diff --git a/README.md b/README.md
index eaed8acf36..65b79e4784 100644
--- a/README.md
+++ b/README.md
@@ -129,7 +129,7 @@ Transforms expect and return the following dimensions.
 * `MuLawDecode`: (channel, time) -> (channel, time)
 * `Resample`: (channel, time) -> (channel, time)
 
-Complex numbers are supported via tensors of dimension (..., 2), and torchaudio provides `complex_norm` and `angle` to convert such a tensor into its magnitude and phase.
+Complex numbers are supported via tensors of dimension (..., 2), and torchaudio provides `complex_norm` and `angle` to convert such a tensor into its magnitude and phase. Here, and in the documentation, we use an ellipsis "..." as a placeholder for the rest of the dimensions of a tensor, e.g. optional batching and channel dimensions.
 
 Contributing Guidelines
 -----------------------
diff --git a/test/test_functional.py b/test/test_functional.py
index be0804b6c6..90d9c77321 100644
--- a/test/test_functional.py
+++ b/test/test_functional.py
@@ -21,6 +21,10 @@ class TestFunctional(unittest.TestCase):
     number_of_trials = 100
     specgram = torch.tensor([1., 2., 3., 4.])
 
+    test_dirpath, test_dir = common_utils.create_temp_assets_dir()
+    test_filepath = os.path.join(test_dirpath, 'assets',
+                                 'steam-train-whistle-daniel_simon.mp3')
+
     def _test_compute_deltas(self, specgram, expected, win_length=3, atol=1e-6, rtol=1e-8):
         computed = F.compute_deltas(specgram, win_length=win_length)
         self.assertTrue(computed.shape == expected.shape, (computed.shape, expected.shape))
@@ -46,6 +50,20 @@ def test_compute_deltas_randn(self):
         computed = F.compute_deltas(specgram, win_length=win_length)
         self.assertTrue(computed.shape == specgram.shape, (computed.shape, specgram.shape))
 
+    def test_batch_pitch(self):
+        waveform, sample_rate = torchaudio.load(self.test_filepath)
+
+        # Single then transform then batch
+        expected = F.detect_pitch_frequency(waveform, sample_rate)
+        expected = expected.unsqueeze(0).repeat(3, 1, 1)
+
+        # Batch then transform
+        waveform = waveform.unsqueeze(0).repeat(3, 1, 1)
+        computed = F.detect_pitch_frequency(waveform, sample_rate)
+
+        self.assertTrue(computed.shape == expected.shape, (computed.shape, expected.shape))
+        self.assertTrue(torch.allclose(computed, expected))
+
     def _compare_estimate(self, sound, estimate, atol=1e-6, rtol=1e-8):
         # trim sound for case when constructed signal is shorter than original
         sound = sound[..., :estimate.size(-1)]
@@ -58,6 +76,8 @@ def _test_istft_is_inverse_of_stft(self, kwargs):
         # operation to check whether we can reconstruct signal
         for data_size in self.data_sizes:
             for i in range(self.number_of_trials):
+
+                # Non-batch
                 sound = common_utils.random_float_tensor(i, data_size)
 
                 stft = torch.stft(sound, **kwargs)
@@ -65,6 +85,14 @@ def _test_istft_is_inverse_of_stft(self, kwargs):
 
                 self._compare_estimate(sound, estimate)
 
+                # Batch
+                stft = torch.stft(sound, **kwargs)
+                stft = stft.repeat(3, 1, 1, 1, 1)
+                sound = sound.repeat(3, 1, 1)
+
+                estimate = torchaudio.functional.istft(stft, length=sound.size(1), **kwargs)
+                self._compare_estimate(sound, estimate)
+
     def test_istft_is_inverse_of_stft1(self):
         # hann_window, centered, normalized, onesided
         kwargs1 = {
@@ -326,15 +354,30 @@ def test_pitch(self):
         for filename, freq_ref in tests:
             waveform, sample_rate = torchaudio.load(filename)
 
-            # Convert to stereo for testing purposes
-            waveform = waveform.repeat(2, 1, 1)
-
             freq = torchaudio.functional.detect_pitch_frequency(waveform, sample_rate)
 
             threshold = 1
             s = ((freq - freq_ref).abs() > threshold).sum()
             self.assertFalse(s)
 
+            # Convert to stereo and batch for testing purposes
+            freq = freq.repeat(3, 2, 1, 1)
+            waveform = waveform.repeat(3, 2, 1, 1)
+
+            freq2 = torchaudio.functional.detect_pitch_frequency(waveform, sample_rate)
+
+            assert torch.allclose(freq, freq2, atol=1e-5)
+
+    def _test_batch(self, functional):
+        waveform, sample_rate = torchaudio.load(self.test_filepath)  # (2, 278756), 44100
+
+        # Single then transform then batch
+        expected = functional(waveform).unsqueeze(0).repeat(3, 1, 1, 1)
+
+        # Batch then transform
+        waveform = waveform.unsqueeze(0).repeat(3, 1, 1)
+        computed = functional(waveform)
+
 
 def _num_stft_bins(signal_len, fft_len, hop_length, pad):
     return (signal_len + 2 * pad - fft_len + hop_length) // hop_length
diff --git a/test/test_transforms.py b/test/test_transforms.py
index a438c4481c..82594bad01 100644
--- a/test/test_transforms.py
+++ b/test/test_transforms.py
@@ -313,6 +313,45 @@ def test_compute_deltas_twochannel(self):
         computed = transform(specgram)
         self.assertTrue(computed.shape == specgram.shape, (computed.shape, specgram.shape))
 
+    def test_batch_compute_deltas(self):
+        specgram = torch.randn(2, 31, 2786)
+
+        # Single then transform then batch
+        expected = transforms.ComputeDeltas()(specgram).repeat(3, 1, 1, 1)
+
+        # Batch then transform
+        computed = transforms.ComputeDeltas()(specgram.repeat(3, 1, 1, 1))
+
+        # shape = (3, 2, 201, 1394)
+        self.assertTrue(computed.shape == expected.shape, (computed.shape, expected.shape))
+        self.assertTrue(torch.allclose(computed, expected))
+
+    def test_batch_mulaw(self):
+        waveform, sample_rate = torchaudio.load(self.test_filepath)  # (2, 278756), 44100
+
+        # Single then transform then batch
+        waveform_encoded = transforms.MuLawEncoding()(waveform)
+        expected = waveform_encoded.unsqueeze(0).repeat(3, 1, 1)
+
+        # Batch then transform
+        waveform_batched = waveform.unsqueeze(0).repeat(3, 1, 1)
+        computed = transforms.MuLawEncoding()(waveform_batched)
+
+        # shape = (3, 2, 201, 1394)
+        self.assertTrue(computed.shape == expected.shape, (computed.shape, expected.shape))
+        self.assertTrue(torch.allclose(computed, expected))
+
+        # Single then transform then batch
+        waveform_decoded = transforms.MuLawDecoding()(waveform_encoded)
+        expected = waveform_decoded.unsqueeze(0).repeat(3, 1, 1)
+
+        # Batch then transform
+        computed = transforms.MuLawDecoding()(computed)
+
+        # shape = (3, 2, 201, 1394)
+        self.assertTrue(computed.shape == expected.shape, (computed.shape, expected.shape))
+        self.assertTrue(torch.allclose(computed, expected))
+
     def test_batch_spectrogram(self):
         waveform, sample_rate = torchaudio.load(self.test_filepath)
 
diff --git a/torchaudio/functional.py b/torchaudio/functional.py
index 4397ddd51b..44b52cf277 100644
--- a/torchaudio/functional.py
+++ b/torchaudio/functional.py
@@ -114,16 +114,20 @@ def istft(
             original signal length). (Default: whole signal)
 
     Returns:
-        torch.Tensor: Least squares estimation of the original signal of size
-        (channel, signal_length) or (signal_length)
+        torch.Tensor: Least squares estimation of the original signal of size (..., 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, "Incorrect stft dimension: %d" % (stft_matrix_dim)
+    assert stft_matrix.nelement() > 0
 
     if stft_matrix_dim == 3:
         # add a channel dimension
         stft_matrix = stft_matrix.unsqueeze(0)
 
+    # pack batch
+    shape = stft_matrix.size()
+    stft_matrix = stft_matrix.reshape(-1, *shape[-3:])
+
     dtype = stft_matrix.dtype
     device = stft_matrix.device
     fft_size = stft_matrix.size(1)
@@ -208,8 +212,12 @@ def istft(
 
     y = (y / window_envelop).squeeze(1)  # size (channel, expected_signal_len)
 
+    # unpack batch
+    y = y.reshape(shape[:-3] + y.shape[-1:])
+
     if stft_matrix_dim == 3:  # remove the channel dimension
         y = y.squeeze(0)
+
     return y
 
 
@@ -514,14 +522,14 @@ def phase_vocoder(complex_specgrams, rate, phase_advance):
                               dtype=complex_specgrams.dtype)
 
     alphas = time_steps % 1.0
-    phase_0 = angle(complex_specgrams[:, :, :1])
+    phase_0 = angle(complex_specgrams[..., :1, :])
 
     # Time Padding
     complex_specgrams = torch.nn.functional.pad(complex_specgrams, [0, 0, 0, 2])
 
     # (new_bins, freq, 2)
-    complex_specgrams_0 = complex_specgrams[:, :, time_steps.long()]
-    complex_specgrams_1 = complex_specgrams[:, :, (time_steps + 1).long()]
+    complex_specgrams_0 = complex_specgrams.index_select(-2, time_steps.long())
+    complex_specgrams_1 = complex_specgrams.index_select(-2, (time_steps + 1).long())
 
     angle_0 = angle(complex_specgrams_0)
     angle_1 = angle(complex_specgrams_1)
@@ -534,7 +542,7 @@ def phase_vocoder(complex_specgrams, rate, phase_advance):
 
     # Compute Phase Accum
     phase = phase + phase_advance
-    phase = torch.cat([phase_0, phase[:, :, :-1]], dim=-1)
+    phase = torch.cat([phase_0, phase[..., :-1]], dim=-1)
     phase_acc = torch.cumsum(phase, -1)
 
     mag = alphas * norm_1 + (1 - alphas) * norm_0
@@ -554,7 +562,7 @@ def lfilter(waveform, a_coeffs, b_coeffs):
     Performs an IIR filter by evaluating difference equation.
 
     Args:
-        waveform (torch.Tensor): audio waveform of dimension of `(channel, time)`.  Must be normalized to -1 to 1.
+        waveform (torch.Tensor): audio waveform of dimension of `(..., time)`.  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).
@@ -563,10 +571,16 @@ def lfilter(waveform, a_coeffs, b_coeffs):
                                  Must be same size as a_coeffs (pad with 0's as necessary).
 
     Returns:
-        output_waveform (torch.Tensor): Dimension of `(channel, time)`.  Output will be clipped to -1 to 1.
+        output_waveform (torch.Tensor): Dimension of `(..., time)`.  Output will be clipped to -1 to 1.
 
     """
 
+    dim = waveform.dim()
+
+    # pack batch
+    shape = waveform.size()
+    waveform = waveform.reshape(-1, shape[-1])
+
     assert(a_coeffs.size(0) == b_coeffs.size(0))
     assert(len(waveform.size()) == 2)
     assert(waveform.device == a_coeffs.device)
@@ -606,7 +620,14 @@ def lfilter(waveform, a_coeffs, b_coeffs):
 
         padded_output_waveform[:, i_sample + n_order - 1] = o0
 
-    return torch.min(ones, torch.max(ones * -1, padded_output_waveform[:, (n_order - 1):]))
+    output = torch.min(
+        ones, torch.max(ones * -1, padded_output_waveform[:, (n_order - 1):])
+    )
+
+    # unpack batch
+    output = output.reshape(shape[:-1] + output.shape[-1:])
+
+    return output
 
 
 @torch.jit.script
@@ -817,12 +838,12 @@ def compute_deltas(specgram, win_length=5, mode="replicate"):
     :math:`N` is (`win_length`-1)//2.
 
     Args:
-        specgram (torch.Tensor): Tensor of audio of dimension (channel, freq, time)
+        specgram (torch.Tensor): Tensor of audio of dimension (..., freq, time)
         win_length (int): The window length used for computing delta
         mode (str): Mode parameter passed to padding
 
     Returns:
-        deltas (torch.Tensor): Tensor of audio of dimension (channel, freq, time)
+        deltas (torch.Tensor): Tensor of audio of dimension (..., freq, time)
 
     Example
         >>> specgram = torch.randn(1, 40, 1000)
@@ -830,9 +851,11 @@ def compute_deltas(specgram, win_length=5, mode="replicate"):
         >>> delta2 = compute_deltas(delta)
     """
 
+    # pack batch
+    shape = specgram.size()
+    specgram = specgram.reshape(1, -1, shape[-1])
+
     assert win_length >= 3
-    assert specgram.dim() == 3
-    assert not specgram.shape[1] % specgram.shape[0]
 
     n = (win_length - 1) // 2
 
@@ -844,12 +867,15 @@ def compute_deltas(specgram, win_length=5, mode="replicate"):
     kernel = (
         torch
         .arange(-n, n + 1, 1, device=specgram.device, dtype=specgram.dtype)
-        .repeat(specgram.shape[1], specgram.shape[0], 1)
+        .repeat(specgram.shape[1], 1, 1)
     )
 
-    return torch.nn.functional.conv1d(
-        specgram, kernel, groups=specgram.shape[1] // specgram.shape[0]
-    ) / denom
+    output = torch.nn.functional.conv1d(specgram, kernel, groups=specgram.shape[1]) / denom
+
+    # unpack batch
+    output = output.reshape(shape)
+
+    return output
 
 
 @torch.jit.script
@@ -982,16 +1008,22 @@ def detect_pitch_frequency(
     It is implemented using normalized cross-correlation function and median smoothing.
 
     Args:
-        waveform (torch.Tensor): Tensor of audio of dimension (channel, freq, time)
+        waveform (torch.Tensor): Tensor of audio of dimension (..., freq, time)
         sample_rate (int): The sample rate of the waveform (Hz)
         win_length (int): The window length for median smoothing (in number of frames)
         freq_low (int): Lowest frequency that can be detected (Hz)
         freq_high (int): Highest frequency that can be detected (Hz)
 
     Returns:
-        freq (torch.Tensor): Tensor of audio of dimension (channel, frame)
+        freq (torch.Tensor): Tensor of audio of dimension (..., frame)
     """
 
+    dim = waveform.dim()
+
+    # pack batch
+    shape = waveform.size()
+    waveform = waveform.reshape([-1] + shape[-1:])
+
     nccf = _compute_nccf(waveform, sample_rate, frame_time, freq_low)
     indices = _find_max_per_frame(nccf, sample_rate, freq_high)
     indices = _median_smoothing(indices, win_length)
@@ -1000,4 +1032,7 @@ def detect_pitch_frequency(
     EPSILON = 10 ** (-9)
     freq = sample_rate / (EPSILON + indices.to(torch.float))
 
+    # unpack batch
+    freq = freq.reshape(shape[:-1] + freq.shape[-1:])
+
     return freq