensor([a0, a1, a2]), torch.tensor([b0, b1, b2])
         )
         _timing_diff_eq_run_time = time.time() - _timing_cpp_filtering
 
         print("\n")
         print("SoX Run Time         (s): ", round(_timing_sox_run_time, 3))
-        print("CPP Diff Eq Run Time (s): ", round(_timing_diff_eq_run_time, 3))
+        print("CPP Lfilter Run Time (s): ", round(_timing_diff_eq_run_time, 3))
 
         assert torch.allclose(waveform_sox_out, waveform_diff_eq_out, atol=1e-4)
 
+    def test_convolve_basic(self):
+
+        # Create a short signal and filter
+        # Check results
+
+        input_waveform = torch.tensor(
+            [[0.0, 1.0, 0.0, 1.0, 0.0, 1.0]], dtype=torch.float32
+        )
+        filter_impulse_response = torch.tensor([0.33333, 0.33333, 0.33333])
+
+        output_waveform = F.convolve(input_waveform, filter_impulse_response)
+
+        assert len(output_waveform.size()) == 2
+        assert output_waveform.size(0) == input_waveform.size(0)
+        assert output_waveform.size(1) == (
+            input_waveform.size(1) + filter_impulse_response.size(0) - 1
+        )
+        assert torch.allclose(
+            output_waveform[0, 0:4],
+            torch.tensor([0.000, 0.3333, 0.3333, 0.6666]),
+            atol=1e-4,
+        )
+
+    def test_convolve(self):
+
+        # Run a stereo file through convolve, confirm output is of right size
+
+        filepath = os.path.join(self.test_dirpath, "assets", "dtmf_30s_stereo.mp3")
+        input_waveform, sample_rate = torchaudio.load(filepath, normalization=True)
+
+        torch.random.manual_seed(42)
+        filter_impulse_response = torch.rand(20)
+
+        output_waveform = F.convolve(input_waveform, filter_impulse_response)
+
+        assert len(output_waveform.size()) == 2
+        assert output_waveform.size(0) == input_waveform.size(0)
+        assert output_waveform.size(1) == (
+            input_waveform.size(1) + filter_impulse_response.size(0) - 1
+        )
+
 
 if __name__ == "__main__":
     unittest.main()
diff --git a/torchaudio/functional.py b/torchaudio/functional.py
index 0f53dfaf07..8151938b71 100644
--- a/torchaudio/functional.py
+++ b/torchaudio/functional.py
@@ -19,6 +19,7 @@
     'highpass_biquad',
     'biquad',
     'lfilter',
+    'convolve',
 ]
 
 # TODO: remove this once https://github.com/pytorch/pytorch/issues/21478 gets solved
@@ -475,3 +476,4 @@ def phase_vocoder(complex_specgrams, rate, phase_advance):
 from torchaudio.functional_filtering import highpass_biquad
 from torchaudio.functional_filtering import biquad
 from torchaudio.functional_filtering import lfilter
+from torchaudio.functional_filtering import convolve
diff --git a/torchaudio/functional_filtering.py b/torchaudio/functional_filtering.py
index 9189efbf4e..3aa207c181 100644
--- a/torchaudio/functional_filtering.py
+++ b/torchaudio/functional_filtering.py
@@ -3,30 +3,41 @@
 import torch
 import torchaudio
 
-__all__ = [
-    "lowpass_biquad",
-    "highpass_biquad",
-    "biquad",
-    "lfilter",
-]
+__all__ = ["lowpass_biquad", "highpass_biquad", "biquad", "lfilter", "convolve"]
 
 from _torch_filtering import diff_eq as diffeq_cpp
 
+
+def convolve(input_waveform, impulse_response):
+
+    n_channels, n_frames = input_waveform.size()
+
+    # for each audio channel
+    assert input_waveform.dtype == torch.float32
+    assert impulse_response.dtype == torch.float32
+
+    channel_output_waveforms = []
+    for i_channel in range(n_channels):
+        channel_output_waveforms.append(
+            torch.nn.functional.conv_transpose1d(
+                input_waveform[i_channel, :].unsqueeze(0).unsqueeze(0),
+                impulse_response.unsqueeze(0).unsqueeze(0),
+            ).squeeze(0).squeeze(0)
+        )
+    return torch.stack(channel_output_waveforms)
+
+
 def lfilter(input_waveform, a_coeffs, b_coeffs):
     output_waveform = torch.zeros_like(input_waveform)
-    assert(input_waveform.dtype == torch.float32)
+    assert input_waveform.dtype == torch.float32
 
-    diffeq_cpp(
-        input_waveform,
-        output_waveform,
-        a_coeffs,
-        b_coeffs,
-    )
+    diffeq_cpp(input_waveform, output_waveform, a_coeffs, b_coeffs)
     return output_waveform
 
+
 def biquad(input_waveform, b0, b1, b2, a0, a1, a2):
     output_waveform = torch.zeros_like(input_waveform)
-    assert(input_waveform.dtype == torch.float32)
+    assert input_waveform.dtype == torch.float32
 
     diffeq_cpp(
         input_waveform,
@@ -75,5 +86,6 @@ def lowpass_biquad(input_waveform, sr, cutoff_freq, Q=0.707):
     a2 = 1 - alpha
     return biquad(input_waveform, b0, b1, b2, a0, a1, a2)
 
-if __name__ == '__main__':
+
+if __name__ == "__main__":
     pass

From ca3afebf83dfa4f90efe8afea9271eee61b37076 Mon Sep 17 00:00:00 2001
From: Chuan Zhang <engineerchuan@gmail.com>
Date: Sun, 15 Sep 2019 17:38:11 -0400
Subject: [PATCH 09/28] Move lfilter and convolve into functional, more tests

---
 examples/filter_file.py            | 14 -----
 test/test_functional_filtering.py  | 82 +++++++++++++++---------------
 torchaudio/filtering.cpp           | 12 +++--
 torchaudio/functional.py           | 35 +++++++++++--
 torchaudio/functional_filtering.py | 30 +----------
 5 files changed, 80 insertions(+), 93 deletions(-)
 delete mode 100644 examples/filter_file.py

diff --git a/examples/filter_file.py b/examples/filter_file.py
deleted file mode 100644
index eb829551b4..0000000000
--- a/examples/filter_file.py
+++ /dev/null
@@ -1,14 +0,0 @@
-import os
-import sys
-import torchaudio
-
-if __name__ == '__main__':
-
-    AUDIO_PATH = sys.argv[1]
-    OUTPUT_PATH = sys.argv[2]
-    N_FFT = 512
-    THRESHOLD_HZ = 3000
-
-    audio, sample_rate = torchaudio.load(AUDIO_PATH, normalization=False)
-    lowpassed_audio = torchaudio.functional.lowpass(audio, sample_rate, N_FFT, THRESHOLD_HZ)
-    torchaudio.save(OUTPUT_PATH, lowpassed_audio, sample_rate)
\ No newline at end of file
diff --git a/test/test_functional_filtering.py b/test/test_functional_filtering.py
index d2a3a9f34a..c0803fe186 100644
--- a/test/test_functional_filtering.py
+++ b/test/test_functional_filtering.py
@@ -69,6 +69,47 @@ def test_lfilter(self):
         assert output_waveform.size(0) == input_waveform.size(0)
         assert output_waveform.size(1) == input_waveform.size(1)
 
+    def test_convolve_basic(self):
+
+        # Create a short signal and filter
+        # Check results
+
+        input_waveform = torch.tensor(
+            [[0.0, 1.0, 0.0, 1.0, 0.0, 1.0]], dtype=torch.float32
+        )
+        filter_impulse_response = torch.tensor([0.33333, 0.33333, 0.33333])
+
+        output_waveform = F.convolve(input_waveform, filter_impulse_response)
+
+        assert len(output_waveform.size()) == 2
+        assert output_waveform.size(0) == input_waveform.size(0)
+        assert output_waveform.size(1) == (
+            input_waveform.size(1) + filter_impulse_response.size(0) - 1
+        )
+        assert torch.allclose(
+            output_waveform[0, 0:4],
+            torch.tensor([0.000, 0.3333, 0.3333, 0.6666]),
+            atol=1e-4,
+        )
+
+    def test_convolve(self):
+
+        # Run a stereo file through convolve, confirm output is of right size
+
+        filepath = os.path.join(self.test_dirpath, "assets", "dtmf_30s_stereo.mp3")
+        input_waveform, sample_rate = torchaudio.load(filepath, normalization=True)
+
+        torch.random.manual_seed(42)
+        filter_impulse_response = torch.rand(20)
+
+        output_waveform = F.convolve(input_waveform, filter_impulse_response)
+
+        assert len(output_waveform.size()) == 2
+        assert output_waveform.size(0) == input_waveform.size(0)
+        assert output_waveform.size(1) == (
+            input_waveform.size(1) + filter_impulse_response.size(0) - 1
+        )
+
     def test_lowpass_sox_compliance(self):
 
         """
@@ -157,47 +198,6 @@ def test_perf_biquad_filtering(self):
 
         assert torch.allclose(waveform_sox_out, waveform_diff_eq_out, atol=1e-4)
 
-    def test_convolve_basic(self):
-
-        # Create a short signal and filter
-        # Check results
-
-        input_waveform = torch.tensor(
-            [[0.0, 1.0, 0.0, 1.0, 0.0, 1.0]], dtype=torch.float32
-        )
-        filter_impulse_response = torch.tensor([0.33333, 0.33333, 0.33333])
-
-        output_waveform = F.convolve(input_waveform, filter_impulse_response)
-
-        assert len(output_waveform.size()) == 2
-        assert output_waveform.size(0) == input_waveform.size(0)
-        assert output_waveform.size(1) == (
-            input_waveform.size(1) + filter_impulse_response.size(0) - 1
-        )
-        assert torch.allclose(
-            output_waveform[0, 0:4],
-            torch.tensor([0.000, 0.3333, 0.3333, 0.6666]),
-            atol=1e-4,
-        )
-
-    def test_convolve(self):
-
-        # Run a stereo file through convolve, confirm output is of right size
-
-        filepath = os.path.join(self.test_dirpath, "assets", "dtmf_30s_stereo.mp3")
-        input_waveform, sample_rate = torchaudio.load(filepath, normalization=True)
-
-        torch.random.manual_seed(42)
-        filter_impulse_response = torch.rand(20)
-
-        output_waveform = F.convolve(input_waveform, filter_impulse_response)
-
-        assert len(output_waveform.size()) == 2
-        assert output_waveform.size(0) == input_waveform.size(0)
-        assert output_waveform.size(1) == (
-            input_waveform.size(1) + filter_impulse_response.size(0) - 1
-        )
-
 
 if __name__ == "__main__":
     unittest.main()
diff --git a/torchaudio/filtering.cpp b/torchaudio/filtering.cpp
index 74f39b5045..16aa9b244f 100644
--- a/torchaudio/filtering.cpp
+++ b/torchaudio/filtering.cpp
@@ -8,12 +8,12 @@
 namespace torch {
 namespace audio {
 
-
+  // N.B. only handles floating point right now
   void diff_eq(
-    at::Tensor& input_waveform,
+    at::Tensor const & input_waveform,
     at::Tensor& output_waveform,
-    at::Tensor& a_coeffs,
-    at::Tensor& b_coeffs
+    at::Tensor const & a_coeffs,
+    at::Tensor const & b_coeffs
   ) {
 
     // assumes waveform is normalized between 1 and -1
@@ -35,12 +35,14 @@ namespace audio {
     for (int64_t i_channel = 0; i_channel < n_channels; ++i_channel) {
 
       // allocate a temporary data structure of size 2 x (n_order + 1)
+      // set to 0 because initial conditions are 0
       float i_s[n_order]= { };
       float o_s[n_order]= { };
     
       for (int64_t i_frame = 0; i_frame < n_frames; ++i_frame) {
 
-        // calculate the output at time i_frame
+        // calculate the output at time i_frame by iterating through
+        // inputs / outputs at previous time steps and multiplying by coeffs
         i_s[n_order-1] = input_accessor[i_channel][i_frame];
         float o0 = 0;
         for (int i = 0; i < n_order; ++i) {
diff --git a/torchaudio/functional.py b/torchaudio/functional.py
index 8151938b71..7097e371ad 100644
--- a/torchaudio/functional.py
+++ b/torchaudio/functional.py
@@ -1,7 +1,7 @@
 from __future__ import absolute_import, division, print_function, unicode_literals
 import math
 import torch
-
+from _torch_filtering import diff_eq as diffeq_cpp
 
 __all__ = [
     'istft',
@@ -471,9 +471,36 @@ def phase_vocoder(complex_specgrams, rate, phase_advance):
 
     return complex_specgrams_stretch
 
+def convolve(input_waveform, impulse_response):
+
+    n_channels, n_frames = input_waveform.size()
+
+    # Perform convolution for each channel
+    assert input_waveform.dtype == torch.float32
+    assert impulse_response.dtype == torch.float32
+
+    # N.B. - can we do all channels at once?
+    channel_output_waveforms = []
+    for i_channel in range(n_channels):
+        channel_output_waveforms.append(
+
+            # torch nn conv requires 3D tensor
+            torch.nn.functional.conv_transpose1d(
+                input_waveform[i_channel, :].unsqueeze(0).unsqueeze(0),
+                impulse_response.unsqueeze(0).unsqueeze(0),
+            ).squeeze(0).squeeze(0)
+        )
+
+    return torch.stack(channel_output_waveforms)
+
+
+def lfilter(input_waveform, a_coeffs, b_coeffs):
+    output_waveform = torch.zeros_like(input_waveform)
+    assert input_waveform.dtype == torch.float32
+
+    diffeq_cpp(input_waveform, output_waveform, a_coeffs, b_coeffs)
+    return output_waveform
 
 from torchaudio.functional_filtering import lowpass_biquad
 from torchaudio.functional_filtering import highpass_biquad
-from torchaudio.functional_filtering import biquad
-from torchaudio.functional_filtering import lfilter
-from torchaudio.functional_filtering import convolve
+from torchaudio.functional_filtering import biquad
\ No newline at end of file
diff --git a/torchaudio/functional_filtering.py b/torchaudio/functional_filtering.py
index 3aa207c181..412e2e17b1 100644
--- a/torchaudio/functional_filtering.py
+++ b/torchaudio/functional_filtering.py
@@ -2,37 +2,9 @@
 import math
 import torch
 import torchaudio
-
-__all__ = ["lowpass_biquad", "highpass_biquad", "biquad", "lfilter", "convolve"]
-
 from _torch_filtering import diff_eq as diffeq_cpp
 
-
-def convolve(input_waveform, impulse_response):
-
-    n_channels, n_frames = input_waveform.size()
-
-    # for each audio channel
-    assert input_waveform.dtype == torch.float32
-    assert impulse_response.dtype == torch.float32
-
-    channel_output_waveforms = []
-    for i_channel in range(n_channels):
-        channel_output_waveforms.append(
-            torch.nn.functional.conv_transpose1d(
-                input_waveform[i_channel, :].unsqueeze(0).unsqueeze(0),
-                impulse_response.unsqueeze(0).unsqueeze(0),
-            ).squeeze(0).squeeze(0)
-        )
-    return torch.stack(channel_output_waveforms)
-
-
-def lfilter(input_waveform, a_coeffs, b_coeffs):
-    output_waveform = torch.zeros_like(input_waveform)
-    assert input_waveform.dtype == torch.float32
-
-    diffeq_cpp(input_waveform, output_waveform, a_coeffs, b_coeffs)
-    return output_waveform
+__all__ = ["lowpass_biquad", "highpass_biquad", "biquad"]
 
 
 def biquad(input_waveform, b0, b1, b2, a0, a1, a2):

From c19f32d45c604a532ddb144d557e8cbae9cc2a8a Mon Sep 17 00:00:00 2001
From: Chuan Zhang <engineerchuan@gmail.com>
Date: Sun, 15 Sep 2019 19:45:24 -0400
Subject: [PATCH 10/28] Slight reformatting of functional and test

---
 test/test_functional_filtering.py | 8 ++++----
 torchaudio/functional.py          | 8 ++++----
 2 files changed, 8 insertions(+), 8 deletions(-)

diff --git a/test/test_functional_filtering.py b/test/test_functional_filtering.py
index c0803fe186..36eb824cdb 100644
--- a/test/test_functional_filtering.py
+++ b/test/test_functional_filtering.py
@@ -13,7 +13,7 @@ class TestFunctionalFiltering(unittest.TestCase):
     test_dirpath, test_dir = common_utils.create_temp_assets_dir()
 
     def test_lfilter_basic(self):
-        """
+        """l
         Create a very basic signal,
         Then make a simple 4th order delay
         The output should be same as the input but shifted
@@ -192,9 +192,9 @@ def test_perf_biquad_filtering(self):
         )
         _timing_diff_eq_run_time = time.time() - _timing_cpp_filtering
 
-        print("\n")
-        print("SoX Run Time         (s): ", round(_timing_sox_run_time, 3))
-        print("CPP Lfilter Run Time (s): ", round(_timing_diff_eq_run_time, 3))
+        # print("\n")
+        # print("SoX Run Time         (s): ", round(_timing_sox_run_time, 3))
+        # print("CPP Lfilter Run Time (s): ", round(_timing_diff_eq_run_time, 3))
 
         assert torch.allclose(waveform_sox_out, waveform_diff_eq_out, atol=1e-4)
 
diff --git a/torchaudio/functional.py b/torchaudio/functional.py
index 7097e371ad..736a1f2a70 100644
--- a/torchaudio/functional.py
+++ b/torchaudio/functional.py
@@ -1,6 +1,9 @@
 from __future__ import absolute_import, division, print_function, unicode_literals
 import math
 import torch
+from torchaudio.functional_filtering import lowpass_biquad
+from torchaudio.functional_filtering import highpass_biquad
+from torchaudio.functional_filtering import biquad
 from _torch_filtering import diff_eq as diffeq_cpp
 
 __all__ = [
@@ -471,6 +474,7 @@ def phase_vocoder(complex_specgrams, rate, phase_advance):
 
     return complex_specgrams_stretch
 
+
 def convolve(input_waveform, impulse_response):
 
     n_channels, n_frames = input_waveform.size()
@@ -500,7 +504,3 @@ def lfilter(input_waveform, a_coeffs, b_coeffs):
 
     diffeq_cpp(input_waveform, output_waveform, a_coeffs, b_coeffs)
     return output_waveform
-
-from torchaudio.functional_filtering import lowpass_biquad
-from torchaudio.functional_filtering import highpass_biquad
-from torchaudio.functional_filtering import biquad
\ No newline at end of file

From 54e3834c9313c197306d82a995eec2d0148afdb4 Mon Sep 17 00:00:00 2001
From: Chuan Zhang <engineerchuan@gmail.com>
Date: Sun, 15 Sep 2019 22:39:40 -0400
Subject: [PATCH 11/28] added additional documentation for convolve and
 lfilter, renamed functional_filtering to functional_sox_convenience

---
 torchaudio/functional.py                      | 33 +++++++++++++++++--
 ...ering.py => functional_sox_convenience.py} |  0
 2 files changed, 30 insertions(+), 3 deletions(-)
 rename torchaudio/{functional_filtering.py => functional_sox_convenience.py} (100%)

diff --git a/torchaudio/functional.py b/torchaudio/functional.py
index 736a1f2a70..a3fdb45bcd 100644
--- a/torchaudio/functional.py
+++ b/torchaudio/functional.py
@@ -1,9 +1,7 @@
 from __future__ import absolute_import, division, print_function, unicode_literals
 import math
 import torch
-from torchaudio.functional_filtering import lowpass_biquad
-from torchaudio.functional_filtering import highpass_biquad
-from torchaudio.functional_filtering import biquad
+from torchaudio.functional_sox_convenience import lowpass_biquad, highpass_biquad, biquad
 from _torch_filtering import diff_eq as diffeq_cpp
 
 __all__ = [
@@ -476,6 +474,16 @@ def phase_vocoder(complex_specgrams, rate, phase_advance):
 
 
 def convolve(input_waveform, impulse_response):
+    r"""Evaluate 1D convolution of impulse response on input waveform by channel
+    Thin wrapper around torch.nn.functional.conv_transpose1d
+
+    Args:
+        input_waveform (torch.Tensor): Tensor shape of `(n_channels, n_frames)`
+        impulse_response (torch.Tensor): Tensor shape of `(n_response_length)`
+
+    Returns:
+        torch.Tensor: output waveform filtered, shape `(n_channels, n_frames + n_response_length - 1)`
+    """
 
     n_channels, n_frames = input_waveform.size()
 
@@ -499,6 +507,25 @@ def convolve(input_waveform, impulse_response):
 
 
 def lfilter(input_waveform, a_coeffs, b_coeffs):
+    r"""Evaluate a difference equation on an input waveform
+    of form a0 * y[n] = b0 * x[n] + b1 * x[n-1] + ... - a1 * y[n-1] - a2 * y[n-2] ....
+    All initial inputs / outputs are zero
+
+    Args:
+        input_waveform (torch.Tensor): Tensor shape of `(n_channels, n_frames)`
+        a_coeffs (torch.Tensor): difference equation denominator coefficients ordered
+                   by time delay, e.g. [a0, a1, a2, ...], shape `(n_coeffs)`
+        b_coeffs (torch.Tensor): difference equation numerator coefficients ordered
+                   by time delay, e.g. [b0, b1, b2, ...], shape `(n_coeffs)`
+
+        N.B. a_coeffs and b_coeffs should be the exact same length, padding with 0's
+        may be required
+        N.B. all tensors must be of float32 type
+
+    Returns:
+        torch.Tensor: output waveform filtered, shape `(n_channels, n_frames)`
+    """
+
     output_waveform = torch.zeros_like(input_waveform)
     assert input_waveform.dtype == torch.float32
 
diff --git a/torchaudio/functional_filtering.py b/torchaudio/functional_sox_convenience.py
similarity index 100%
rename from torchaudio/functional_filtering.py
rename to torchaudio/functional_sox_convenience.py

From c5534c28d50419d8ead6e4610debea33a4b48b01 Mon Sep 17 00:00:00 2001
From: Chuan Zhang <engineerchuan@gmail.com>
Date: Sun, 15 Sep 2019 23:00:34 -0400
Subject: [PATCH 12/28] Fix documentation per issue 
 https://github.com/pytorch/audio/issues/98

---
 torchaudio/__init__.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/torchaudio/__init__.py b/torchaudio/__init__.py
index dd89e45d4f..47c84b0fcf 100644
--- a/torchaudio/__init__.py
+++ b/torchaudio/__init__.py
@@ -30,7 +30,7 @@ def load(filepath,
         filepath (str or pathlib.Path): Path to audio file
         out (torch.Tensor, optional): An output tensor to use instead of creating one. (Default: ``None``)
         normalization (bool, number, or callable, optional): If boolean `True`, then output is divided by `1 << 31`
-            (assumes signed 32-bit audio), and normalizes to `[0, 1]`.
+            (assumes signed 32-bit audio), and normalizes to `[-1, 1]`.
             If `number`, then output is divided by that number
             If `callable`, then the output is passed as a parameter
             to the given function, then the output is divided by

From ae5de6a57c2d8165371db7b3111fb63bf2159e26 Mon Sep 17 00:00:00 2001
From: Chuan Zhang <engineerchuan@gmail.com>
Date: Mon, 16 Sep 2019 14:38:50 -0400
Subject: [PATCH 13/28] Delete sox_convenience, delete convolve wrapper

---
 test/test_functional_filtering.py        |  41 ----
 torchaudio/filtering.cpp                 |  46 +++--
 torchaudio/functional.py                 | 251 +++++++++++++----------
 torchaudio/functional_sox_convenience.py |  63 ------
 4 files changed, 166 insertions(+), 235 deletions(-)
 delete mode 100644 torchaudio/functional_sox_convenience.py

diff --git a/test/test_functional_filtering.py b/test/test_functional_filtering.py
index 36eb824cdb..af63d462a6 100644
--- a/test/test_functional_filtering.py
+++ b/test/test_functional_filtering.py
@@ -69,47 +69,6 @@ def test_lfilter(self):
         assert output_waveform.size(0) == input_waveform.size(0)
         assert output_waveform.size(1) == input_waveform.size(1)
 
-    def test_convolve_basic(self):
-
-        # Create a short signal and filter
-        # Check results
-
-        input_waveform = torch.tensor(
-            [[0.0, 1.0, 0.0, 1.0, 0.0, 1.0]], dtype=torch.float32
-        )
-        filter_impulse_response = torch.tensor([0.33333, 0.33333, 0.33333])
-
-        output_waveform = F.convolve(input_waveform, filter_impulse_response)
-
-        assert len(output_waveform.size()) == 2
-        assert output_waveform.size(0) == input_waveform.size(0)
-        assert output_waveform.size(1) == (
-            input_waveform.size(1) + filter_impulse_response.size(0) - 1
-        )
-        assert torch.allclose(
-            output_waveform[0, 0:4],
-            torch.tensor([0.000, 0.3333, 0.3333, 0.6666]),
-            atol=1e-4,
-        )
-
-    def test_convolve(self):
-
-        # Run a stereo file through convolve, confirm output is of right size
-
-        filepath = os.path.join(self.test_dirpath, "assets", "dtmf_30s_stereo.mp3")
-        input_waveform, sample_rate = torchaudio.load(filepath, normalization=True)
-
-        torch.random.manual_seed(42)
-        filter_impulse_response = torch.rand(20)
-
-        output_waveform = F.convolve(input_waveform, filter_impulse_response)
-
-        assert len(output_waveform.size()) == 2
-        assert output_waveform.size(0) == input_waveform.size(0)
-        assert output_waveform.size(1) == (
-            input_waveform.size(1) + filter_impulse_response.size(0) - 1
-        )
-
     def test_lowpass_sox_compliance(self):
 
         """
diff --git a/torchaudio/filtering.cpp b/torchaudio/filtering.cpp
index 16aa9b244f..1b45f4e09d 100644
--- a/torchaudio/filtering.cpp
+++ b/torchaudio/filtering.cpp
@@ -1,36 +1,41 @@
 #include <torch/extension.h>
-
-//#include <algorithm>
-//#include <cstdint>
-//#include <stdexcept>
-//#include <vector>
+#ifdef WITH_CUDA
+#include <cuda.h>
+#endif
 
 namespace torch {
 namespace audio {
 
   // N.B. only handles floating point right now
-  void diff_eq(
-    at::Tensor const & input_waveform,
-    at::Tensor& output_waveform,
+  at::Tensor lfilter(
+    at::Tensor const & waveform,
     at::Tensor const & a_coeffs,
     at::Tensor const & b_coeffs
   ) {
 
     // assumes waveform is normalized between 1 and -1
+    assert(waveform.dtype == torch::float32);
+    assert(a_coeffs.size(0) == b_coeffs.size(0));
+    int n_order = a_coeffs.size(0); // n'th order - 1 filter
 
-    int64_t n_channels = input_waveform.size(0);
-    int64_t n_frames = input_waveform.size(1);
+    int64_t n_channels = waveform.size(0);
+    int64_t n_frames = waveform.size(1);
 
-    assert(output_waveform.size(0) == n_channels);
-    assert(output_waveform.size(1) == n_frames);
+    // initialize the output tensor
+    torch::Tensor output_waveform = torch::zeros({n_channels, n_frames});
 
-    auto input_accessor = input_waveform.accessor<float,2>();
+#ifdef WITH_CUDA
+    auto input_accessor = waveform.packed_accessor64<float,2>();
+    auto output_accessor = output_waveform.packed_accessor64<float,2>();    
+    auto a_coeffs_accessor = a_coeffs.packed_accessor64<float,1>();
+    auto b_coeffs_accessor = b_coeffs.packed_accessor64<float,1>();
+#endif
+#ifndef WITH_CUDA
+    auto input_accessor = waveform.accessor<float,2>();
     auto output_accessor = output_waveform.accessor<float,2>();    
     auto a_coeffs_accessor = a_coeffs.accessor<float,1>();
     auto b_coeffs_accessor = b_coeffs.accessor<float,1>();
-
-    int n_order = a_coeffs.size(0); // n'th order - 1 filter
-    assert(a_coeffs.size(0) == b_coeffs.size(0));
+#endif
 
     for (int64_t i_channel = 0; i_channel < n_channels; ++i_channel) {
 
@@ -67,6 +72,7 @@ namespace audio {
         }
       }
     }
+    return output_waveform;
   }
 
 }}
@@ -74,7 +80,11 @@ namespace audio {
 
 PYBIND11_MODULE(_torch_filtering, m) {
   m.def(
-      "diff_eq",
-      &torch::audio::diff_eq,
+      "lfilter",
+      &torch::audio::lfilter,
       "Executes difference equation");
+#ifdef WITH_CUDA
+  m.attr("CUDA_VERSION") = CUDA_VERSION;
+#endif
+
 }
diff --git a/torchaudio/functional.py b/torchaudio/functional.py
index a3fdb45bcd..4522fdef91 100644
--- a/torchaudio/functional.py
+++ b/torchaudio/functional.py
@@ -1,46 +1,65 @@
 from __future__ import absolute_import, division, print_function, unicode_literals
 import math
 import torch
-from torchaudio.functional_sox_convenience import lowpass_biquad, highpass_biquad, biquad
-from _torch_filtering import diff_eq as diffeq_cpp
+from _torch_filtering import lfilter
 
 __all__ = [
-    'istft',
-    'spectrogram',
-    'amplitude_to_DB',
-    'create_fb_matrix',
-    'create_dct',
-    'mu_law_encoding',
-    'mu_law_decoding',
-    'complex_norm',
-    'angle',
-    'magphase',
-    'phase_vocoder',
-    'lowpass_biquad',
-    'highpass_biquad',
-    'biquad',
-    'lfilter',
-    'convolve',
+    "istft",
+    "spectrogram",
+    "amplitude_to_DB",
+    "create_fb_matrix",
+    "create_dct",
+    "mu_law_encoding",
+    "mu_law_decoding",
+    "complex_norm",
+    "angle",
+    "magphase",
+    "phase_vocoder",
+    "lowpass_biquad",
+    "highpass_biquad",
+    "biquad",
+    "lfilter",
 ]
 
 # TODO: remove this once https://github.com/pytorch/pytorch/issues/21478 gets solved
 @torch.jit.ignore
-def _stft(waveform, n_fft, hop_length, win_length, window, center, pad_mode, normalized, onesided):
+def _stft(
+    waveform,
+    n_fft,
+    hop_length,
+    win_length,
+    window,
+    center,
+    pad_mode,
+    normalized,
+    onesided,
+):
     # type: (Tensor, int, Optional[int], Optional[int], Optional[Tensor], bool, str, bool, bool) -> Tensor
-    return torch.stft(waveform, n_fft, hop_length, win_length, window, center, pad_mode, normalized, onesided)
-
-
-def istft(stft_matrix,          # type: Tensor
-          n_fft,                # type: int
-          hop_length=None,      # type: Optional[int]
-          win_length=None,      # type: Optional[int]
-          window=None,          # type: Optional[Tensor]
-          center=True,          # type: bool
-          pad_mode='reflect',   # type: str
-          normalized=False,     # type: bool
-          onesided=True,        # type: bool
-          length=None           # type: Optional[int]
-          ):
+    return torch.stft(
+        waveform,
+        n_fft,
+        hop_length,
+        win_length,
+        window,
+        center,
+        pad_mode,
+        normalized,
+        onesided,
+    )
+
+
+def istft(
+    stft_matrix,  # type: Tensor
+    n_fft,  # type: int
+    hop_length=None,  # type: Optional[int]
+    win_length=None,  # type: Optional[int]
+    window=None,  # type: Optional[Tensor]
+    center=True,  # type: bool
+    pad_mode="reflect",  # type: str
+    normalized=False,  # type: bool
+    onesided=True,  # type: bool
+    length=None,  # type: Optional[int]
+):
     # type: (...) -> Tensor
     r"""Inverse short time Fourier Transform. This is expected to be the inverse of torch.stft.
     It has the same parameters (+ additional optional parameter of ``length``) and it should return the
@@ -95,7 +114,7 @@ def istft(stft_matrix,          # type: Tensor
         (channel, signal_length) or (signal_length)
     """
     stft_matrix_dim = stft_matrix.dim()
-    assert 3 <= stft_matrix_dim <= 4, ('Incorrect stft dimension: %d' % (stft_matrix_dim))
+    assert 3 <= stft_matrix_dim <= 4, "Incorrect stft dimension: %d" % (stft_matrix_dim)
 
     if stft_matrix_dim == 3:
         # add a channel dimension
@@ -104,9 +123,13 @@ def istft(stft_matrix,          # type: Tensor
     dtype = stft_matrix.dtype
     device = stft_matrix.device
     fft_size = stft_matrix.size(1)
-    assert (onesided and n_fft // 2 + 1 == fft_size) or (not onesided and n_fft == fft_size), (
-        'one_sided implies that n_fft // 2 + 1 == fft_size and not one_sided implies n_fft == fft_size. ' +
-        'Given values were onesided: %s, n_fft: %d, fft_size: %d' % ('True' if onesided else False, n_fft, fft_size))
+    assert (onesided and n_fft // 2 + 1 == fft_size) or (
+        not onesided and n_fft == fft_size
+    ), (
+        "one_sided implies that n_fft // 2 + 1 == fft_size and not one_sided implies n_fft == fft_size. "
+        + "Given values were onesided: %s, n_fft: %d, fft_size: %d"
+        % ("True" if onesided else False, n_fft, fft_size)
+    )
 
     # use stft defaults for Optionals
     if win_length is None:
@@ -132,8 +155,9 @@ def istft(stft_matrix,          # type: Tensor
     # win_length and n_fft are synonymous from here on
 
     stft_matrix = stft_matrix.transpose(1, 2)  # size (channel, n_frames, fft_size, 2)
-    stft_matrix = torch.irfft(stft_matrix, 1, normalized,
-                              onesided, signal_sizes=(n_fft,))  # size (channel, n_frames, n_fft)
+    stft_matrix = torch.irfft(
+        stft_matrix, 1, normalized, onesided, signal_sizes=(n_fft,)
+    )  # size (channel, n_frames, n_fft)
 
     assert stft_matrix.size(2) == n_fft
     n_frames = stft_matrix.size(1)
@@ -142,18 +166,23 @@ def istft(stft_matrix,          # type: Tensor
     # each column of a channel is a frame which needs to be overlap added at the right place
     ytmp = ytmp.transpose(1, 2)  # size (channel, n_fft, n_frames)
 
-    eye = torch.eye(n_fft, requires_grad=False,
-                    device=device, dtype=dtype).unsqueeze(1)  # size (n_fft, 1, n_fft)
+    eye = torch.eye(n_fft, requires_grad=False, device=device, dtype=dtype).unsqueeze(
+        1
+    )  # size (n_fft, 1, n_fft)
 
     # this does overlap add where the frames of ytmp are added such that the i'th frame of
     # ytmp is added starting at i*hop_length in the output
     y = torch.nn.functional.conv_transpose1d(
-        ytmp, eye, stride=hop_length, padding=0)  # size (channel, 1, expected_signal_len)
+        ytmp, eye, stride=hop_length, padding=0
+    )  # size (channel, 1, expected_signal_len)
 
     # do the same for the window function
-    window_sq = window.pow(2).view(n_fft, 1).repeat((1, n_frames)).unsqueeze(0)  # size (1, n_fft, n_frames)
+    window_sq = (
+        window.pow(2).view(n_fft, 1).repeat((1, n_frames)).unsqueeze(0)
+    )  # size (1, n_fft, n_frames)
     window_envelop = torch.nn.functional.conv_transpose1d(
-        window_sq, eye, stride=hop_length, padding=0)  # size (1, 1, expected_signal_len)
+        window_sq, eye, stride=hop_length, padding=0
+    )  # size (1, 1, expected_signal_len)
 
     expected_signal_len = n_fft + hop_length * (n_frames - 1)
     assert y.size(2) == expected_signal_len
@@ -169,7 +198,9 @@ def istft(stft_matrix,          # type: Tensor
 
     # check NOLA non-zero overlap condition
     window_envelop_lowest = window_envelop.abs().min()
-    assert window_envelop_lowest > 1e-11, ('window overlap add min: %f' % (window_envelop_lowest))
+    assert window_envelop_lowest > 1e-11, "window overlap add min: %f" % (
+        window_envelop_lowest
+    )
 
     y = (y / window_envelop).squeeze(1)  # size (channel, expected_signal_len)
 
@@ -179,7 +210,9 @@ def istft(stft_matrix,          # type: Tensor
 
 
 @torch.jit.script
-def spectrogram(waveform, pad, window, n_fft, hop_length, win_length, power, normalized):
+def spectrogram(
+    waveform, pad, window, n_fft, hop_length, win_length, power, normalized
+):
     # type: (Tensor, int, Tensor, int, int, int, int, bool) -> Tensor
     r"""Create a spectrogram from a raw audio signal.
 
@@ -206,8 +239,9 @@ def spectrogram(waveform, pad, window, n_fft, hop_length, win_length, power, nor
         waveform = torch.nn.functional.pad(waveform, (pad, pad), "constant")
 
     # default values are consistent with librosa.core.spectrum._spectrogram
-    spec_f = _stft(waveform, n_fft, hop_length, win_length, window,
-                   True, 'reflect', False, True)
+    spec_f = _stft(
+        waveform, n_fft, hop_length, win_length, window, True, "reflect", False, True
+    )
 
     if normalized:
         spec_f /= window.pow(2).sum().sqrt()
@@ -239,8 +273,9 @@ def amplitude_to_DB(x, multiplier, amin, db_multiplier, top_db=None):
     x_db -= multiplier * db_multiplier
 
     if top_db is not None:
-        new_x_db_max = torch.tensor(float(x_db.max()) - top_db,
-                                    dtype=x_db.dtype, device=x_db.device)
+        new_x_db_max = torch.tensor(
+            float(x_db.max()) - top_db, dtype=x_db.dtype, device=x_db.device
+        )
         x_db = torch.max(x_db, new_x_db_max)
 
     return x_db
@@ -268,17 +303,17 @@ def create_fb_matrix(n_freqs, f_min, f_max, n_mels):
     freqs = torch.linspace(f_min, f_max, n_freqs)
     # calculate mel freq bins
     # hertz to mel(f) is 2595. * math.log10(1. + (f / 700.))
-    m_min = 0. if f_min == 0 else 2595. * math.log10(1. + (f_min / 700.))
-    m_max = 2595. * math.log10(1. + (f_max / 700.))
+    m_min = 0.0 if f_min == 0 else 2595.0 * math.log10(1.0 + (f_min / 700.0))
+    m_max = 2595.0 * math.log10(1.0 + (f_max / 700.0))
     m_pts = torch.linspace(m_min, m_max, n_mels + 2)
     # mel to hertz(mel) is 700. * (10**(mel / 2595.) - 1.)
-    f_pts = 700. * (10**(m_pts / 2595.) - 1.)
+    f_pts = 700.0 * (10 ** (m_pts / 2595.0) - 1.0)
     # calculate the difference between each mel point and each stft freq point in hertz
     f_diff = f_pts[1:] - f_pts[:-1]  # (n_mels + 1)
     slopes = f_pts.unsqueeze(0) - freqs.unsqueeze(1)  # (n_freqs, n_mels + 2)
     # create overlapping triangles
     zero = torch.zeros(1)
-    down_slopes = (-1. * slopes[:, :-2]) / f_diff[:-1]  # (n_freqs, n_mels)
+    down_slopes = (-1.0 * slopes[:, :-2]) / f_diff[:-1]  # (n_freqs, n_mels)
     up_slopes = slopes[:, 2:] / f_diff[1:]  # (n_freqs, n_mels)
     fb = torch.max(zero, torch.min(down_slopes, up_slopes))
     return fb
@@ -306,7 +341,7 @@ def create_dct(n_mfcc, n_mels, norm):
     if norm is None:
         dct *= 2.0
     else:
-        assert norm == 'ortho'
+        assert norm == "ortho"
         dct[0] *= 1.0 / math.sqrt(2.0)
         dct *= math.sqrt(2.0 / float(n_mels))
     return dct.t()
@@ -328,12 +363,11 @@ def mu_law_encoding(x, quantization_channels):
     Returns:
         torch.Tensor: Input after mu-law encoding
     """
-    mu = quantization_channels - 1.
+    mu = quantization_channels - 1.0
     if not x.is_floating_point():
         x = x.to(torch.float)
     mu = torch.tensor(mu, dtype=x.dtype)
-    x_mu = torch.sign(x) * torch.log1p(mu *
-                                       torch.abs(x)) / torch.log1p(mu)
+    x_mu = torch.sign(x) * torch.log1p(mu * torch.abs(x)) / torch.log1p(mu)
     x_mu = ((x_mu + 1) / 2 * mu + 0.5).to(torch.int64)
     return x_mu
 
@@ -354,12 +388,12 @@ def mu_law_decoding(x_mu, quantization_channels):
     Returns:
         torch.Tensor: Input after mu-law decoding
     """
-    mu = quantization_channels - 1.
+    mu = quantization_channels - 1.0
     if not x_mu.is_floating_point():
         x_mu = x_mu.to(torch.float)
     mu = torch.tensor(mu, dtype=x_mu.dtype)
-    x = ((x_mu) / mu) * 2 - 1.
-    x = torch.sign(x) * (torch.exp(torch.abs(x) * torch.log1p(mu)) - 1.) / mu
+    x = ((x_mu) / mu) * 2 - 1.0
+    x = torch.sign(x) * (torch.exp(torch.abs(x) * torch.log1p(mu)) - 1.0) / mu
     return x
 
 
@@ -390,7 +424,7 @@ def angle(complex_tensor):
     return torch.atan2(complex_tensor[..., 1], complex_tensor[..., 0])
 
 
-def magphase(complex_tensor, power=1.):
+def magphase(complex_tensor, power=1.0):
     r"""Separate a complex-valued spectrogram with shape `(*, 2)` into its magnitude and phase.
 
     Args:
@@ -433,13 +467,15 @@ def phase_vocoder(complex_specgrams, rate, phase_advance):
     ndim = complex_specgrams.dim()
     time_slice = [slice(None)] * (ndim - 2)
 
-    time_steps = torch.arange(0,
-                              complex_specgrams.size(-2),
-                              rate,
-                              device=complex_specgrams.device,
-                              dtype=complex_specgrams.dtype)
+    time_steps = torch.arange(
+        0,
+        complex_specgrams.size(-2),
+        rate,
+        device=complex_specgrams.device,
+        dtype=complex_specgrams.dtype,
+    )
 
-    alphas = time_steps % 1.
+    alphas = time_steps % 1.0
     phase_0 = angle(complex_specgrams[time_slice + [slice(1)]])
 
     # Time Padding
@@ -473,61 +509,50 @@ def phase_vocoder(complex_specgrams, rate, phase_advance):
     return complex_specgrams_stretch
 
 
-def convolve(input_waveform, impulse_response):
-    r"""Evaluate 1D convolution of impulse response on input waveform by channel
-    Thin wrapper around torch.nn.functional.conv_transpose1d
+def biquad(waveform, b0, b1, b2, a0, a1, a2):
 
-    Args:
-        input_waveform (torch.Tensor): Tensor shape of `(n_channels, n_frames)`
-        impulse_response (torch.Tensor): Tensor shape of `(n_response_length)`
+    assert waveform.dtype == torch.float32
 
-    Returns:
-        torch.Tensor: output waveform filtered, shape `(n_channels, n_frames + n_response_length - 1)`
-    """
+    output_waveform = lfilter(
+        waveform, torch.tensor([a0, a1, a2]), torch.tensor([b0, b1, b2])
+    )
+    return output_waveform
 
-    n_channels, n_frames = input_waveform.size()
 
-    # Perform convolution for each channel
-    assert input_waveform.dtype == torch.float32
-    assert impulse_response.dtype == torch.float32
+def _dB2Linear(x):
 
-    # N.B. - can we do all channels at once?
-    channel_output_waveforms = []
-    for i_channel in range(n_channels):
-        channel_output_waveforms.append(
+    return math.exp(x * math.log(10) / 20.0)
 
-            # torch nn conv requires 3D tensor
-            torch.nn.functional.conv_transpose1d(
-                input_waveform[i_channel, :].unsqueeze(0).unsqueeze(0),
-                impulse_response.unsqueeze(0).unsqueeze(0),
-            ).squeeze(0).squeeze(0)
-        )
 
-    return torch.stack(channel_output_waveforms)
+def highpass_biquad(waveform, sr, cutoff_freq, Q=0.707):
 
+    GAIN = 1
+    w0 = 2 * math.pi * cutoff_freq / sr
+    A = math.exp(GAIN / 40.0 * math.log(10))
+    alpha = math.sin(w0) / 2 / Q
+    mult = _dB2Linear(max(GAIN, 0))
 
-def lfilter(input_waveform, a_coeffs, b_coeffs):
-    r"""Evaluate a difference equation on an input waveform
-    of form a0 * y[n] = b0 * x[n] + b1 * x[n-1] + ... - a1 * y[n-1] - a2 * y[n-2] ....
-    All initial inputs / outputs are zero
+    b0 = (1 + math.cos(w0)) / 2
+    b1 = -1 - math.cos(w0)
+    b2 = b0
+    a0 = 1 + alpha
+    a1 = -2 * math.cos(w0)
+    a2 = 1 - alpha
+    return biquad(waveform, b0, b1, b2, a0, a1, a2)
 
-    Args:
-        input_waveform (torch.Tensor): Tensor shape of `(n_channels, n_frames)`
-        a_coeffs (torch.Tensor): difference equation denominator coefficients ordered
-                   by time delay, e.g. [a0, a1, a2, ...], shape `(n_coeffs)`
-        b_coeffs (torch.Tensor): difference equation numerator coefficients ordered
-                   by time delay, e.g. [b0, b1, b2, ...], shape `(n_coeffs)`
 
-        N.B. a_coeffs and b_coeffs should be the exact same length, padding with 0's
-        may be required
-        N.B. all tensors must be of float32 type
+def lowpass_biquad(waveform, sr, cutoff_freq, Q=0.707):
 
-    Returns:
-        torch.Tensor: output waveform filtered, shape `(n_channels, n_frames)`
-    """
+    GAIN = 1
+    w0 = 2 * math.pi * cutoff_freq / sr
+    A = math.exp(GAIN / 40.0 * math.log(10))
+    alpha = math.sin(w0) / 2 / Q
+    mult = _dB2Linear(max(GAIN, 0))
 
-    output_waveform = torch.zeros_like(input_waveform)
-    assert input_waveform.dtype == torch.float32
-
-    diffeq_cpp(input_waveform, output_waveform, a_coeffs, b_coeffs)
-    return output_waveform
+    b0 = (1 - math.cos(w0)) / 2
+    b1 = 1 - math.cos(w0)
+    b2 = b0
+    a0 = 1 + alpha
+    a1 = -2 * math.cos(w0)
+    a2 = 1 - alpha
+    return biquad(waveform, b0, b1, b2, a0, a1, a2)
diff --git a/torchaudio/functional_sox_convenience.py b/torchaudio/functional_sox_convenience.py
deleted file mode 100644
index 412e2e17b1..0000000000
--- a/torchaudio/functional_sox_convenience.py
+++ /dev/null
@@ -1,63 +0,0 @@
-from __future__ import absolute_import, division, print_function, unicode_literals
-import math
-import torch
-import torchaudio
-from _torch_filtering import diff_eq as diffeq_cpp
-
-__all__ = ["lowpass_biquad", "highpass_biquad", "biquad"]
-
-
-def biquad(input_waveform, b0, b1, b2, a0, a1, a2):
-    output_waveform = torch.zeros_like(input_waveform)
-    assert input_waveform.dtype == torch.float32
-
-    diffeq_cpp(
-        input_waveform,
-        output_waveform,
-        torch.tensor([a0, a1, a2]),
-        torch.tensor([b0, b1, b2]),
-    )
-    return output_waveform
-
-
-def _dB2Linear(x):
-
-    return math.exp(x * math.log(10) / 20.0)
-
-
-def highpass_biquad(input_waveform, sr, cutoff_freq, Q=0.707):
-
-    GAIN = 1
-    w0 = 2 * math.pi * cutoff_freq / sr
-    A = math.exp(GAIN / 40.0 * math.log(10))
-    alpha = math.sin(w0) / 2 / Q
-    mult = _dB2Linear(max(GAIN, 0))
-
-    b0 = (1 + math.cos(w0)) / 2
-    b1 = -1 - math.cos(w0)
-    b2 = b0
-    a0 = 1 + alpha
-    a1 = -2 * math.cos(w0)
-    a2 = 1 - alpha
-    return biquad(input_waveform, b0, b1, b2, a0, a1, a2)
-
-
-def lowpass_biquad(input_waveform, sr, cutoff_freq, Q=0.707):
-
-    GAIN = 1
-    w0 = 2 * math.pi * cutoff_freq / sr
-    A = math.exp(GAIN / 40.0 * math.log(10))
-    alpha = math.sin(w0) / 2 / Q
-    mult = _dB2Linear(max(GAIN, 0))
-
-    b0 = (1 - math.cos(w0)) / 2
-    b1 = 1 - math.cos(w0)
-    b2 = b0
-    a0 = 1 + alpha
-    a1 = -2 * math.cos(w0)
-    a2 = 1 - alpha
-    return biquad(input_waveform, b0, b1, b2, a0, a1, a2)
-
-
-if __name__ == "__main__":
-    pass

From ebf3d9e4c951a8a89c77b0fddab2f34604bcec78 Mon Sep 17 00:00:00 2001
From: Chuan Zhang <engineerchuan@gmail.com>
Date: Mon, 16 Sep 2019 14:47:48 -0400
Subject: [PATCH 14/28] Unwind other issue to separate PR, clean up

---
 test/test_functional_filtering.py | 28 ++++++++++++++--------------
 torchaudio/__init__.py            |  2 +-
 torchaudio/filtering.cpp          |  2 +-
 torchaudio/functional.py          |  2 +-
 4 files changed, 17 insertions(+), 17 deletions(-)

diff --git a/test/test_functional_filtering.py b/test/test_functional_filtering.py
index af63d462a6..4c22cf1548 100644
--- a/test/test_functional_filtering.py
+++ b/test/test_functional_filtering.py
@@ -13,20 +13,20 @@ class TestFunctionalFiltering(unittest.TestCase):
     test_dirpath, test_dir = common_utils.create_temp_assets_dir()
 
     def test_lfilter_basic(self):
-        """l
+        """
         Create a very basic signal,
         Then make a simple 4th order delay
         The output should be same as the input but shifted
         """
 
         torch.random.manual_seed(42)
-        input_waveform = torch.rand(2, 1000)
+        waveform = torch.rand(2, 1000)
         b_coeffs = torch.tensor([0, 0, 0, 1], dtype=torch.float32)
         a_coeffs = torch.tensor([1, 0, 0, 0], dtype=torch.float32)
-        output_waveform = F.lfilter(input_waveform, a_coeffs, b_coeffs)
+        output_waveform = F.lfilter(waveform, a_coeffs, b_coeffs)
 
         assert torch.allclose(
-            input_waveform[:, 0:-3], output_waveform[:, 3:], atol=1e-5
+            waveform[:, 0:-3], output_waveform[:, 3:], atol=1e-5
         )
 
     def test_lfilter(self):
@@ -63,11 +63,11 @@ def test_lfilter(self):
         )
 
         filepath = os.path.join(self.test_dirpath, "assets", "dtmf_30s_stereo.mp3")
-        input_waveform, sample_rate = torchaudio.load(filepath, normalization=True)
-        output_waveform = F.lfilter(input_waveform, a_coeffs, b_coeffs)
+        waveform, sample_rate = torchaudio.load(filepath, normalization=True)
+        output_waveform = F.lfilter(waveform, a_coeffs, b_coeffs)
         assert len(output_waveform.size()) == 2
-        assert output_waveform.size(0) == input_waveform.size(0)
-        assert output_waveform.size(1) == input_waveform.size(1)
+        assert output_waveform.size(0) == waveform.size(0)
+        assert output_waveform.size(1) == waveform.size(1)
 
     def test_lowpass_sox_compliance(self):
 
@@ -86,10 +86,10 @@ def test_lowpass_sox_compliance(self):
         E.append_effect_to_chain("lowpass", [CUTOFF_FREQ])
         sox_output_waveform, sr = E.sox_build_flow_effects()
 
-        input_waveform, sample_rate = torchaudio.load(
+        waveform, sample_rate = torchaudio.load(
             noise_filepath, normalization=True
         )
-        output_waveform = F.lowpass_biquad(input_waveform, sample_rate, CUTOFF_FREQ)
+        output_waveform = F.lowpass_biquad(waveform, sample_rate, CUTOFF_FREQ)
 
         assert torch.allclose(sox_output_waveform, output_waveform, atol=1e-4)
 
@@ -109,10 +109,10 @@ def test_highpass_sox_compliance(self):
         E.append_effect_to_chain("highpass", [CUTOFF_FREQ])
         sox_output_waveform, sr = E.sox_build_flow_effects()
 
-        input_waveform, sample_rate = torchaudio.load(
+        waveform, sample_rate = torchaudio.load(
             noise_filepath, normalization=True
         )
-        output_waveform = F.highpass_biquad(input_waveform, sample_rate, CUTOFF_FREQ)
+        output_waveform = F.highpass_biquad(waveform, sample_rate, CUTOFF_FREQ)
 
         # TBD - this fails at the 1e-4 level, debug why
         assert torch.allclose(sox_output_waveform, output_waveform, atol=1e-3)
@@ -145,9 +145,9 @@ def test_perf_biquad_filtering(self):
 
         # C++ Diff Eq Filter
         _timing_cpp_filtering = time.time()
-        input_waveform, sample_rate = torchaudio.load(fn_sine, normalization=True)
+        waveform, sample_rate = torchaudio.load(fn_sine, normalization=True)
         waveform_diff_eq_out = F.lfilter(
-            input_waveform, torch.tensor([a0, a1, a2]), torch.tensor([b0, b1, b2])
+            waveform, torch.tensor([a0, a1, a2]), torch.tensor([b0, b1, b2])
         )
         _timing_diff_eq_run_time = time.time() - _timing_cpp_filtering
 
diff --git a/torchaudio/__init__.py b/torchaudio/__init__.py
index 542b5afc6d..138c2b7458 100644
--- a/torchaudio/__init__.py
+++ b/torchaudio/__init__.py
@@ -34,7 +34,7 @@ def load(filepath,
         filepath (str or pathlib.Path): Path to audio file
         out (torch.Tensor, optional): An output tensor to use instead of creating one. (Default: ``None``)
         normalization (bool, number, or callable, optional): If boolean `True`, then output is divided by `1 << 31`
-            (assumes signed 32-bit audio), and normalizes to `[-1, 1]`.
+            (assumes signed 32-bit audio), and normalizes to `[0, 1]`.
             If `number`, then output is divided by that number
             If `callable`, then the output is passed as a parameter
             to the given function, then the output is divided by
diff --git a/torchaudio/filtering.cpp b/torchaudio/filtering.cpp
index 1b45f4e09d..8521398363 100644
--- a/torchaudio/filtering.cpp
+++ b/torchaudio/filtering.cpp
@@ -6,7 +6,7 @@
 namespace torch {
 namespace audio {
 
-  // N.B. only handles floating point right now
+  // N.B. TBD - Test with CUDA
   at::Tensor lfilter(
     at::Tensor const & waveform,
     at::Tensor const & a_coeffs,
diff --git a/torchaudio/functional.py b/torchaudio/functional.py
index 4522fdef91..76a549a5d0 100644
--- a/torchaudio/functional.py
+++ b/torchaudio/functional.py
@@ -511,7 +511,7 @@ def phase_vocoder(complex_specgrams, rate, phase_advance):
 
 def biquad(waveform, b0, b1, b2, a0, a1, a2):
 
-    assert waveform.dtype == torch.float32
+    assert(waveform.dtype == torch.float32)
 
     output_waveform = lfilter(
         waveform, torch.tensor([a0, a1, a2]), torch.tensor([b0, b1, b2])

From 361a2262a9e5d0aa4e7befdee4649a669801d4c4 Mon Sep 17 00:00:00 2001
From: Chuan Zhang <engineerchuan@gmail.com>
Date: Mon, 16 Sep 2019 14:56:06 -0400
Subject: [PATCH 15/28] Follow naming convention for sample rate in functional

---
 torchaudio/functional.py | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/torchaudio/functional.py b/torchaudio/functional.py
index 76a549a5d0..8e2790156d 100644
--- a/torchaudio/functional.py
+++ b/torchaudio/functional.py
@@ -524,10 +524,10 @@ def _dB2Linear(x):
     return math.exp(x * math.log(10) / 20.0)
 
 
-def highpass_biquad(waveform, sr, cutoff_freq, Q=0.707):
+def highpass_biquad(waveform, sample_rate, cutoff_freq, Q=0.707):
 
     GAIN = 1
-    w0 = 2 * math.pi * cutoff_freq / sr
+    w0 = 2 * math.pi * cutoff_freq / sample_rate
     A = math.exp(GAIN / 40.0 * math.log(10))
     alpha = math.sin(w0) / 2 / Q
     mult = _dB2Linear(max(GAIN, 0))
@@ -541,10 +541,10 @@ def highpass_biquad(waveform, sr, cutoff_freq, Q=0.707):
     return biquad(waveform, b0, b1, b2, a0, a1, a2)
 
 
-def lowpass_biquad(waveform, sr, cutoff_freq, Q=0.707):
+def lowpass_biquad(waveform, sample_rate, cutoff_freq, Q=0.707):
 
     GAIN = 1
-    w0 = 2 * math.pi * cutoff_freq / sr
+    w0 = 2 * math.pi * cutoff_freq / sample_rate
     A = math.exp(GAIN / 40.0 * math.log(10))
     alpha = math.sin(w0) / 2 / Q
     mult = _dB2Linear(max(GAIN, 0))

From 288aedcd026c7ec065b88965f0f264ec0ea403e9 Mon Sep 17 00:00:00 2001
From: Chuan Zhang <engineerchuan@gmail.com>
Date: Mon, 16 Sep 2019 15:39:35 -0400
Subject: [PATCH 16/28] use memset instead of implicit initialization

---
 torchaudio/filtering.cpp | 5 +++--
 1 file changed, 3 insertions(+), 2 deletions(-)

diff --git a/torchaudio/filtering.cpp b/torchaudio/filtering.cpp
index 8521398363..9d811d3124 100644
--- a/torchaudio/filtering.cpp
+++ b/torchaudio/filtering.cpp
@@ -41,8 +41,9 @@ namespace audio {
 
       // allocate a temporary data structure of size 2 x (n_order + 1)
       // set to 0 because initial conditions are 0
-      float i_s[n_order]= { };
-      float o_s[n_order]= { };
+      float i_s[n_order], o_s[n_order];
+      memset( i_s, 0, n_order*sizeof(float) );
+      memset( o_s, 0, n_order*sizeof(float) );
     
       for (int64_t i_frame = 0; i_frame < n_frames; ++i_frame) {
 

From 4115a1436f2672bf7e0843342cf783097341fdca Mon Sep 17 00:00:00 2001
From: Chuan Zhang <engineerchuan@gmail.com>
Date: Mon, 16 Sep 2019 17:09:42 -0400
Subject: [PATCH 17/28] fix failing vctk manifest test to account for adding
 more test audios into assets

---
 test/test_datasets_vctk.py | 5 ++++-
 1 file changed, 4 insertions(+), 1 deletion(-)

diff --git a/test/test_datasets_vctk.py b/test/test_datasets_vctk.py
index 4d3477c338..d650225fe0 100644
--- a/test/test_datasets_vctk.py
+++ b/test/test_datasets_vctk.py
@@ -23,10 +23,13 @@ def test_is_audio_file(self):
     def test_make_manifest(self):
         audios = vctk.make_manifest(self.test_dirpath)
         files = ['kaldi_file.wav', 'kaldi_file_8000.wav',
-                 'sinewave.wav', 'steam-train-whistle-daniel_simon.mp3']
+                 'sinewave.wav', 'steam-train-whistle-daniel_simon.mp3',
+                 'dtmf_30s_stereo.mp3', 'whitenoise_1min.mp3', 'whitenoise.mp3']
         files = [self.get_full_path(file) for file in files]
 
+        files.sort()
         audios.sort()
+
         self.assertEqual(files, audios, msg='files %s did not match audios %s' % (files, audios))
 
     def test_read_audio_downsample_false(self):

From 5469c4d75c54b393e7cb56016a62adf208ed98b4 Mon Sep 17 00:00:00 2001
From: Chuan Zhang <engineerchuan@gmail.com>
Date: Mon, 16 Sep 2019 22:33:34 -0400
Subject: [PATCH 18/28] Trying out a tensor slicing based approach

---
 test/test_functional_filtering.py | 25 ++++++++++-
 torchaudio/filtering.cpp          | 71 +++++++++++++++++++++++++++++--
 torchaudio/functional.py          |  2 +-
 3 files changed, 93 insertions(+), 5 deletions(-)

diff --git a/test/test_functional_filtering.py b/test/test_functional_filtering.py
index 4c22cf1548..6abfaf2d4a 100644
--- a/test/test_functional_filtering.py
+++ b/test/test_functional_filtering.py
@@ -20,7 +20,7 @@ def test_lfilter_basic(self):
         """
 
         torch.random.manual_seed(42)
-        waveform = torch.rand(2, 1000)
+        waveform = torch.rand(2, 10000)
         b_coeffs = torch.tensor([0, 0, 0, 1], dtype=torch.float32)
         a_coeffs = torch.tensor([1, 0, 0, 0], dtype=torch.float32)
         output_waveform = F.lfilter(waveform, a_coeffs, b_coeffs)
@@ -28,6 +28,28 @@ def test_lfilter_basic(self):
         assert torch.allclose(
             waveform[:, 0:-3], output_waveform[:, 3:], atol=1e-5
         )
+    
+    def test_lfilter_loop_vs_tensor(self):
+    
+        torch.random.manual_seed(42)
+        waveform = torch.rand(2, 100000)
+        b_coeffs = torch.tensor([0.3, 0.4, 0, 1], dtype=torch.float32)
+        a_coeffs = torch.tensor([1, 0.2, 0.2, 0], dtype=torch.float32)
+        import time
+        tensor_time_start = time.time()
+        output_waveform1 = F.lfilter_tensor(waveform, a_coeffs, b_coeffs)
+        tensor_time_taken = time.time() - tensor_time_start
+        loop_time_start = time.time()
+        output_waveform2 = F.lfilter(waveform, a_coeffs, b_coeffs)
+        loop_time_taken = time.time() - loop_time_start
+
+        print("\n")
+        print("Looped Implementation took: ", loop_time_taken)
+        print("Tensor Implementation took: ", tensor_time_taken)
+
+        assert torch.allclose(
+            output_waveform1, output_waveform2, atol=1e-5
+        )        
 
     def test_lfilter(self):
         """
@@ -113,6 +135,7 @@ def test_highpass_sox_compliance(self):
             noise_filepath, normalization=True
         )
         output_waveform = F.highpass_biquad(waveform, sample_rate, CUTOFF_FREQ)
+        
 
         # TBD - this fails at the 1e-4 level, debug why
         assert torch.allclose(sox_output_waveform, output_waveform, atol=1e-3)
diff --git a/torchaudio/filtering.cpp b/torchaudio/filtering.cpp
index 9d811d3124..7d858d4170 100644
--- a/torchaudio/filtering.cpp
+++ b/torchaudio/filtering.cpp
@@ -6,6 +6,67 @@
 namespace torch {
 namespace audio {
 
+at::Tensor lfilter_tensor(
+    at::Tensor const & waveform,
+    at::Tensor const & a_coeffs,
+    at::Tensor const & b_coeffs
+  ) {
+
+    // assumes waveform is normalized between 1 and -1
+    assert(waveform.dtype == torch::float32);
+    assert(a_coeffs.size(0) == b_coeffs.size(0));
+    int n_order = a_coeffs.size(0); // n'th order - 1 filter
+    assert(n_order > 0);
+
+    int64_t n_channels = waveform.size(0);
+    int64_t n_frames = waveform.size(1);
+
+    // Allocate padded input and output waveform, copy in the input waveform
+    at::Tensor padded_waveform = torch::zeros({n_channels, n_frames + n_order - 1}, torch::TensorOptions().dtype(torch::kFloat32));
+    at::Tensor padded_output_waveform = torch::zeros({n_channels, n_frames + n_order - 1}, torch::TensorOptions().dtype(torch::kFloat32));
+    padded_waveform.slice(0, 0, n_channels).slice(1, n_order - 1, n_order + n_frames - 1) = waveform;
+
+    // Create [n_channels, n_order] structure for a and b coefficients
+    at::Tensor a_coeffs_filled = a_coeffs.repeat({n_channels, 1});
+    at::Tensor b_coeffs_filled = b_coeffs.repeat({n_channels, 1});
+
+    // few more temporary data structure
+    at::Tensor o0 = torch::zeros({n_channels, 1}, torch::TensorOptions().dtype(torch::kFloat32));
+    at::Tensor ones = torch::ones({n_channels, n_frames + n_order - 1});
+    at::Tensor negones = torch::ones({n_channels, n_frames + n_order -1 }) * -1;
+
+    for (int64_t i_frame = 0; i_frame < n_frames; ++i_frame) {
+
+      // calculate the output at time i_frame
+      // initialize it!
+      o0 = torch::zeros({n_channels, 1}, torch::TensorOptions().dtype(torch::kFloat32));
+
+      for (int i_offset = 0; i_offset < n_order; ++i_offset) {
+
+        at::Tensor const & input_time_offset = padded_waveform.slice(0, 0, n_channels).slice(1, i_frame + n_order - 1 - i_offset, i_frame + n_order - 1 - i_offset + 1);
+        at::Tensor const & output_time_offset = padded_output_waveform.slice(0, 0, n_channels).slice(1, i_frame + n_order - 1 - i_offset, i_frame+ n_order - 1 - i_offset + 1);
+        at::Tensor const & a_coeffs_offset = a_coeffs_filled.slice(0, 0, n_channels).slice(1, i_offset, i_offset + 1);
+        at::Tensor const & b_coeffs_offset = b_coeffs_filled.slice(0, 0, n_channels).slice(1, i_offset, i_offset + 1);        
+
+        // Multiply by the coefficients
+        o0 = torch::addcmul(o0, input_time_offset, b_coeffs_offset, 1);
+        if (i_offset != n_order - 1) {
+          o0 = torch::addcmul(o0, output_time_offset, a_coeffs_offset, -1);
+        }
+      }
+      // normalize by a0
+      o0 = torch::div(o0, a_coeffs_filled.slice(0, 0, n_channels).slice(1, 0, 1));
+
+      // Set the output
+      padded_output_waveform.slice(0, 0, n_channels).slice(1, i_frame + n_order - 1, i_frame + n_order - 1 + 1) = o0;
+      
+    }
+
+    // return clipped, and without initial conditions
+    return torch::min(ones, torch::max(negones, padded_output_waveform)).slice(0, 0, n_channels).slice(1, n_order - 1, n_order + n_frames - 1);
+  }
+
+
   // N.B. TBD - Test with CUDA
   at::Tensor lfilter(
     at::Tensor const & waveform,
@@ -44,7 +105,7 @@ namespace audio {
       float i_s[n_order], o_s[n_order];
       memset( i_s, 0, n_order*sizeof(float) );
       memset( o_s, 0, n_order*sizeof(float) );
-    
+
       for (int64_t i_frame = 0; i_frame < n_frames; ++i_frame) {
 
         // calculate the output at time i_frame by iterating through
@@ -65,7 +126,7 @@ namespace audio {
         if (o0 > 1) o0 = 1;
         if (o0 < -1) o0 = -1;
         output_accessor[i_channel][i_frame] = o0;
-        
+
         // shift everything over by one time step
         for (int i = 0; i < (n_order - 1); ++i) {
           i_s[i] = i_s[i+1];
@@ -80,10 +141,14 @@ namespace audio {
 
 
 PYBIND11_MODULE(_torch_filtering, m) {
+  m.def(
+      "lfilter_tensor",
+      &torch::audio::lfilter_tensor,
+      "Executes difference equation with tensor");
   m.def(
       "lfilter",
       &torch::audio::lfilter,
-      "Executes difference equation");
+      "Executes difference equation");      
 #ifdef WITH_CUDA
   m.attr("CUDA_VERSION") = CUDA_VERSION;
 #endif
diff --git a/torchaudio/functional.py b/torchaudio/functional.py
index 8e2790156d..faa79a8a90 100644
--- a/torchaudio/functional.py
+++ b/torchaudio/functional.py
@@ -1,7 +1,7 @@
 from __future__ import absolute_import, division, print_function, unicode_literals
 import math
 import torch
-from _torch_filtering import lfilter
+from _torch_filtering import lfilter, lfilter_tensor
 
 __all__ = [
     "istft",

From 59cb5ce1ec45d169a552d4736912c664f93d7d48 Mon Sep 17 00:00:00 2001
From: Chuan Zhang <engineerchuan@gmail.com>
Date: Tue, 17 Sep 2019 08:38:36 -0400
Subject: [PATCH 19/28] Adding documentation for lfilter, biquad,
 highpass_biquad, lowpass_biquad

---
 docs/source/functional.rst | 20 ++++++++++++++++++
 torchaudio/filtering.cpp   | 16 +++++++++++++-
 torchaudio/functional.py   | 43 ++++++++++++++++++++++++++++++++++++--
 3 files changed, 76 insertions(+), 3 deletions(-)

diff --git a/docs/source/functional.rst b/docs/source/functional.rst
index a8d57bb36c..817f3e9cd8 100644
--- a/docs/source/functional.rst
+++ b/docs/source/functional.rst
@@ -62,3 +62,23 @@ Functions to perform common audio operations.
 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 
 .. autofunction:: phase_vocoder
+
+:hidden:`lfilter`
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+.. autofunction:: lfilter
+
+:hidden:`biquad`
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+.. autofunction:: biquad
+
+:hidden:`highpass_biquad`
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+.. autofunction:: highpass_biquad
+
+:hidden:`lowpass_biquad`
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+.. autofunction:: lowpass_biquad
diff --git a/torchaudio/filtering.cpp b/torchaudio/filtering.cpp
index 7d858d4170..d44225f3ba 100644
--- a/torchaudio/filtering.cpp
+++ b/torchaudio/filtering.cpp
@@ -141,6 +141,8 @@ at::Tensor lfilter_tensor(
 
 
 PYBIND11_MODULE(_torch_filtering, m) {
+  py::options options;
+  options.disable_function_signatures();
   m.def(
       "lfilter_tensor",
       &torch::audio::lfilter_tensor,
@@ -148,7 +150,19 @@ PYBIND11_MODULE(_torch_filtering, m) {
   m.def(
       "lfilter",
       &torch::audio::lfilter,
-      "Executes difference equation");      
+      R"mydelimiter(lfilter(waveform, a_coeffs, b_coeffs)
+
+    Performs an IIR filter by evaluating difference equation.
+
+    Args:
+        waveform (torch.Tensor): audio waveform of dimension of `(n_channel, n_frames)`
+        a_coeffs (torch.Tensor): denominator coefficients of difference equation of dimension of `(n_order + 1)`.  Lower delays coefficients are first, e.g. `[a0, a1, a2, ...]`.  Must be same size as b_coeffs (pad with 0's as necessary).
+        b_coeffs (torch.Tensor): numerator coefficients of difference equation of dimension of `(n_order + 1)`.  Lower delays coefficients are first, e.g. `[b0, b1, b2, ...]`. Must be same size as a_coeffs (pad with 0's as necessary).
+        
+    Returns:
+        output_waveform (torch.Tensor): Dimension of `(n_channel, n_frames)`
+
+      )mydelimiter");      
 #ifdef WITH_CUDA
   m.attr("CUDA_VERSION") = CUDA_VERSION;
 #endif
diff --git a/torchaudio/functional.py b/torchaudio/functional.py
index faa79a8a90..44af24bf04 100644
--- a/torchaudio/functional.py
+++ b/torchaudio/functional.py
@@ -510,6 +510,22 @@ def phase_vocoder(complex_specgrams, rate, phase_advance):
 
 
 def biquad(waveform, b0, b1, b2, a0, a1, a2):
+    # type: (Tensor, float, float, float, float, float, float) -> Tensor
+    r"""Performs a biquad filter of input tensor.  Initial conditions set to 0.
+    https://en.wikipedia.org/wiki/Digital_biquad_filter
+
+    Args:
+        waveform (torch.Tensor): audio waveform of dimension of `(n_channel, n_frames)`
+        b0 (float): numerator coefficient of current input, x[n]
+        b1 (float): numerator coefficient of input one time step ago x[n-1]
+        b2 (float): numerator coefficient of input two time steps ago x[n-2]
+        a0 (float): denominator coefficient of current output y[n], typically 1
+        a1 (float): denominator coefficient of current output y[n-1]
+        a2 (float): denominator coefficient of current output y[n-2]
+
+    Returns:
+        output_waveform (torch.Tensor): Dimension of `(n_channel, n_frames)`
+    """
 
     assert(waveform.dtype == torch.float32)
 
@@ -520,13 +536,24 @@ def biquad(waveform, b0, b1, b2, a0, a1, a2):
 
 
 def _dB2Linear(x):
-
     return math.exp(x * math.log(10) / 20.0)
 
 
 def highpass_biquad(waveform, sample_rate, cutoff_freq, Q=0.707):
+    # type: (Tensor, int, float, Optional[float]) -> Tensor
+    r"""Designs biquad highpass filter and performs filtering.  Similar to SoX implementation.
 
-    GAIN = 1
+    Args:
+        waveform (torch.Tensor): audio waveform of dimension of `(n_channel, n_frames)`
+        sample_rate (int): sampling rate of the waveform, e.g. 44100 (Hz)
+        cutoff_freq (float): filter cutoff frequency
+        Q (float): https://en.wikipedia.org/wiki/Q_factor
+
+    Returns:
+        output_waveform (torch.Tensor): Dimension of `(n_channel, n_frames)`
+    """
+
+    GAIN = 1 # TBD - add as a parameter
     w0 = 2 * math.pi * cutoff_freq / sample_rate
     A = math.exp(GAIN / 40.0 * math.log(10))
     alpha = math.sin(w0) / 2 / Q
@@ -542,6 +569,18 @@ def highpass_biquad(waveform, sample_rate, cutoff_freq, Q=0.707):
 
 
 def lowpass_biquad(waveform, sample_rate, cutoff_freq, Q=0.707):
+    # type: (Tensor, int, float, Optional[float]) -> Tensor
+    r"""Designs biquad lowpass filter and performs filtering.  Similar to SoX implementation.
+
+    Args:
+        waveform (torch.Tensor): audio waveform of dimension of `(n_channel, n_frames)`
+        sample_rate (int): sampling rate of the waveform, e.g. 44100 (Hz)
+        cutoff_freq (float): filter cutoff frequency
+        Q (float): https://en.wikipedia.org/wiki/Q_factor
+
+    Returns:
+        output_waveform (torch.Tensor): Dimension of `(n_channel, n_frames)`
+    """
 
     GAIN = 1
     w0 = 2 * math.pi * cutoff_freq / sample_rate

From 388a0c03898ce07e5d7e529d191a0495c285dc19 Mon Sep 17 00:00:00 2001
From: Chuan Zhang <engineerchuan@gmail.com>
Date: Tue, 17 Sep 2019 11:35:58 -0400
Subject: [PATCH 20/28] added matrix based implementation of lfilter

---
 test/test_functional_filtering.py | 25 ++++++++----
 torchaudio/filtering.cpp          | 63 +++++++++++++++++++++++++++++++
 torchaudio/functional.py          |  4 +-
 3 files changed, 82 insertions(+), 10 deletions(-)

diff --git a/test/test_functional_filtering.py b/test/test_functional_filtering.py
index 6abfaf2d4a..4fe57fce74 100644
--- a/test/test_functional_filtering.py
+++ b/test/test_functional_filtering.py
@@ -28,28 +28,38 @@ def test_lfilter_basic(self):
         assert torch.allclose(
             waveform[:, 0:-3], output_waveform[:, 3:], atol=1e-5
         )
-    
+
     def test_lfilter_loop_vs_tensor(self):
-    
+
         torch.random.manual_seed(42)
         waveform = torch.rand(2, 100000)
-        b_coeffs = torch.tensor([0.3, 0.4, 0, 1], dtype=torch.float32)
-        a_coeffs = torch.tensor([1, 0.2, 0.2, 0], dtype=torch.float32)
+        b_coeffs = torch.tensor([0, 0.1, 0.1, 1], dtype=torch.float32)
+        a_coeffs = torch.tensor([1, 0.2, 0, 0], dtype=torch.float32)
         import time
+
         tensor_time_start = time.time()
         output_waveform1 = F.lfilter_tensor(waveform, a_coeffs, b_coeffs)
         tensor_time_taken = time.time() - tensor_time_start
+
         loop_time_start = time.time()
         output_waveform2 = F.lfilter(waveform, a_coeffs, b_coeffs)
         loop_time_taken = time.time() - loop_time_start
 
+        tensor_matrix_time_start = time.time()
+        output_waveform3 = F.lfilter_tensor_matrix(waveform, a_coeffs, b_coeffs)
+        tensor_matrix_time_taken = time.time() - tensor_matrix_time_start
+
         print("\n")
-        print("Looped Implementation took: ", loop_time_taken)
-        print("Tensor Implementation took: ", tensor_time_taken)
+        print("Looped Implementation took       : ", loop_time_taken)
+        print("Tensor Implementation took       : ", tensor_time_taken)
+        print("Tensor Matrix Implementation took: ", tensor_matrix_time_taken)
 
         assert torch.allclose(
             output_waveform1, output_waveform2, atol=1e-5
-        )        
+        )
+        assert torch.allclose(
+            output_waveform1, output_waveform3, atol=1e-5
+        )
 
     def test_lfilter(self):
         """
@@ -135,7 +145,6 @@ def test_highpass_sox_compliance(self):
             noise_filepath, normalization=True
         )
         output_waveform = F.highpass_biquad(waveform, sample_rate, CUTOFF_FREQ)
-        
 
         # TBD - this fails at the 1e-4 level, debug why
         assert torch.allclose(sox_output_waveform, output_waveform, atol=1e-3)
diff --git a/torchaudio/filtering.cpp b/torchaudio/filtering.cpp
index d44225f3ba..ef04a57b46 100644
--- a/torchaudio/filtering.cpp
+++ b/torchaudio/filtering.cpp
@@ -6,6 +6,65 @@
 namespace torch {
 namespace audio {
 
+
+at::Tensor lfilter_tensor_matrix(
+    at::Tensor const & waveform,
+    at::Tensor const & a_coeffs,
+    at::Tensor const & b_coeffs
+  ) {
+
+    // assumes waveform is normalized between 1 and -1
+    assert(waveform.dtype == torch::float32);
+    assert(a_coeffs.size(0) == b_coeffs.size(0));
+    int n_order = a_coeffs.size(0); // n'th order - 1 filter
+    assert(n_order > 0);
+
+    int64_t n_channels = waveform.size(0);
+    int64_t n_frames = waveform.size(1);
+
+    // Allocate padded input and output waveform, copy in the input waveform
+    at::Tensor padded_waveform = torch::zeros({n_channels, n_frames + n_order - 1}, torch::TensorOptions().dtype(torch::kFloat32));
+    at::Tensor padded_output_waveform = torch::zeros({n_channels, n_frames + n_order - 1}, torch::TensorOptions().dtype(torch::kFloat32));
+    padded_waveform.slice(0, 0, n_channels).slice(1, n_order - 1, n_order + n_frames - 1) = waveform;
+
+    // Create [n_order, n_channels] structure for a and b coefficients
+    at::Tensor a_coeffs_filled = at::transpose(at::flip(a_coeffs, {0,}).repeat({n_channels, 1}), 0, 1);
+    at::Tensor b_coeffs_filled = at::transpose(at::flip(b_coeffs, {0,}).repeat({n_channels, 1}), 0, 1);
+
+    // few more temporary data structure
+    at::Tensor o0 = torch::zeros({n_channels, 1}, torch::TensorOptions().dtype(torch::kFloat32));
+    at::Tensor ones = torch::ones({n_channels, n_frames + n_order - 1});
+    at::Tensor negones = torch::ones({n_channels, n_frames + n_order -1 }) * -1;
+    at::Tensor normalization_a0 = torch::unsqueeze(a_coeffs[0], {0,}).repeat({n_channels, 1});
+
+
+    for (int64_t i_frame = 0; i_frame < n_frames; ++i_frame) {
+
+      // calculate the output at time i_frame for all channels
+      o0 = torch::zeros({n_channels, 1}, torch::TensorOptions().dtype(torch::kFloat32));
+
+      // time window of input and output, size [n_channels, n_order]
+      at::Tensor const & input_window = padded_waveform.slice(0, 0, n_channels).slice(1, i_frame, i_frame + n_order);
+      at::Tensor const & output_window = padded_output_waveform.slice(0, 0, n_channels).slice(1, i_frame, i_frame+ n_order);
+
+      // matrix multiply to get [n_channels x n_channels], extract diagonal and unsqueeze to get [n_channels, 1] result for a frame
+      at::Tensor inp_result = torch::unsqueeze(torch::diag(torch::mm(input_window, b_coeffs_filled)), 1);
+      at::Tensor out_result = torch::unsqueeze(torch::diag(torch::mm(output_window, a_coeffs_filled)), 1);
+
+      o0.add_(inp_result);
+      o0.sub_(out_result);
+
+      // normalize by a0
+      o0.div_(normalization_a0);
+
+      // Set the output
+      padded_output_waveform.slice(0, 0, n_channels).slice(1, i_frame + n_order - 1, i_frame + n_order - 1 + 1) = o0;
+
+    }
+    // return clipped, and without initial conditions
+    return torch::min(ones, torch::max(negones, padded_output_waveform)).slice(0, 0, n_channels).slice(1, n_order - 1, n_order + n_frames - 1);
+  }
+
 at::Tensor lfilter_tensor(
     at::Tensor const & waveform,
     at::Tensor const & a_coeffs,
@@ -147,6 +206,10 @@ PYBIND11_MODULE(_torch_filtering, m) {
       "lfilter_tensor",
       &torch::audio::lfilter_tensor,
       "Executes difference equation with tensor");
+  m.def(
+      "lfilter_tensor_matrix",
+      &torch::audio::lfilter_tensor_matrix,
+      "Executes difference equation with tensor");
   m.def(
       "lfilter",
       &torch::audio::lfilter,
diff --git a/torchaudio/functional.py b/torchaudio/functional.py
index 44af24bf04..5a79f97dcf 100644
--- a/torchaudio/functional.py
+++ b/torchaudio/functional.py
@@ -1,7 +1,7 @@
 from __future__ import absolute_import, division, print_function, unicode_literals
 import math
 import torch
-from _torch_filtering import lfilter, lfilter_tensor
+from _torch_filtering import lfilter, lfilter_tensor, lfilter_tensor_matrix
 
 __all__ = [
     "istft",
@@ -553,7 +553,7 @@ def highpass_biquad(waveform, sample_rate, cutoff_freq, Q=0.707):
         output_waveform (torch.Tensor): Dimension of `(n_channel, n_frames)`
     """
 
-    GAIN = 1 # TBD - add as a parameter
+    GAIN = 1  # TBD - add as a parameter
     w0 = 2 * math.pi * cutoff_freq / sample_rate
     A = math.exp(GAIN / 40.0 * math.log(10))
     alpha = math.sin(w0) / 2 / Q

From 98b9ec1864be95686362c215452980938111efde Mon Sep 17 00:00:00 2001
From: Chuan Zhang <engineerchuan@gmail.com>
Date: Tue, 17 Sep 2019 15:43:21 -0400
Subject: [PATCH 21/28] adding python lfilter implementation

---
 test/test_functional_filtering.py | 21 ++++++++---
 torchaudio/filtering.cpp          |  4 +-
 torchaudio/functional.py          | 61 +++++++++++++++++++++++++++++++
 3 files changed, 79 insertions(+), 7 deletions(-)

diff --git a/test/test_functional_filtering.py b/test/test_functional_filtering.py
index 4fe57fce74..e48e2d2f27 100644
--- a/test/test_functional_filtering.py
+++ b/test/test_functional_filtering.py
@@ -29,10 +29,13 @@ def test_lfilter_basic(self):
             waveform[:, 0:-3], output_waveform[:, 3:], atol=1e-5
         )
 
-    def test_lfilter_loop_vs_tensor(self):
+    def test_lfilter_multiple_implementations(self):
+
+        # Run all implementations of lfilter
+        # Test that they are the same as each other
 
         torch.random.manual_seed(42)
-        waveform = torch.rand(2, 100000)
+        waveform = torch.rand(2, 44100 * 5)
         b_coeffs = torch.tensor([0, 0.1, 0.1, 1], dtype=torch.float32)
         a_coeffs = torch.tensor([1, 0.2, 0, 0], dtype=torch.float32)
         import time
@@ -49,10 +52,15 @@ def test_lfilter_loop_vs_tensor(self):
         output_waveform3 = F.lfilter_tensor_matrix(waveform, a_coeffs, b_coeffs)
         tensor_matrix_time_taken = time.time() - tensor_matrix_time_start
 
+        python_time_start = time.time()
+        output_waveform4 = F.lfilter_python(waveform, a_coeffs, b_coeffs)
+        python_time_taken = time.time() - python_time_start
+
         print("\n")
-        print("Looped Implementation took       : ", loop_time_taken)
-        print("Tensor Implementation took       : ", tensor_time_taken)
-        print("Tensor Matrix Implementation took: ", tensor_matrix_time_taken)
+        print("Element Wise Implementation took  : ", loop_time_taken)
+        print("Tensor Implementation took        : ", tensor_time_taken)
+        print("Tensor Matrix Implementation took : ", tensor_matrix_time_taken)
+        print("Python Implementation took        : ", python_time_taken)
 
         assert torch.allclose(
             output_waveform1, output_waveform2, atol=1e-5
@@ -60,6 +68,9 @@ def test_lfilter_loop_vs_tensor(self):
         assert torch.allclose(
             output_waveform1, output_waveform3, atol=1e-5
         )
+        assert torch.allclose(
+            output_waveform1, output_waveform4, atol=1e-5
+        )
 
     def test_lfilter(self):
         """
diff --git a/torchaudio/filtering.cpp b/torchaudio/filtering.cpp
index ef04a57b46..b17fb09eb1 100644
--- a/torchaudio/filtering.cpp
+++ b/torchaudio/filtering.cpp
@@ -218,12 +218,12 @@ PYBIND11_MODULE(_torch_filtering, m) {
     Performs an IIR filter by evaluating difference equation.
 
     Args:
-        waveform (torch.Tensor): audio waveform of dimension of `(n_channel, n_frames)`
+        waveform (torch.Tensor): audio waveform of dimension of `(n_channel, n_frames)`. Must be normalized to -1 to 1.
         a_coeffs (torch.Tensor): denominator coefficients of difference equation of dimension of `(n_order + 1)`.  Lower delays coefficients are first, e.g. `[a0, a1, a2, ...]`.  Must be same size as b_coeffs (pad with 0's as necessary).
         b_coeffs (torch.Tensor): numerator coefficients of difference equation of dimension of `(n_order + 1)`.  Lower delays coefficients are first, e.g. `[b0, b1, b2, ...]`. Must be same size as a_coeffs (pad with 0's as necessary).
         
     Returns:
-        output_waveform (torch.Tensor): Dimension of `(n_channel, n_frames)`
+        output_waveform (torch.Tensor): Dimension of `(n_channel, n_frames)` Output will be clipped to -1 to 1.
 
       )mydelimiter");      
 #ifdef WITH_CUDA
diff --git a/torchaudio/functional.py b/torchaudio/functional.py
index 5a79f97dcf..0361f6aaeb 100644
--- a/torchaudio/functional.py
+++ b/torchaudio/functional.py
@@ -19,6 +19,9 @@
     "highpass_biquad",
     "biquad",
     "lfilter",
+    "lfilter_tensor",
+    "lfilter_tensor_matrix",
+    "lfilter_python",
 ]
 
 # TODO: remove this once https://github.com/pytorch/pytorch/issues/21478 gets solved
@@ -595,3 +598,61 @@ def lowpass_biquad(waveform, sample_rate, cutoff_freq, Q=0.707):
     a1 = -2 * math.cos(w0)
     a2 = 1 - alpha
     return biquad(waveform, b0, b1, b2, a0, a1, a2)
+
+
+def lfilter_python(waveform, a_coeffs, b_coeffs):
+    # type: (Tensor, Tensor, Tensor) -> Tensor
+    r"""
+    Performs an IIR filter by evaluating difference equation.
+
+    Args:
+        waveform (torch.Tensor): audio waveform of dimension of `(n_channel, n_frames)`.  Must be normalized to -1 to 1.
+        a_coeffs (torch.Tensor): denominator coefficients of difference equation of dimension of `(n_order + 1)`.
+                                Lower delays coefficients are first, e.g. `[a0, a1, a2, ...]`.
+                                Must be same size as b_coeffs (pad with 0's as necessary).
+        b_coeffs (torch.Tensor): numerator coefficients of difference equation of dimension of `(n_order + 1)`.
+                                 Lower delays coefficients are first, e.g. `[b0, b1, b2, ...]`.
+                                 Must be same size as a_coeffs (pad with 0's as necessary).
+
+    Returns:
+        output_waveform (torch.Tensor): Dimension of `(n_channel, n_frames)`.  Output will be clipped to -1 to 1.
+
+    """
+
+    assert(waveform.dtype == torch.float32)
+    assert(a_coeffs.size(0) == b_coeffs.size(0))
+    assert(len(waveform.size()) == 2)
+
+    n_channels, n_frames = waveform.size()
+    n_order = a_coeffs.size(0)
+    assert(n_order > 0)
+
+    # Pad the input and create output
+    padded_waveform = torch.zeros(n_channels, n_frames + n_order - 1)
+    padded_waveform[:, 3:] = waveform
+    padded_output_waveform = torch.zeros(n_channels, n_frames + n_order - 1)
+
+    # Set up the coefficients matrix
+    # Flip order, repeat, and transpose
+    a_coeffs_filled = a_coeffs.flip(0).repeat(n_channels, 1).t()
+    b_coeffs_filled = b_coeffs.flip(0).repeat(n_channels, 1).t()
+
+    # Set up a few other utilities
+    a0_repeated = torch.ones(n_channels) * a_coeffs[0]
+    ones = torch.ones(n_channels, n_frames)
+
+    for i_frame in range(n_frames):
+
+        o0 = torch.zeros(n_channels)
+
+        windowed_input_signal = padded_waveform[:, i_frame:(i_frame + n_order)]
+        windowed_output_signal = padded_output_waveform[:, i_frame:(i_frame + n_order)]
+
+        o0.add_(torch.diag(torch.mm(windowed_input_signal, b_coeffs_filled)))
+        o0.sub_(torch.diag(torch.mm(windowed_output_signal, a_coeffs_filled)))
+
+        o0.div_(a0_repeated)
+
+        padded_output_waveform[:, i_frame + n_order - 1] = o0
+
+    return torch.min(ones, torch.max(ones * -1, padded_output_waveform[:, 3:]))

From f4c84c86719a6ce9b159c6e7cee6750dc482fee1 Mon Sep 17 00:00:00 2001
From: Chuan Zhang <engineerchuan@gmail.com>
Date: Tue, 17 Sep 2019 17:34:50 -0400
Subject: [PATCH 22/28] Unwind cpp implementations for a separate PR

---
 setup.py                          |   8 -
 test/test_functional_filtering.py |  53 +------
 torchaudio/filtering.cpp          | 233 ------------------------------
 torchaudio/filtering.h            |  21 ---
 torchaudio/functional.py          |  10 +-
 5 files changed, 8 insertions(+), 317 deletions(-)
 delete mode 100644 torchaudio/filtering.cpp
 delete mode 100644 torchaudio/filtering.h

diff --git a/setup.py b/setup.py
index 4822a6e9d0..9ed91f2468 100644
--- a/setup.py
+++ b/setup.py
@@ -113,14 +113,6 @@ def check_env_flag(name, default=''):
             extra_compile_args=eca,
             extra_objects=extra_objects,
             extra_link_args=ela),
-        CppExtension(
-            '_torch_filtering',
-            ['torchaudio/filtering.cpp'],
-            libraries=libraries,
-            include_dirs=include_dirs,
-            extra_compile_args=eca,
-            extra_objects=extra_objects,
-            extra_link_args=ela),
     ],
     cmdclass={'build_ext': BuildExtension},
     install_requires=[pytorch_package_dep]
diff --git a/test/test_functional_filtering.py b/test/test_functional_filtering.py
index e48e2d2f27..4d2e8da839 100644
--- a/test/test_functional_filtering.py
+++ b/test/test_functional_filtering.py
@@ -20,7 +20,7 @@ def test_lfilter_basic(self):
         """
 
         torch.random.manual_seed(42)
-        waveform = torch.rand(2, 10000)
+        waveform = torch.rand(2, 44100 * 10)
         b_coeffs = torch.tensor([0, 0, 0, 1], dtype=torch.float32)
         a_coeffs = torch.tensor([1, 0, 0, 0], dtype=torch.float32)
         output_waveform = F.lfilter(waveform, a_coeffs, b_coeffs)
@@ -29,49 +29,6 @@ def test_lfilter_basic(self):
             waveform[:, 0:-3], output_waveform[:, 3:], atol=1e-5
         )
 
-    def test_lfilter_multiple_implementations(self):
-
-        # Run all implementations of lfilter
-        # Test that they are the same as each other
-
-        torch.random.manual_seed(42)
-        waveform = torch.rand(2, 44100 * 5)
-        b_coeffs = torch.tensor([0, 0.1, 0.1, 1], dtype=torch.float32)
-        a_coeffs = torch.tensor([1, 0.2, 0, 0], dtype=torch.float32)
-        import time
-
-        tensor_time_start = time.time()
-        output_waveform1 = F.lfilter_tensor(waveform, a_coeffs, b_coeffs)
-        tensor_time_taken = time.time() - tensor_time_start
-
-        loop_time_start = time.time()
-        output_waveform2 = F.lfilter(waveform, a_coeffs, b_coeffs)
-        loop_time_taken = time.time() - loop_time_start
-
-        tensor_matrix_time_start = time.time()
-        output_waveform3 = F.lfilter_tensor_matrix(waveform, a_coeffs, b_coeffs)
-        tensor_matrix_time_taken = time.time() - tensor_matrix_time_start
-
-        python_time_start = time.time()
-        output_waveform4 = F.lfilter_python(waveform, a_coeffs, b_coeffs)
-        python_time_taken = time.time() - python_time_start
-
-        print("\n")
-        print("Element Wise Implementation took  : ", loop_time_taken)
-        print("Tensor Implementation took        : ", tensor_time_taken)
-        print("Tensor Matrix Implementation took : ", tensor_matrix_time_taken)
-        print("Python Implementation took        : ", python_time_taken)
-
-        assert torch.allclose(
-            output_waveform1, output_waveform2, atol=1e-5
-        )
-        assert torch.allclose(
-            output_waveform1, output_waveform3, atol=1e-5
-        )
-        assert torch.allclose(
-            output_waveform1, output_waveform4, atol=1e-5
-        )
-
     def test_lfilter(self):
         """
         Design an IIR lowpass filter using scipy.signal filter design
@@ -105,7 +62,7 @@ def test_lfilter(self):
             ]
         )
 
-        filepath = os.path.join(self.test_dirpath, "assets", "dtmf_30s_stereo.mp3")
+        filepath = os.path.join(self.test_dirpath, "assets", "whitenoise.mp3")
         waveform, sample_rate = torchaudio.load(filepath, normalization=True)
         output_waveform = F.lfilter(waveform, a_coeffs, b_coeffs)
         assert len(output_waveform.size()) == 2
@@ -122,7 +79,7 @@ def test_lowpass_sox_compliance(self):
         CUTOFF_FREQ = 3000
 
         noise_filepath = os.path.join(
-            self.test_dirpath, "assets", "whitenoise_1min.mp3"
+            self.test_dirpath, "assets", "whitenoise.mp3"
         )
         E = torchaudio.sox_effects.SoxEffectsChain()
         E.set_input_file(noise_filepath)
@@ -145,7 +102,7 @@ def test_highpass_sox_compliance(self):
         CUTOFF_FREQ = 2000
 
         noise_filepath = os.path.join(
-            self.test_dirpath, "assets", "whitenoise_1min.mp3"
+            self.test_dirpath, "assets", "whitenoise.mp3"
         )
         E = torchaudio.sox_effects.SoxEffectsChain()
         E.set_input_file(noise_filepath)
@@ -169,7 +126,7 @@ def test_perf_biquad_filtering(self):
         Current results: C++ implementation approximately same speed
         """
 
-        fn_sine = os.path.join(self.test_dirpath, "assets", "whitenoise_1min.mp3")
+        fn_sine = os.path.join(self.test_dirpath, "assets", "whitenoise.mp3")
 
         b0 = 0.4
         b1 = 0.2
diff --git a/torchaudio/filtering.cpp b/torchaudio/filtering.cpp
deleted file mode 100644
index b17fb09eb1..0000000000
--- a/torchaudio/filtering.cpp
+++ /dev/null
@@ -1,233 +0,0 @@
-#include <torch/extension.h>
-#ifdef WITH_CUDA
-#include <cuda.h>
-#endif
-
-namespace torch {
-namespace audio {
-
-
-at::Tensor lfilter_tensor_matrix(
-    at::Tensor const & waveform,
-    at::Tensor const & a_coeffs,
-    at::Tensor const & b_coeffs
-  ) {
-
-    // assumes waveform is normalized between 1 and -1
-    assert(waveform.dtype == torch::float32);
-    assert(a_coeffs.size(0) == b_coeffs.size(0));
-    int n_order = a_coeffs.size(0); // n'th order - 1 filter
-    assert(n_order > 0);
-
-    int64_t n_channels = waveform.size(0);
-    int64_t n_frames = waveform.size(1);
-
-    // Allocate padded input and output waveform, copy in the input waveform
-    at::Tensor padded_waveform = torch::zeros({n_channels, n_frames + n_order - 1}, torch::TensorOptions().dtype(torch::kFloat32));
-    at::Tensor padded_output_waveform = torch::zeros({n_channels, n_frames + n_order - 1}, torch::TensorOptions().dtype(torch::kFloat32));
-    padded_waveform.slice(0, 0, n_channels).slice(1, n_order - 1, n_order + n_frames - 1) = waveform;
-
-    // Create [n_order, n_channels] structure for a and b coefficients
-    at::Tensor a_coeffs_filled = at::transpose(at::flip(a_coeffs, {0,}).repeat({n_channels, 1}), 0, 1);
-    at::Tensor b_coeffs_filled = at::transpose(at::flip(b_coeffs, {0,}).repeat({n_channels, 1}), 0, 1);
-
-    // few more temporary data structure
-    at::Tensor o0 = torch::zeros({n_channels, 1}, torch::TensorOptions().dtype(torch::kFloat32));
-    at::Tensor ones = torch::ones({n_channels, n_frames + n_order - 1});
-    at::Tensor negones = torch::ones({n_channels, n_frames + n_order -1 }) * -1;
-    at::Tensor normalization_a0 = torch::unsqueeze(a_coeffs[0], {0,}).repeat({n_channels, 1});
-
-
-    for (int64_t i_frame = 0; i_frame < n_frames; ++i_frame) {
-
-      // calculate the output at time i_frame for all channels
-      o0 = torch::zeros({n_channels, 1}, torch::TensorOptions().dtype(torch::kFloat32));
-
-      // time window of input and output, size [n_channels, n_order]
-      at::Tensor const & input_window = padded_waveform.slice(0, 0, n_channels).slice(1, i_frame, i_frame + n_order);
-      at::Tensor const & output_window = padded_output_waveform.slice(0, 0, n_channels).slice(1, i_frame, i_frame+ n_order);
-
-      // matrix multiply to get [n_channels x n_channels], extract diagonal and unsqueeze to get [n_channels, 1] result for a frame
-      at::Tensor inp_result = torch::unsqueeze(torch::diag(torch::mm(input_window, b_coeffs_filled)), 1);
-      at::Tensor out_result = torch::unsqueeze(torch::diag(torch::mm(output_window, a_coeffs_filled)), 1);
-
-      o0.add_(inp_result);
-      o0.sub_(out_result);
-
-      // normalize by a0
-      o0.div_(normalization_a0);
-
-      // Set the output
-      padded_output_waveform.slice(0, 0, n_channels).slice(1, i_frame + n_order - 1, i_frame + n_order - 1 + 1) = o0;
-
-    }
-    // return clipped, and without initial conditions
-    return torch::min(ones, torch::max(negones, padded_output_waveform)).slice(0, 0, n_channels).slice(1, n_order - 1, n_order + n_frames - 1);
-  }
-
-at::Tensor lfilter_tensor(
-    at::Tensor const & waveform,
-    at::Tensor const & a_coeffs,
-    at::Tensor const & b_coeffs
-  ) {
-
-    // assumes waveform is normalized between 1 and -1
-    assert(waveform.dtype == torch::float32);
-    assert(a_coeffs.size(0) == b_coeffs.size(0));
-    int n_order = a_coeffs.size(0); // n'th order - 1 filter
-    assert(n_order > 0);
-
-    int64_t n_channels = waveform.size(0);
-    int64_t n_frames = waveform.size(1);
-
-    // Allocate padded input and output waveform, copy in the input waveform
-    at::Tensor padded_waveform = torch::zeros({n_channels, n_frames + n_order - 1}, torch::TensorOptions().dtype(torch::kFloat32));
-    at::Tensor padded_output_waveform = torch::zeros({n_channels, n_frames + n_order - 1}, torch::TensorOptions().dtype(torch::kFloat32));
-    padded_waveform.slice(0, 0, n_channels).slice(1, n_order - 1, n_order + n_frames - 1) = waveform;
-
-    // Create [n_channels, n_order] structure for a and b coefficients
-    at::Tensor a_coeffs_filled = a_coeffs.repeat({n_channels, 1});
-    at::Tensor b_coeffs_filled = b_coeffs.repeat({n_channels, 1});
-
-    // few more temporary data structure
-    at::Tensor o0 = torch::zeros({n_channels, 1}, torch::TensorOptions().dtype(torch::kFloat32));
-    at::Tensor ones = torch::ones({n_channels, n_frames + n_order - 1});
-    at::Tensor negones = torch::ones({n_channels, n_frames + n_order -1 }) * -1;
-
-    for (int64_t i_frame = 0; i_frame < n_frames; ++i_frame) {
-
-      // calculate the output at time i_frame
-      // initialize it!
-      o0 = torch::zeros({n_channels, 1}, torch::TensorOptions().dtype(torch::kFloat32));
-
-      for (int i_offset = 0; i_offset < n_order; ++i_offset) {
-
-        at::Tensor const & input_time_offset = padded_waveform.slice(0, 0, n_channels).slice(1, i_frame + n_order - 1 - i_offset, i_frame + n_order - 1 - i_offset + 1);
-        at::Tensor const & output_time_offset = padded_output_waveform.slice(0, 0, n_channels).slice(1, i_frame + n_order - 1 - i_offset, i_frame+ n_order - 1 - i_offset + 1);
-        at::Tensor const & a_coeffs_offset = a_coeffs_filled.slice(0, 0, n_channels).slice(1, i_offset, i_offset + 1);
-        at::Tensor const & b_coeffs_offset = b_coeffs_filled.slice(0, 0, n_channels).slice(1, i_offset, i_offset + 1);        
-
-        // Multiply by the coefficients
-        o0 = torch::addcmul(o0, input_time_offset, b_coeffs_offset, 1);
-        if (i_offset != n_order - 1) {
-          o0 = torch::addcmul(o0, output_time_offset, a_coeffs_offset, -1);
-        }
-      }
-      // normalize by a0
-      o0 = torch::div(o0, a_coeffs_filled.slice(0, 0, n_channels).slice(1, 0, 1));
-
-      // Set the output
-      padded_output_waveform.slice(0, 0, n_channels).slice(1, i_frame + n_order - 1, i_frame + n_order - 1 + 1) = o0;
-      
-    }
-
-    // return clipped, and without initial conditions
-    return torch::min(ones, torch::max(negones, padded_output_waveform)).slice(0, 0, n_channels).slice(1, n_order - 1, n_order + n_frames - 1);
-  }
-
-
-  // N.B. TBD - Test with CUDA
-  at::Tensor lfilter(
-    at::Tensor const & waveform,
-    at::Tensor const & a_coeffs,
-    at::Tensor const & b_coeffs
-  ) {
-
-    // assumes waveform is normalized between 1 and -1
-    assert(waveform.dtype == torch::float32);
-    assert(a_coeffs.size(0) == b_coeffs.size(0));
-    int n_order = a_coeffs.size(0); // n'th order - 1 filter
-
-    int64_t n_channels = waveform.size(0);
-    int64_t n_frames = waveform.size(1);
-
-    // initialize the output tensor
-    torch::Tensor output_waveform = torch::zeros({n_channels, n_frames});
-
-#ifdef WITH_CUDA
-    auto input_accessor = waveform.packed_accessor64<float,2>();
-    auto output_accessor = output_waveform.packed_accessor64<float,2>();    
-    auto a_coeffs_accessor = a_coeffs.packed_accessor64<float,1>();
-    auto b_coeffs_accessor = b_coeffs.packed_accessor64<float,1>();
-#endif
-#ifndef WITH_CUDA
-    auto input_accessor = waveform.accessor<float,2>();
-    auto output_accessor = output_waveform.accessor<float,2>();    
-    auto a_coeffs_accessor = a_coeffs.accessor<float,1>();
-    auto b_coeffs_accessor = b_coeffs.accessor<float,1>();
-#endif
-
-    for (int64_t i_channel = 0; i_channel < n_channels; ++i_channel) {
-
-      // allocate a temporary data structure of size 2 x (n_order + 1)
-      // set to 0 because initial conditions are 0
-      float i_s[n_order], o_s[n_order];
-      memset( i_s, 0, n_order*sizeof(float) );
-      memset( o_s, 0, n_order*sizeof(float) );
-
-      for (int64_t i_frame = 0; i_frame < n_frames; ++i_frame) {
-
-        // calculate the output at time i_frame by iterating through
-        // inputs / outputs at previous time steps and multiplying by coeffs
-        i_s[n_order-1] = input_accessor[i_channel][i_frame];
-        float o0 = 0;
-        for (int i = 0; i < n_order; ++i) {
-          o0 += i_s[i] * b_coeffs_accessor[n_order - i - 1];
-          if (i != n_order - 1) {
-            o0 -= o_s[i] * a_coeffs_accessor[n_order - i - 1];
-          }
-        }
-        o0 = o0 / a_coeffs_accessor[0];
-
-        o_s[n_order-1] = o0;
-
-        // clip and drop into output
-        if (o0 > 1) o0 = 1;
-        if (o0 < -1) o0 = -1;
-        output_accessor[i_channel][i_frame] = o0;
-
-        // shift everything over by one time step
-        for (int i = 0; i < (n_order - 1); ++i) {
-          i_s[i] = i_s[i+1];
-          o_s[i] = o_s[i+1];
-        }
-      }
-    }
-    return output_waveform;
-  }
-
-}}
-
-
-PYBIND11_MODULE(_torch_filtering, m) {
-  py::options options;
-  options.disable_function_signatures();
-  m.def(
-      "lfilter_tensor",
-      &torch::audio::lfilter_tensor,
-      "Executes difference equation with tensor");
-  m.def(
-      "lfilter_tensor_matrix",
-      &torch::audio::lfilter_tensor_matrix,
-      "Executes difference equation with tensor");
-  m.def(
-      "lfilter",
-      &torch::audio::lfilter,
-      R"mydelimiter(lfilter(waveform, a_coeffs, b_coeffs)
-
-    Performs an IIR filter by evaluating difference equation.
-
-    Args:
-        waveform (torch.Tensor): audio waveform of dimension of `(n_channel, n_frames)`. Must be normalized to -1 to 1.
-        a_coeffs (torch.Tensor): denominator coefficients of difference equation of dimension of `(n_order + 1)`.  Lower delays coefficients are first, e.g. `[a0, a1, a2, ...]`.  Must be same size as b_coeffs (pad with 0's as necessary).
-        b_coeffs (torch.Tensor): numerator coefficients of difference equation of dimension of `(n_order + 1)`.  Lower delays coefficients are first, e.g. `[b0, b1, b2, ...]`. Must be same size as a_coeffs (pad with 0's as necessary).
-        
-    Returns:
-        output_waveform (torch.Tensor): Dimension of `(n_channel, n_frames)` Output will be clipped to -1 to 1.
-
-      )mydelimiter");      
-#ifdef WITH_CUDA
-  m.attr("CUDA_VERSION") = CUDA_VERSION;
-#endif
-
-}
diff --git a/torchaudio/filtering.h b/torchaudio/filtering.h
deleted file mode 100644
index 908cf691ff..0000000000
--- a/torchaudio/filtering.h
+++ /dev/null
@@ -1,21 +0,0 @@
-#include <string>
-
-namespace at {
-struct Tensor;
-} // namespace at
-
-namespace torch { namespace audio {
-
-/// Takes a tensor and performs a biquad difference function
-
-int biquad(
-    at::Tensor& input_waveform,
-    at::Tensor output_waveform,
-    float a0,
-    float a1,
-    float a2,
-    float b0,
-    float b1,
-    float b2
-);
-}} // namespace torch::audio
diff --git a/torchaudio/functional.py b/torchaudio/functional.py
index 0361f6aaeb..779414236c 100644
--- a/torchaudio/functional.py
+++ b/torchaudio/functional.py
@@ -1,7 +1,6 @@
 from __future__ import absolute_import, division, print_function, unicode_literals
 import math
 import torch
-from _torch_filtering import lfilter, lfilter_tensor, lfilter_tensor_matrix
 
 __all__ = [
     "istft",
@@ -19,9 +18,6 @@
     "highpass_biquad",
     "biquad",
     "lfilter",
-    "lfilter_tensor",
-    "lfilter_tensor_matrix",
-    "lfilter_python",
 ]
 
 # TODO: remove this once https://github.com/pytorch/pytorch/issues/21478 gets solved
@@ -600,7 +596,7 @@ def lowpass_biquad(waveform, sample_rate, cutoff_freq, Q=0.707):
     return biquad(waveform, b0, b1, b2, a0, a1, a2)
 
 
-def lfilter_python(waveform, a_coeffs, b_coeffs):
+def lfilter(waveform, a_coeffs, b_coeffs):
     # type: (Tensor, Tensor, Tensor) -> Tensor
     r"""
     Performs an IIR filter by evaluating difference equation.
@@ -629,7 +625,7 @@ def lfilter_python(waveform, a_coeffs, b_coeffs):
 
     # Pad the input and create output
     padded_waveform = torch.zeros(n_channels, n_frames + n_order - 1)
-    padded_waveform[:, 3:] = waveform
+    padded_waveform[:, (n_order - 1):] = waveform
     padded_output_waveform = torch.zeros(n_channels, n_frames + n_order - 1)
 
     # Set up the coefficients matrix
@@ -655,4 +651,4 @@ def lfilter_python(waveform, a_coeffs, b_coeffs):
 
         padded_output_waveform[:, i_frame + n_order - 1] = o0
 
-    return torch.min(ones, torch.max(ones * -1, padded_output_waveform[:, 3:]))
+    return torch.min(ones, torch.max(ones * -1, padded_output_waveform[:, (n_order - 1):]))

From 866de478afe7b1426e2bbce665b6c31a5b229d9a Mon Sep 17 00:00:00 2001
From: Chuan Zhang <engineerchuan@gmail.com>
Date: Tue, 17 Sep 2019 19:37:42 -0400
Subject: [PATCH 23/28] factor out biquad, lowpass, highpass to sox
 compatibility

---
 torchaudio/functional.py                   | 89 +-------------------
 torchaudio/functional_sox_compatibility.py | 98 ++++++++++++++++++++++
 2 files changed, 99 insertions(+), 88 deletions(-)
 create mode 100644 torchaudio/functional_sox_compatibility.py

diff --git a/torchaudio/functional.py b/torchaudio/functional.py
index 779414236c..8e9b9dc203 100644
--- a/torchaudio/functional.py
+++ b/torchaudio/functional.py
@@ -1,6 +1,7 @@
 from __future__ import absolute_import, division, print_function, unicode_literals
 import math
 import torch
+from torchaudio.functional_sox_compatibility import biquad, lowpass_biquad, highpass_biquad
 
 __all__ = [
     "istft",
@@ -508,94 +509,6 @@ def phase_vocoder(complex_specgrams, rate, phase_advance):
     return complex_specgrams_stretch
 
 
-def biquad(waveform, b0, b1, b2, a0, a1, a2):
-    # type: (Tensor, float, float, float, float, float, float) -> Tensor
-    r"""Performs a biquad filter of input tensor.  Initial conditions set to 0.
-    https://en.wikipedia.org/wiki/Digital_biquad_filter
-
-    Args:
-        waveform (torch.Tensor): audio waveform of dimension of `(n_channel, n_frames)`
-        b0 (float): numerator coefficient of current input, x[n]
-        b1 (float): numerator coefficient of input one time step ago x[n-1]
-        b2 (float): numerator coefficient of input two time steps ago x[n-2]
-        a0 (float): denominator coefficient of current output y[n], typically 1
-        a1 (float): denominator coefficient of current output y[n-1]
-        a2 (float): denominator coefficient of current output y[n-2]
-
-    Returns:
-        output_waveform (torch.Tensor): Dimension of `(n_channel, n_frames)`
-    """
-
-    assert(waveform.dtype == torch.float32)
-
-    output_waveform = lfilter(
-        waveform, torch.tensor([a0, a1, a2]), torch.tensor([b0, b1, b2])
-    )
-    return output_waveform
-
-
-def _dB2Linear(x):
-    return math.exp(x * math.log(10) / 20.0)
-
-
-def highpass_biquad(waveform, sample_rate, cutoff_freq, Q=0.707):
-    # type: (Tensor, int, float, Optional[float]) -> Tensor
-    r"""Designs biquad highpass filter and performs filtering.  Similar to SoX implementation.
-
-    Args:
-        waveform (torch.Tensor): audio waveform of dimension of `(n_channel, n_frames)`
-        sample_rate (int): sampling rate of the waveform, e.g. 44100 (Hz)
-        cutoff_freq (float): filter cutoff frequency
-        Q (float): https://en.wikipedia.org/wiki/Q_factor
-
-    Returns:
-        output_waveform (torch.Tensor): Dimension of `(n_channel, n_frames)`
-    """
-
-    GAIN = 1  # TBD - add as a parameter
-    w0 = 2 * math.pi * cutoff_freq / sample_rate
-    A = math.exp(GAIN / 40.0 * math.log(10))
-    alpha = math.sin(w0) / 2 / Q
-    mult = _dB2Linear(max(GAIN, 0))
-
-    b0 = (1 + math.cos(w0)) / 2
-    b1 = -1 - math.cos(w0)
-    b2 = b0
-    a0 = 1 + alpha
-    a1 = -2 * math.cos(w0)
-    a2 = 1 - alpha
-    return biquad(waveform, b0, b1, b2, a0, a1, a2)
-
-
-def lowpass_biquad(waveform, sample_rate, cutoff_freq, Q=0.707):
-    # type: (Tensor, int, float, Optional[float]) -> Tensor
-    r"""Designs biquad lowpass filter and performs filtering.  Similar to SoX implementation.
-
-    Args:
-        waveform (torch.Tensor): audio waveform of dimension of `(n_channel, n_frames)`
-        sample_rate (int): sampling rate of the waveform, e.g. 44100 (Hz)
-        cutoff_freq (float): filter cutoff frequency
-        Q (float): https://en.wikipedia.org/wiki/Q_factor
-
-    Returns:
-        output_waveform (torch.Tensor): Dimension of `(n_channel, n_frames)`
-    """
-
-    GAIN = 1
-    w0 = 2 * math.pi * cutoff_freq / sample_rate
-    A = math.exp(GAIN / 40.0 * math.log(10))
-    alpha = math.sin(w0) / 2 / Q
-    mult = _dB2Linear(max(GAIN, 0))
-
-    b0 = (1 - math.cos(w0)) / 2
-    b1 = 1 - math.cos(w0)
-    b2 = b0
-    a0 = 1 + alpha
-    a1 = -2 * math.cos(w0)
-    a2 = 1 - alpha
-    return biquad(waveform, b0, b1, b2, a0, a1, a2)
-
-
 def lfilter(waveform, a_coeffs, b_coeffs):
     # type: (Tensor, Tensor, Tensor) -> Tensor
     r"""
diff --git a/torchaudio/functional_sox_compatibility.py b/torchaudio/functional_sox_compatibility.py
new file mode 100644
index 0000000000..620c588c8c
--- /dev/null
+++ b/torchaudio/functional_sox_compatibility.py
@@ -0,0 +1,98 @@
+from __future__ import absolute_import, division, print_function, unicode_literals
+import math
+import torch
+import torchaudio
+
+__all__ = [
+    "lowpass_biquad",
+    "highpass_biquad",
+    "biquad",
+]
+
+
+def biquad(waveform, b0, b1, b2, a0, a1, a2):
+    # type: (Tensor, float, float, float, float, float, float) -> Tensor
+    r"""Performs a biquad filter of input tensor.  Initial conditions set to 0.
+    https://en.wikipedia.org/wiki/Digital_biquad_filter
+
+    Args:
+        waveform (torch.Tensor): audio waveform of dimension of `(n_channel, n_frames)`
+        b0 (float): numerator coefficient of current input, x[n]
+        b1 (float): numerator coefficient of input one time step ago x[n-1]
+        b2 (float): numerator coefficient of input two time steps ago x[n-2]
+        a0 (float): denominator coefficient of current output y[n], typically 1
+        a1 (float): denominator coefficient of current output y[n-1]
+        a2 (float): denominator coefficient of current output y[n-2]
+
+    Returns:
+        output_waveform (torch.Tensor): Dimension of `(n_channel, n_frames)`
+    """
+
+    assert(waveform.dtype == torch.float32)
+
+    output_waveform = torchaudio.functional.lfilter(
+        waveform, torch.tensor([a0, a1, a2]), torch.tensor([b0, b1, b2])
+    )
+    return output_waveform
+
+
+def _dB2Linear(x):
+    return math.exp(x * math.log(10) / 20.0)
+
+
+def highpass_biquad(waveform, sample_rate, cutoff_freq, Q=0.707):
+    # type: (Tensor, int, float, Optional[float]) -> Tensor
+    r"""Designs biquad highpass filter and performs filtering.  Similar to SoX implementation.
+
+    Args:
+        waveform (torch.Tensor): audio waveform of dimension of `(n_channel, n_frames)`
+        sample_rate (int): sampling rate of the waveform, e.g. 44100 (Hz)
+        cutoff_freq (float): filter cutoff frequency
+        Q (float): https://en.wikipedia.org/wiki/Q_factor
+
+    Returns:
+        output_waveform (torch.Tensor): Dimension of `(n_channel, n_frames)`
+    """
+
+    GAIN = 1  # TBD - add as a parameter
+    w0 = 2 * math.pi * cutoff_freq / sample_rate
+    A = math.exp(GAIN / 40.0 * math.log(10))
+    alpha = math.sin(w0) / 2 / Q
+    mult = _dB2Linear(max(GAIN, 0))
+
+    b0 = (1 + math.cos(w0)) / 2
+    b1 = -1 - math.cos(w0)
+    b2 = b0
+    a0 = 1 + alpha
+    a1 = -2 * math.cos(w0)
+    a2 = 1 - alpha
+    return biquad(waveform, b0, b1, b2, a0, a1, a2)
+
+
+def lowpass_biquad(waveform, sample_rate, cutoff_freq, Q=0.707):
+    # type: (Tensor, int, float, Optional[float]) -> Tensor
+    r"""Designs biquad lowpass filter and performs filtering.  Similar to SoX implementation.
+
+    Args:
+        waveform (torch.Tensor): audio waveform of dimension of `(n_channel, n_frames)`
+        sample_rate (int): sampling rate of the waveform, e.g. 44100 (Hz)
+        cutoff_freq (float): filter cutoff frequency
+        Q (float): https://en.wikipedia.org/wiki/Q_factor
+
+    Returns:
+        output_waveform (torch.Tensor): Dimension of `(n_channel, n_frames)`
+    """
+
+    GAIN = 1
+    w0 = 2 * math.pi * cutoff_freq / sample_rate
+    A = math.exp(GAIN / 40.0 * math.log(10))
+    alpha = math.sin(w0) / 2 / Q
+    mult = _dB2Linear(max(GAIN, 0))
+
+    b0 = (1 - math.cos(w0)) / 2
+    b1 = 1 - math.cos(w0)
+    b2 = b0
+    a0 = 1 + alpha
+    a1 = -2 * math.cos(w0)
+    a2 = 1 - alpha
+    return biquad(waveform, b0, b1, b2, a0, a1, a2)

From 33362942eb19cad301122618aef2f846474f9c55 Mon Sep 17 00:00:00 2001
From: Chuan Zhang <engineerchuan@gmail.com>
Date: Tue, 17 Sep 2019 19:57:33 -0400
Subject: [PATCH 24/28] Adding documentation for functional sox compatibility

---
 docs/source/functional.rst                   | 15 ------------
 docs/source/functional_sox_compatibility.rst | 24 ++++++++++++++++++++
 docs/source/index.rst                        |  1 +
 test/test_functional_filtering.py            | 16 ++++++-------
 torchaudio/functional.py                     |  4 ----
 5 files changed, 33 insertions(+), 27 deletions(-)
 create mode 100644 docs/source/functional_sox_compatibility.rst

diff --git a/docs/source/functional.rst b/docs/source/functional.rst
index 817f3e9cd8..c362c1329b 100644
--- a/docs/source/functional.rst
+++ b/docs/source/functional.rst
@@ -67,18 +67,3 @@ Functions to perform common audio operations.
 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 
 .. autofunction:: lfilter
-
-:hidden:`biquad`
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-.. autofunction:: biquad
-
-:hidden:`highpass_biquad`
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-.. autofunction:: highpass_biquad
-
-:hidden:`lowpass_biquad`
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-.. autofunction:: lowpass_biquad
diff --git a/docs/source/functional_sox_compatibility.rst b/docs/source/functional_sox_compatibility.rst
new file mode 100644
index 0000000000..e92598a485
--- /dev/null
+++ b/docs/source/functional_sox_compatibility.rst
@@ -0,0 +1,24 @@
+.. role:: hidden
+    :class: hidden-section
+
+torchaudio.functional_sox_compatibility
+=======================================
+
+.. currentmodule:: torchaudio.functional_sox_compatibility
+
+SoX compatibility functions
+
+:hidden:`biquad`
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+.. autofunction:: biquad
+
+:hidden:`highpass_biquad`
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+.. autofunction:: highpass_biquad
+
+:hidden:`lowpass_biquad`
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+.. autofunction:: lowpass_biquad
diff --git a/docs/source/index.rst b/docs/source/index.rst
index c6d0efde69..0565dde234 100644
--- a/docs/source/index.rst
+++ b/docs/source/index.rst
@@ -13,6 +13,7 @@ The :mod:`torchaudio` package consists of I/O, popular datasets and common audio
    kaldi_io
    transforms
    functional
+   functional_sox_compatibility
 
 .. automodule:: torchaudio
    :members:
diff --git a/test/test_functional_filtering.py b/test/test_functional_filtering.py
index 4d2e8da839..d38887bf0b 100644
--- a/test/test_functional_filtering.py
+++ b/test/test_functional_filtering.py
@@ -4,6 +4,7 @@
 import torch
 import torchaudio
 import torchaudio.functional as F
+import torchaudio.functional_sox_compatibility as FSOX
 import unittest
 import common_utils
 import time
@@ -89,7 +90,7 @@ def test_lowpass_sox_compliance(self):
         waveform, sample_rate = torchaudio.load(
             noise_filepath, normalization=True
         )
-        output_waveform = F.lowpass_biquad(waveform, sample_rate, CUTOFF_FREQ)
+        output_waveform = FSOX.lowpass_biquad(waveform, sample_rate, CUTOFF_FREQ)
 
         assert torch.allclose(sox_output_waveform, output_waveform, atol=1e-4)
 
@@ -112,7 +113,7 @@ def test_highpass_sox_compliance(self):
         waveform, sample_rate = torchaudio.load(
             noise_filepath, normalization=True
         )
-        output_waveform = F.highpass_biquad(waveform, sample_rate, CUTOFF_FREQ)
+        output_waveform = FSOX.highpass_biquad(waveform, sample_rate, CUTOFF_FREQ)
 
         # TBD - this fails at the 1e-4 level, debug why
         assert torch.allclose(sox_output_waveform, output_waveform, atol=1e-3)
@@ -143,19 +144,18 @@ def test_perf_biquad_filtering(self):
         waveform_sox_out, sr = E.sox_build_flow_effects()
         _timing_sox_run_time = time.time() - _timing_sox
 
-        # C++ Diff Eq Filter
-        _timing_cpp_filtering = time.time()
+        _timing_lfilter_filtering = time.time()
         waveform, sample_rate = torchaudio.load(fn_sine, normalization=True)
-        waveform_diff_eq_out = F.lfilter(
+        waveform_lfilter_out = F.lfilter(
             waveform, torch.tensor([a0, a1, a2]), torch.tensor([b0, b1, b2])
         )
-        _timing_diff_eq_run_time = time.time() - _timing_cpp_filtering
+        _timing_lfilter_run_time = time.time() - _timing_lfilter_filtering
 
         # print("\n")
         # print("SoX Run Time         (s): ", round(_timing_sox_run_time, 3))
-        # print("CPP Lfilter Run Time (s): ", round(_timing_diff_eq_run_time, 3))
+        # print("Lfilter Run Time (s): ", round(_timing_lfilter_run_time, 3))
 
-        assert torch.allclose(waveform_sox_out, waveform_diff_eq_out, atol=1e-4)
+        assert torch.allclose(waveform_sox_out, waveform_lfilter_out, atol=1e-4)
 
 
 if __name__ == "__main__":
diff --git a/torchaudio/functional.py b/torchaudio/functional.py
index 8e9b9dc203..f2fa880439 100644
--- a/torchaudio/functional.py
+++ b/torchaudio/functional.py
@@ -1,7 +1,6 @@
 from __future__ import absolute_import, division, print_function, unicode_literals
 import math
 import torch
-from torchaudio.functional_sox_compatibility import biquad, lowpass_biquad, highpass_biquad
 
 __all__ = [
     "istft",
@@ -15,9 +14,6 @@
     "angle",
     "magphase",
     "phase_vocoder",
-    "lowpass_biquad",
-    "highpass_biquad",
-    "biquad",
     "lfilter",
 ]
 

From 9608edde15729a873336ff009c66b2cce1c1e0c6 Mon Sep 17 00:00:00 2001
From: Chuan Zhang <engineerchuan@gmail.com>
Date: Wed, 18 Sep 2019 07:20:11 -0700
Subject: [PATCH 25/28] removed some print statements, mainly to kick build
 tests again

---
 test/test_functional_filtering.py | 4 ----
 1 file changed, 4 deletions(-)

diff --git a/test/test_functional_filtering.py b/test/test_functional_filtering.py
index d38887bf0b..592939cf54 100644
--- a/test/test_functional_filtering.py
+++ b/test/test_functional_filtering.py
@@ -151,10 +151,6 @@ def test_perf_biquad_filtering(self):
         )
         _timing_lfilter_run_time = time.time() - _timing_lfilter_filtering
 
-        # print("\n")
-        # print("SoX Run Time         (s): ", round(_timing_sox_run_time, 3))
-        # print("Lfilter Run Time (s): ", round(_timing_lfilter_run_time, 3))
-
         assert torch.allclose(waveform_sox_out, waveform_lfilter_out, atol=1e-4)
 
 

From 445d717bac46d9478bb300a083386ebfaf43d0ed Mon Sep 17 00:00:00 2001
From: Chuan Zhang <engineerchuan@gmail.com>
Date: Wed, 18 Sep 2019 08:35:15 -0700
Subject: [PATCH 26/28] moved previous sox compatibility into functional

---
 docs/source/functional.rst                   | 15 +++
 docs/source/functional_sox_compatibility.rst | 24 -----
 docs/source/index.rst                        |  1 -
 test/test_functional_filtering.py            | 15 ++-
 torchaudio/functional.py                     | 90 ++++++++++++++++++
 torchaudio/functional_sox_compatibility.py   | 98 --------------------
 6 files changed, 112 insertions(+), 131 deletions(-)
 delete mode 100644 docs/source/functional_sox_compatibility.rst
 delete mode 100644 torchaudio/functional_sox_compatibility.py

diff --git a/docs/source/functional.rst b/docs/source/functional.rst
index c362c1329b..9968bfadf7 100644
--- a/docs/source/functional.rst
+++ b/docs/source/functional.rst
@@ -67,3 +67,18 @@ Functions to perform common audio operations.
 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 
 .. autofunction:: lfilter
+
+:hidden:`biquad`
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+.. autofunction:: biquad
+
+:hidden:`lowpass_biquad`
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+.. autofunction:: lowpass_biquad
+
+:hidden:`highpass_biquad`
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+.. autofunction:: highpass_biquad
diff --git a/docs/source/functional_sox_compatibility.rst b/docs/source/functional_sox_compatibility.rst
deleted file mode 100644
index e92598a485..0000000000
--- a/docs/source/functional_sox_compatibility.rst
+++ /dev/null
@@ -1,24 +0,0 @@
-.. role:: hidden
-    :class: hidden-section
-
-torchaudio.functional_sox_compatibility
-=======================================
-
-.. currentmodule:: torchaudio.functional_sox_compatibility
-
-SoX compatibility functions
-
-:hidden:`biquad`
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-.. autofunction:: biquad
-
-:hidden:`highpass_biquad`
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-.. autofunction:: highpass_biquad
-
-:hidden:`lowpass_biquad`
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-.. autofunction:: lowpass_biquad
diff --git a/docs/source/index.rst b/docs/source/index.rst
index 0565dde234..c6d0efde69 100644
--- a/docs/source/index.rst
+++ b/docs/source/index.rst
@@ -13,7 +13,6 @@ The :mod:`torchaudio` package consists of I/O, popular datasets and common audio
    kaldi_io
    transforms
    functional
-   functional_sox_compatibility
 
 .. automodule:: torchaudio
    :members:
diff --git a/test/test_functional_filtering.py b/test/test_functional_filtering.py
index 592939cf54..0012119a26 100644
--- a/test/test_functional_filtering.py
+++ b/test/test_functional_filtering.py
@@ -4,7 +4,6 @@
 import torch
 import torchaudio
 import torchaudio.functional as F
-import torchaudio.functional_sox_compatibility as FSOX
 import unittest
 import common_utils
 import time
@@ -35,9 +34,9 @@ def test_lfilter(self):
         Design an IIR lowpass filter using scipy.signal filter design
         https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.iirdesign.html#scipy.signal.iirdesign
 
-        from scipy.signal import iirdesign
-        b, a = iirdesign(0.2, 0.3, 1, 60)
-
+        Example
+          >>> from scipy.signal import iirdesign
+          >>> b, a = iirdesign(0.2, 0.3, 1, 60)
         """
 
         b_coeffs = torch.tensor(
@@ -70,7 +69,7 @@ def test_lfilter(self):
         assert output_waveform.size(0) == waveform.size(0)
         assert output_waveform.size(1) == waveform.size(1)
 
-    def test_lowpass_sox_compliance(self):
+    def test_lowpass(self):
 
         """
         Run a biquad lowpass filter using SoX vs torchaudio's lfilter
@@ -90,11 +89,11 @@ def test_lowpass_sox_compliance(self):
         waveform, sample_rate = torchaudio.load(
             noise_filepath, normalization=True
         )
-        output_waveform = FSOX.lowpass_biquad(waveform, sample_rate, CUTOFF_FREQ)
+        output_waveform = F.lowpass_biquad(waveform, sample_rate, CUTOFF_FREQ)
 
         assert torch.allclose(sox_output_waveform, output_waveform, atol=1e-4)
 
-    def test_highpass_sox_compliance(self):
+    def test_highpass(self):
         """
         Run a biquad highpass filter using SoX vs torchaudio's lfilter
         Results should be very close
@@ -113,7 +112,7 @@ def test_highpass_sox_compliance(self):
         waveform, sample_rate = torchaudio.load(
             noise_filepath, normalization=True
         )
-        output_waveform = FSOX.highpass_biquad(waveform, sample_rate, CUTOFF_FREQ)
+        output_waveform = F.highpass_biquad(waveform, sample_rate, CUTOFF_FREQ)
 
         # TBD - this fails at the 1e-4 level, debug why
         assert torch.allclose(sox_output_waveform, output_waveform, atol=1e-3)
diff --git a/torchaudio/functional.py b/torchaudio/functional.py
index f2fa880439..a1f73c6c7c 100644
--- a/torchaudio/functional.py
+++ b/torchaudio/functional.py
@@ -15,6 +15,9 @@
     "magphase",
     "phase_vocoder",
     "lfilter",
+    "lowpass_biquad",
+    "highpass_biquad",
+    "biquad",
 ]
 
 # TODO: remove this once https://github.com/pytorch/pytorch/issues/21478 gets solved
@@ -561,3 +564,90 @@ def lfilter(waveform, a_coeffs, b_coeffs):
         padded_output_waveform[:, i_frame + n_order - 1] = o0
 
     return torch.min(ones, torch.max(ones * -1, padded_output_waveform[:, (n_order - 1):]))
+
+def biquad(waveform, b0, b1, b2, a0, a1, a2):
+    # type: (Tensor, float, float, float, float, float, float) -> Tensor
+    r"""Performs a biquad filter of input tensor.  Initial conditions set to 0.
+    https://en.wikipedia.org/wiki/Digital_biquad_filter
+
+    Args:
+        waveform (torch.Tensor): audio waveform of dimension of `(n_channel, n_frames)`
+        b0 (float): numerator coefficient of current input, x[n]
+        b1 (float): numerator coefficient of input one time step ago x[n-1]
+        b2 (float): numerator coefficient of input two time steps ago x[n-2]
+        a0 (float): denominator coefficient of current output y[n], typically 1
+        a1 (float): denominator coefficient of current output y[n-1]
+        a2 (float): denominator coefficient of current output y[n-2]
+
+    Returns:
+        output_waveform (torch.Tensor): Dimension of `(n_channel, n_frames)`
+    """
+
+    assert(waveform.dtype == torch.float32)
+
+    output_waveform = torchaudio.functional.lfilter(
+        waveform, torch.tensor([a0, a1, a2]), torch.tensor([b0, b1, b2])
+    )
+    return output_waveform
+
+
+def _dB2Linear(x):
+    return math.exp(x * math.log(10) / 20.0)
+
+
+def highpass_biquad(waveform, sample_rate, cutoff_freq, Q=0.707):
+    # type: (Tensor, int, float, Optional[float]) -> Tensor
+    r"""Designs biquad highpass filter and performs filtering.  Similar to SoX implementation.
+
+    Args:
+        waveform (torch.Tensor): audio waveform of dimension of `(n_channel, n_frames)`
+        sample_rate (int): sampling rate of the waveform, e.g. 44100 (Hz)
+        cutoff_freq (float): filter cutoff frequency
+        Q (float): https://en.wikipedia.org/wiki/Q_factor
+
+    Returns:
+        output_waveform (torch.Tensor): Dimension of `(n_channel, n_frames)`
+    """
+
+    GAIN = 1  # TBD - add as a parameter
+    w0 = 2 * math.pi * cutoff_freq / sample_rate
+    A = math.exp(GAIN / 40.0 * math.log(10))
+    alpha = math.sin(w0) / 2 / Q
+    mult = _dB2Linear(max(GAIN, 0))
+
+    b0 = (1 + math.cos(w0)) / 2
+    b1 = -1 - math.cos(w0)
+    b2 = b0
+    a0 = 1 + alpha
+    a1 = -2 * math.cos(w0)
+    a2 = 1 - alpha
+    return biquad(waveform, b0, b1, b2, a0, a1, a2)
+
+
+def lowpass_biquad(waveform, sample_rate, cutoff_freq, Q=0.707):
+    # type: (Tensor, int, float, Optional[float]) -> Tensor
+    r"""Designs biquad lowpass filter and performs filtering.  Similar to SoX implementation.
+
+    Args:
+        waveform (torch.Tensor): audio waveform of dimension of `(n_channel, n_frames)`
+        sample_rate (int): sampling rate of the waveform, e.g. 44100 (Hz)
+        cutoff_freq (float): filter cutoff frequency
+        Q (float): https://en.wikipedia.org/wiki/Q_factor
+
+    Returns:
+        output_waveform (torch.Tensor): Dimension of `(n_channel, n_frames)`
+    """
+
+    GAIN = 1
+    w0 = 2 * math.pi * cutoff_freq / sample_rate
+    A = math.exp(GAIN / 40.0 * math.log(10))
+    alpha = math.sin(w0) / 2 / Q
+    mult = _dB2Linear(max(GAIN, 0))
+
+    b0 = (1 - math.cos(w0)) / 2
+    b1 = 1 - math.cos(w0)
+    b2 = b0
+    a0 = 1 + alpha
+    a1 = -2 * math.cos(w0)
+    a2 = 1 - alpha
+    return biquad(waveform, b0, b1, b2, a0, a1, a2)
diff --git a/torchaudio/functional_sox_compatibility.py b/torchaudio/functional_sox_compatibility.py
deleted file mode 100644
index 620c588c8c..0000000000
--- a/torchaudio/functional_sox_compatibility.py
+++ /dev/null
@@ -1,98 +0,0 @@
-from __future__ import absolute_import, division, print_function, unicode_literals
-import math
-import torch
-import torchaudio
-
-__all__ = [
-    "lowpass_biquad",
-    "highpass_biquad",
-    "biquad",
-]
-
-
-def biquad(waveform, b0, b1, b2, a0, a1, a2):
-    # type: (Tensor, float, float, float, float, float, float) -> Tensor
-    r"""Performs a biquad filter of input tensor.  Initial conditions set to 0.
-    https://en.wikipedia.org/wiki/Digital_biquad_filter
-
-    Args:
-        waveform (torch.Tensor): audio waveform of dimension of `(n_channel, n_frames)`
-        b0 (float): numerator coefficient of current input, x[n]
-        b1 (float): numerator coefficient of input one time step ago x[n-1]
-        b2 (float): numerator coefficient of input two time steps ago x[n-2]
-        a0 (float): denominator coefficient of current output y[n], typically 1
-        a1 (float): denominator coefficient of current output y[n-1]
-        a2 (float): denominator coefficient of current output y[n-2]
-
-    Returns:
-        output_waveform (torch.Tensor): Dimension of `(n_channel, n_frames)`
-    """
-
-    assert(waveform.dtype == torch.float32)
-
-    output_waveform = torchaudio.functional.lfilter(
-        waveform, torch.tensor([a0, a1, a2]), torch.tensor([b0, b1, b2])
-    )
-    return output_waveform
-
-
-def _dB2Linear(x):
-    return math.exp(x * math.log(10) / 20.0)
-
-
-def highpass_biquad(waveform, sample_rate, cutoff_freq, Q=0.707):
-    # type: (Tensor, int, float, Optional[float]) -> Tensor
-    r"""Designs biquad highpass filter and performs filtering.  Similar to SoX implementation.
-
-    Args:
-        waveform (torch.Tensor): audio waveform of dimension of `(n_channel, n_frames)`
-        sample_rate (int): sampling rate of the waveform, e.g. 44100 (Hz)
-        cutoff_freq (float): filter cutoff frequency
-        Q (float): https://en.wikipedia.org/wiki/Q_factor
-
-    Returns:
-        output_waveform (torch.Tensor): Dimension of `(n_channel, n_frames)`
-    """
-
-    GAIN = 1  # TBD - add as a parameter
-    w0 = 2 * math.pi * cutoff_freq / sample_rate
-    A = math.exp(GAIN / 40.0 * math.log(10))
-    alpha = math.sin(w0) / 2 / Q
-    mult = _dB2Linear(max(GAIN, 0))
-
-    b0 = (1 + math.cos(w0)) / 2
-    b1 = -1 - math.cos(w0)
-    b2 = b0
-    a0 = 1 + alpha
-    a1 = -2 * math.cos(w0)
-    a2 = 1 - alpha
-    return biquad(waveform, b0, b1, b2, a0, a1, a2)
-
-
-def lowpass_biquad(waveform, sample_rate, cutoff_freq, Q=0.707):
-    # type: (Tensor, int, float, Optional[float]) -> Tensor
-    r"""Designs biquad lowpass filter and performs filtering.  Similar to SoX implementation.
-
-    Args:
-        waveform (torch.Tensor): audio waveform of dimension of `(n_channel, n_frames)`
-        sample_rate (int): sampling rate of the waveform, e.g. 44100 (Hz)
-        cutoff_freq (float): filter cutoff frequency
-        Q (float): https://en.wikipedia.org/wiki/Q_factor
-
-    Returns:
-        output_waveform (torch.Tensor): Dimension of `(n_channel, n_frames)`
-    """
-
-    GAIN = 1
-    w0 = 2 * math.pi * cutoff_freq / sample_rate
-    A = math.exp(GAIN / 40.0 * math.log(10))
-    alpha = math.sin(w0) / 2 / Q
-    mult = _dB2Linear(max(GAIN, 0))
-
-    b0 = (1 - math.cos(w0)) / 2
-    b1 = 1 - math.cos(w0)
-    b2 = b0
-    a0 = 1 + alpha
-    a1 = -2 * math.cos(w0)
-    a2 = 1 - alpha
-    return biquad(waveform, b0, b1, b2, a0, a1, a2)

From c54991a1ec3a03c6ca064c652539ad887e2810f1 Mon Sep 17 00:00:00 2001
From: Chuan Zhang <engineerchuan@gmail.com>
Date: Wed, 18 Sep 2019 08:41:54 -0700
Subject: [PATCH 27/28] Fix module reference in biquad

---
 torchaudio/functional.py | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/torchaudio/functional.py b/torchaudio/functional.py
index a1f73c6c7c..842d8495bf 100644
--- a/torchaudio/functional.py
+++ b/torchaudio/functional.py
@@ -565,6 +565,7 @@ def lfilter(waveform, a_coeffs, b_coeffs):
 
     return torch.min(ones, torch.max(ones * -1, padded_output_waveform[:, (n_order - 1):]))
 
+
 def biquad(waveform, b0, b1, b2, a0, a1, a2):
     # type: (Tensor, float, float, float, float, float, float) -> Tensor
     r"""Performs a biquad filter of input tensor.  Initial conditions set to 0.
@@ -585,7 +586,7 @@ def biquad(waveform, b0, b1, b2, a0, a1, a2):
 
     assert(waveform.dtype == torch.float32)
 
-    output_waveform = torchaudio.functional.lfilter(
+    output_waveform = lfilter(
         waveform, torch.tensor([a0, a1, a2]), torch.tensor([b0, b1, b2])
     )
     return output_waveform

From a4cd66dfb75c8ee7949b6e96b290dea77a2bc208 Mon Sep 17 00:00:00 2001
From: Chuan Zhang <engineerchuan@gmail.com>
Date: Wed, 18 Sep 2019 08:44:22 -0700
Subject: [PATCH 28/28] Small wording tweaks to test docstrings

---
 test/test_functional_filtering.py | 13 ++-----------
 1 file changed, 2 insertions(+), 11 deletions(-)

diff --git a/test/test_functional_filtering.py b/test/test_functional_filtering.py
index 0012119a26..e4ec4f143d 100644
--- a/test/test_functional_filtering.py
+++ b/test/test_functional_filtering.py
@@ -72,8 +72,7 @@ def test_lfilter(self):
     def test_lowpass(self):
 
         """
-        Run a biquad lowpass filter using SoX vs torchaudio's lfilter
-        Results should be very close
+        Test biquad lowpass filter, compare to SoX implementation
         """
 
         CUTOFF_FREQ = 3000
@@ -95,8 +94,7 @@ def test_lowpass(self):
 
     def test_highpass(self):
         """
-        Run a biquad highpass filter using SoX vs torchaudio's lfilter
-        Results should be very close
+        Test biquad highpass filter, compare to SoX implementation
         """
 
         CUTOFF_FREQ = 2000
@@ -118,13 +116,6 @@ def test_highpass(self):
         assert torch.allclose(sox_output_waveform, output_waveform, atol=1e-3)
 
     def test_perf_biquad_filtering(self):
-        """
-        Compare SoX implementation of biquad filtering with C++ implementation
-
-        Test that results are similar and how performance differs
-
-        Current results: C++ implementation approximately same speed
-        """
 
         fn_sine = os.path.join(self.test_dirpath, "assets", "whitenoise.mp3")