diff --git a/test/torchaudio_unittest/functional/functional_cpu_test.py b/test/torchaudio_unittest/functional/functional_cpu_test.py
index 7669d96744..9f4b4f1a64 100644
--- a/test/torchaudio_unittest/functional/functional_cpu_test.py
+++ b/test/torchaudio_unittest/functional/functional_cpu_test.py
@@ -14,7 +14,7 @@
     skipIfNoSox,
 )
 
-from .functional_impl import Lfilter, Spectrogram
+from .functional_impl import Lfilter, Spectrogram, FunctionalComplex
 
 
 class TestLFilterFloat32(Lfilter, common_utils.PytorchTestCase):
@@ -41,6 +41,18 @@ class TestSpectrogramFloat64(Spectrogram, common_utils.PytorchTestCase):
     device = torch.device('cpu')
 
 
+class TestFunctionalComplex64(FunctionalComplex, common_utils.PytorchTestCase):
+    complex_dtype = torch.complex64
+    real_dtype = torch.float32
+    device = torch.device('cpu')
+
+
+class TestFunctionalComplex128(FunctionalComplex, common_utils.PytorchTestCase):
+    complex_dtype = torch.complex128
+    real_dtype = torch.float64
+    device = torch.device('cpu')
+
+
 class TestCreateFBMatrix(common_utils.TorchaudioTestCase):
     def test_no_warning_high_n_freq(self):
         with warnings.catch_warnings(record=True) as w:
diff --git a/test/torchaudio_unittest/functional/functional_cuda_test.py b/test/torchaudio_unittest/functional/functional_cuda_test.py
index f4db6ca3a0..62d9eff3eb 100644
--- a/test/torchaudio_unittest/functional/functional_cuda_test.py
+++ b/test/torchaudio_unittest/functional/functional_cuda_test.py
@@ -2,7 +2,7 @@
 import unittest
 
 from torchaudio_unittest import common_utils
-from .functional_impl import Lfilter, Spectrogram
+from .functional_impl import Lfilter, Spectrogram, FunctionalComplex
 
 
 @common_utils.skipIfNoCuda
@@ -31,3 +31,17 @@ class TestSpectrogramFloat32(Spectrogram, common_utils.PytorchTestCase):
 class TestSpectrogramFloat64(Spectrogram, common_utils.PytorchTestCase):
     dtype = torch.float64
     device = torch.device('cuda')
+
+
+@common_utils.skipIfNoCuda
+class TestFunctionalComplex64(FunctionalComplex, common_utils.PytorchTestCase):
+    complex_dtype = torch.complex64
+    real_dtype = torch.float32
+    device = torch.device('cuda')
+
+
+@common_utils.skipIfNoCuda
+class TestFunctionalComplex128(FunctionalComplex, common_utils.PytorchTestCase):
+    complex_dtype = torch.complex64
+    real_dtype = torch.float32
+    device = torch.device('cuda')
diff --git a/test/torchaudio_unittest/functional/functional_impl.py b/test/torchaudio_unittest/functional/functional_impl.py
index f7f8c17ecb..c4f863fe45 100644
--- a/test/torchaudio_unittest/functional/functional_impl.py
+++ b/test/torchaudio_unittest/functional/functional_impl.py
@@ -2,9 +2,11 @@
 import torch
 import torchaudio.functional as F
 from parameterized import parameterized
+import numpy as np
 from scipy import signal
 
 from torchaudio_unittest import common_utils
+from torchaudio_unittest.common_utils import nested_params
 
 
 class Lfilter(common_utils.TestBaseMixin):
@@ -89,3 +91,39 @@ def test_grad_at_zero(self, power):
         )
         spec.sum().backward()
         assert not x.grad.isnan().sum()
+
+
+class FunctionalComplex(common_utils.TestBaseMixin):
+    complex_dtype = None
+    real_dtype = None
+    device = None
+
+    @nested_params(
+        [0.5, 1.01, 1.3],
+        [True, False],
+    )
+    def test_phase_vocoder_shape(self, rate, test_pseudo_complex):
+        """Verify the output shape of phase vocoder"""
+        hop_length = 256
+        num_freq = 1025
+        num_frames = 400
+        batch_size = 2
+
+        torch.random.manual_seed(42)
+        spec = torch.randn(
+            batch_size, num_freq, num_frames, dtype=self.complex_dtype, device=self.device)
+        if test_pseudo_complex:
+            spec = torch.view_as_real(spec)
+
+        phase_advance = torch.linspace(
+            0,
+            np.pi * hop_length,
+            num_freq,
+            dtype=self.real_dtype, device=self.device)[..., None]
+
+        spec_stretch = F.phase_vocoder(spec, rate=rate, phase_advance=phase_advance)
+
+        assert spec.dim() == spec_stretch.dim()
+        expected_shape = torch.Size([batch_size, num_freq, int(np.ceil(num_frames / rate))])
+        output_shape = (torch.view_as_complex(spec_stretch) if test_pseudo_complex else spec_stretch).shape
+        assert output_shape == expected_shape
diff --git a/test/torchaudio_unittest/functional/librosa_compatibility_test.py b/test/torchaudio_unittest/functional/librosa_compatibility_test.py
index 5905c239d3..f3ddb354ae 100644
--- a/test/torchaudio_unittest/functional/librosa_compatibility_test.py
+++ b/test/torchaudio_unittest/functional/librosa_compatibility_test.py
@@ -1,4 +1,3 @@
-import itertools
 import unittest
 from distutils.version import StrictVersion
 
@@ -15,6 +14,9 @@
     import librosa
 
 from torchaudio_unittest import common_utils
+from torchaudio_unittest.common_utils import (
+    nested_params,
+)
 
 
 @unittest.skipIf(not LIBROSA_AVAILABLE, "Librosa not available")
@@ -130,45 +132,36 @@ def test_resample(self):
 
 
 @unittest.skipIf(not LIBROSA_AVAILABLE, "Librosa not available")
-class TestPhaseVocoder(common_utils.TorchaudioTestCase):
-    @parameterized.expand(list(itertools.product(
-        [(2, 1025, 400, 2)],
+class TestFunctionalComplex(common_utils.TorchaudioTestCase):
+    @nested_params(
         [0.5, 1.01, 1.3],
-        [256]
-    )))
-    def test_phase_vocoder(self, shape, rate, hop_length):
+        [True, False],
+    )
+    def test_phase_vocoder(self, rate, test_pseudo_complex):
+        hop_length = 256
+        num_freq = 1025
+        num_frames = 400
+        torch.random.manual_seed(42)
+
         # Due to cummulative sum, numerical error in using torch.float32 will
         # result in bottom right values of the stretched sectrogram to not
         # match with librosa.
-        torch.random.manual_seed(42)
-        complex_specgrams = torch.randn(*shape)
-        complex_specgrams = complex_specgrams.type(torch.float64)
+        spec = torch.randn(num_freq, num_frames, dtype=torch.complex128)
         phase_advance = torch.linspace(
             0,
             np.pi * hop_length,
-            complex_specgrams.shape[-3],
+            num_freq,
             dtype=torch.float64)[..., None]
 
-        complex_specgrams_stretch = F.phase_vocoder(complex_specgrams, rate=rate, phase_advance=phase_advance)
+        stretched = F.phase_vocoder(
+            torch.view_as_real(spec) if test_pseudo_complex else spec,
+            rate=rate, phase_advance=phase_advance)
 
-        # == Test shape
-        expected_size = list(complex_specgrams.size())
-        expected_size[-2] = int(np.ceil(expected_size[-2] / rate))
-
-        assert complex_specgrams.dim() == complex_specgrams_stretch.dim()
-        assert complex_specgrams_stretch.size() == torch.Size(expected_size)
-
-        # == Test values
-        index = [0] * (complex_specgrams.dim() - 3) + [slice(None)] * 3
-        mono_complex_specgram = complex_specgrams[index].numpy()
-        mono_complex_specgram = mono_complex_specgram[..., 0] + \
-            mono_complex_specgram[..., 1] * 1j
-        expected_complex_stretch = librosa.phase_vocoder(
-            mono_complex_specgram,
+        expected_stretched = librosa.phase_vocoder(
+            spec.numpy(),
             rate=rate,
             hop_length=hop_length)
 
-        complex_stretch = complex_specgrams_stretch[index].numpy()
-        complex_stretch = complex_stretch[..., 0] + 1j * complex_stretch[..., 1]
-
-        self.assertEqual(complex_stretch, torch.from_numpy(expected_complex_stretch), atol=1e-5, rtol=1e-5)
+        self.assertEqual(
+            torch.view_as_complex(stretched) if test_pseudo_complex else stretched,
+            torch.from_numpy(expected_stretched))
diff --git a/test/torchaudio_unittest/functional/torchscript_consistency_cpu_test.py b/test/torchaudio_unittest/functional/torchscript_consistency_cpu_test.py
index 06871f9bde..d9d34eff76 100644
--- a/test/torchaudio_unittest/functional/torchscript_consistency_cpu_test.py
+++ b/test/torchaudio_unittest/functional/torchscript_consistency_cpu_test.py
@@ -1,7 +1,7 @@
 import torch
 
 from torchaudio_unittest.common_utils import PytorchTestCase
-from .torchscript_consistency_impl import Functional
+from .torchscript_consistency_impl import Functional, FunctionalComplex
 
 
 class TestFunctionalFloat32(Functional, PytorchTestCase):
@@ -12,3 +12,15 @@ class TestFunctionalFloat32(Functional, PytorchTestCase):
 class TestFunctionalFloat64(Functional, PytorchTestCase):
     dtype = torch.float64
     device = torch.device('cpu')
+
+
+class TestFunctionalComplex64(FunctionalComplex, PytorchTestCase):
+    complex_dtype = torch.complex64
+    real_dtype = torch.float32
+    device = torch.device('cpu')
+
+
+class TestFunctionalComplex128(FunctionalComplex, PytorchTestCase):
+    complex_dtype = torch.complex128
+    real_dtype = torch.float64
+    device = torch.device('cpu')
diff --git a/test/torchaudio_unittest/functional/torchscript_consistency_cuda_test.py b/test/torchaudio_unittest/functional/torchscript_consistency_cuda_test.py
index 53ccbad3c9..026e09abfa 100644
--- a/test/torchaudio_unittest/functional/torchscript_consistency_cuda_test.py
+++ b/test/torchaudio_unittest/functional/torchscript_consistency_cuda_test.py
@@ -1,7 +1,7 @@
 import torch
 
 from torchaudio_unittest.common_utils import skipIfNoCuda, PytorchTestCase
-from .torchscript_consistency_impl import Functional
+from .torchscript_consistency_impl import Functional, FunctionalComplex
 
 
 @skipIfNoCuda
@@ -14,3 +14,17 @@ class TestFunctionalFloat32(Functional, PytorchTestCase):
 class TestFunctionalFloat64(Functional, PytorchTestCase):
     dtype = torch.float64
     device = torch.device('cuda')
+
+
+@skipIfNoCuda
+class TestFunctionalComplex64(FunctionalComplex, PytorchTestCase):
+    complex_dtype = torch.complex64
+    real_dtype = torch.float32
+    device = torch.device('cuda')
+
+
+@skipIfNoCuda
+class TestFunctionalComplex128(FunctionalComplex, PytorchTestCase):
+    complex_dtype = torch.complex128
+    real_dtype = torch.float64
+    device = torch.device('cuda')
diff --git a/test/torchaudio_unittest/functional/torchscript_consistency_impl.py b/test/torchaudio_unittest/functional/torchscript_consistency_impl.py
index b6aec04d9c..46d1a98233 100644
--- a/test/torchaudio_unittest/functional/torchscript_consistency_impl.py
+++ b/test/torchaudio_unittest/functional/torchscript_consistency_impl.py
@@ -3,6 +3,7 @@
 
 import torch
 import torchaudio.functional as F
+from parameterized import parameterized
 
 from torchaudio_unittest import common_utils
 
@@ -547,21 +548,6 @@ def func(tensor):
         tensor = common_utils.get_whitenoise(sample_rate=44100)
         self._assert_consistency(func, tensor)
 
-    def test_phase_vocoder(self):
-        def func(tensor, device: torch.device = self.device):
-            rate = 0.5
-            hop_length = 256
-            phase_advance = torch.linspace(
-                0,
-                3.14 * hop_length,
-                tensor.shape[-3],
-                dtype=torch.float64,
-            ).to(device)[..., None]
-            return F.phase_vocoder(tensor, rate, phase_advance)
-
-        tensor = torch.randn(2, 1025, 400, 2)
-        self._assert_consistency(func, tensor)
-
     @common_utils.skipIfNoKaldi
     def test_compute_kaldi_pitch(self):
         if self.dtype != torch.float32 or self.device != torch.device('cpu'):
@@ -573,3 +559,40 @@ def func(tensor):
 
         tensor = common_utils.get_whitenoise(sample_rate=44100)
         self._assert_consistency(func, tensor)
+
+
+class FunctionalComplex:
+    complex_dtype = None
+    real_dtype = None
+    device = None
+
+    def _assert_consistency(self, func, tensor, test_pseudo_complex=False):
+        assert tensor.is_complex()
+        tensor = tensor.to(device=self.device, dtype=self.complex_dtype)
+        ts_func = torch.jit.script(func)
+
+        if test_pseudo_complex:
+            tensor = torch.view_as_real(tensor)
+        output = func(tensor)
+        ts_output = ts_func(tensor)
+        self.assertEqual(ts_output, output)
+
+    @parameterized.expand([(True, ), (False, )])
+    def test_phase_vocoder(self, test_paseudo_complex):
+        def func(tensor):
+            is_complex = tensor.is_complex()
+
+            n_freq = tensor.size(-2 if is_complex else -3)
+            rate = 0.5
+            hop_length = 256
+            phase_advance = torch.linspace(
+                0,
+                3.14 * hop_length,
+                n_freq,
+                dtype=(torch.real(tensor) if is_complex else tensor).dtype,
+                device=tensor.device,
+            )[..., None]
+            return F.phase_vocoder(tensor, rate, phase_advance)
+
+        tensor = torch.view_as_complex(torch.randn(2, 1025, 400, 2))
+        self._assert_consistency(func, tensor, test_paseudo_complex)
diff --git a/test/torchaudio_unittest/transforms/batch_consistency_test.py b/test/torchaudio_unittest/transforms/batch_consistency_test.py
index 745401c328..cab68e0152 100644
--- a/test/torchaudio_unittest/transforms/batch_consistency_test.py
+++ b/test/torchaudio_unittest/transforms/batch_consistency_test.py
@@ -1,6 +1,7 @@
 """Test numerical consistency among single input and batched input."""
 import torch
 import torchaudio
+from parameterized import parameterized
 
 from torchaudio_unittest import common_utils
 
@@ -130,40 +131,31 @@ def test_batch_mfcc(self):
         computed = torchaudio.transforms.MFCC()(waveform.repeat(3, 1, 1))
         self.assertEqual(computed, expected, atol=1e-4, rtol=1e-5)
 
-    def test_batch_TimeStretch(self):
-        test_filepath = common_utils.get_asset_path('steam-train-whistle-daniel_simon.wav')
-        waveform, _ = torchaudio.load(test_filepath)  # (2, 278756), 44100
-
+    @parameterized.expand([(True, ), (False, )])
+    def test_batch_TimeStretch(self, test_pseudo_complex):
         rate = 2
+        num_freq = 1025
+        num_frames = 400
 
-        complex_specgrams = torch.view_as_real(
-            torch.stft(
-                input=waveform,
-                n_fft=2048,
-                hop_length=512,
-                win_length=2048,
-                window=torch.hann_window(2048),
-                center=True,
-                pad_mode='reflect',
-                normalized=True,
-                onesided=True,
-                return_complex=True,
-            )
-        )
+        spec = torch.randn(num_freq, num_frames, dtype=torch.complex64)
+        pattern = [3, 1, 1, 1]
+        if test_pseudo_complex:
+            spec = torch.view_as_real(spec)
+            pattern += [1]
 
         # Single then transform then batch
         expected = torchaudio.transforms.TimeStretch(
             fixed_rate=rate,
-            n_freq=1025,
+            n_freq=num_freq,
             hop_length=512,
-        )(complex_specgrams).repeat(3, 1, 1, 1, 1)
+        )(spec).repeat(*pattern)
 
         # Batch then transform
         computed = torchaudio.transforms.TimeStretch(
             fixed_rate=rate,
-            n_freq=1025,
+            n_freq=num_freq,
             hop_length=512,
-        )(complex_specgrams.repeat(3, 1, 1, 1, 1))
+        )(spec.repeat(*pattern))
 
         self.assertEqual(computed, expected, atol=1e-5, rtol=1e-5)
 
diff --git a/test/torchaudio_unittest/transforms/torchscript_consistency_cpu_test.py b/test/torchaudio_unittest/transforms/torchscript_consistency_cpu_test.py
index 9092f3a64b..4de32a57bb 100644
--- a/test/torchaudio_unittest/transforms/torchscript_consistency_cpu_test.py
+++ b/test/torchaudio_unittest/transforms/torchscript_consistency_cpu_test.py
@@ -1,7 +1,7 @@
 import torch
 
 from torchaudio_unittest.common_utils import PytorchTestCase
-from .torchscript_consistency_impl import Transforms
+from .torchscript_consistency_impl import Transforms, TransformsComplex
 
 
 class TestTransformsFloat32(Transforms, PytorchTestCase):
@@ -12,3 +12,15 @@ class TestTransformsFloat32(Transforms, PytorchTestCase):
 class TestTransformsFloat64(Transforms, PytorchTestCase):
     dtype = torch.float64
     device = torch.device('cpu')
+
+
+class TestTransformsComplex64(TransformsComplex, PytorchTestCase):
+    complex_dtype = torch.complex64
+    real_dtype = torch.float32
+    device = torch.device('cpu')
+
+
+class TestTransformsComplex128(TransformsComplex, PytorchTestCase):
+    complex_dtype = torch.complex128
+    real_dtype = torch.float64
+    device = torch.device('cpu')
diff --git a/test/torchaudio_unittest/transforms/torchscript_consistency_cuda_test.py b/test/torchaudio_unittest/transforms/torchscript_consistency_cuda_test.py
index 7425647bab..2435b82589 100644
--- a/test/torchaudio_unittest/transforms/torchscript_consistency_cuda_test.py
+++ b/test/torchaudio_unittest/transforms/torchscript_consistency_cuda_test.py
@@ -1,7 +1,7 @@
 import torch
 
 from torchaudio_unittest.common_utils import skipIfNoCuda, PytorchTestCase
-from .torchscript_consistency_impl import Transforms
+from .torchscript_consistency_impl import Transforms, TransformsComplex
 
 
 @skipIfNoCuda
@@ -14,3 +14,17 @@ class TestTransformsFloat32(Transforms, PytorchTestCase):
 class TestTransformsFloat64(Transforms, PytorchTestCase):
     dtype = torch.float64
     device = torch.device('cuda')
+
+
+@skipIfNoCuda
+class TestTransformsComplex64(TransformsComplex, PytorchTestCase):
+    complex_dtype = torch.complex64
+    real_dtype = torch.float32
+    device = torch.device('cuda')
+
+
+@skipIfNoCuda
+class TestTransformsComplex128(TransformsComplex, PytorchTestCase):
+    complex_dtype = torch.complex128
+    real_dtype = torch.float64
+    device = torch.device('cuda')
diff --git a/test/torchaudio_unittest/transforms/torchscript_consistency_impl.py b/test/torchaudio_unittest/transforms/torchscript_consistency_impl.py
index 492e1e4a92..b2117abdb5 100644
--- a/test/torchaudio_unittest/transforms/torchscript_consistency_impl.py
+++ b/test/torchaudio_unittest/transforms/torchscript_consistency_impl.py
@@ -2,6 +2,7 @@
 
 import torch
 import torchaudio.transforms as T
+from parameterized import parameterized
 
 from torchaudio_unittest import common_utils
 
@@ -58,16 +59,6 @@ def test_MuLawDecoding(self):
         tensor = torch.rand((1, 10))
         self._assert_consistency(T.MuLawDecoding(), tensor)
 
-    def test_TimeStretch(self):
-        n_freq = 400
-        hop_length = 512
-        fixed_rate = 1.3
-        tensor = torch.rand((10, 2, n_freq, 10, 2))
-        self._assert_consistency(
-            T.TimeStretch(n_freq=n_freq, hop_length=hop_length, fixed_rate=fixed_rate),
-            tensor,
-        )
-
     def test_Fade(self):
         waveform = common_utils.get_whitenoise()
         fade_in_len = 3000
@@ -99,3 +90,34 @@ def test_SpectralCentroid(self):
         sample_rate = 44100
         waveform = common_utils.get_whitenoise(sample_rate=sample_rate)
         self._assert_consistency(T.SpectralCentroid(sample_rate=sample_rate), waveform)
+
+
+class TransformsComplex:
+    complex_dtype = None
+    real_dtype = None
+    device = None
+
+    def _assert_consistency(self, transform, tensor, test_pseudo_complex=False):
+        assert tensor.is_complex()
+        tensor = tensor.to(device=self.device, dtype=self.complex_dtype)
+        transform = transform.to(device=self.device, dtype=self.real_dtype)
+        ts_transform = torch.jit.script(transform)
+
+        if test_pseudo_complex:
+            tensor = torch.view_as_real(tensor)
+
+        output = transform(tensor)
+        ts_output = ts_transform(tensor)
+        self.assertEqual(ts_output, output)
+
+    @parameterized.expand([(True, ), (False, )])
+    def test_TimeStretch(self, test_pseudo_complex):
+        n_freq = 400
+        hop_length = 512
+        fixed_rate = 1.3
+        tensor = torch.view_as_complex(torch.rand((10, 2, n_freq, 10, 2)))
+        self._assert_consistency(
+            T.TimeStretch(n_freq=n_freq, hop_length=hop_length, fixed_rate=fixed_rate),
+            tensor,
+            test_pseudo_complex
+        )
diff --git a/torchaudio/functional/functional.py b/torchaudio/functional/functional.py
index 73496bf4cc..a26d7ab7fe 100644
--- a/torchaudio/functional/functional.py
+++ b/torchaudio/functional/functional.py
@@ -565,14 +565,29 @@ def phase_vocoder(
     factor of ``rate``.
 
     Args:
-        complex_specgrams (Tensor): Dimension of `(..., freq, time, complex=2)`
+        complex_specgrams (Tensor):
+            Either a real tensor of dimension of ``(..., freq, num_frame, complex=2)``
+            or a tensor of dimension ``(..., freq, num_frame)`` with complex dtype.
         rate (float): Speed-up factor
         phase_advance (Tensor): Expected phase advance in each bin. Dimension of (freq, 1)
 
     Returns:
-        Tensor: Complex Specgrams Stretch with dimension of `(..., freq, ceil(time/rate), complex=2)`
+        Tensor:
+            Stretched spectrogram. The resulting tensor is of the same dtype as the input
+            spectrogram, but the number of frames is changed to ``ceil(num_frame / rate)``.
 
-    Example
+    Example - With Tensor of complex dtype
+        >>> freq, hop_length = 1025, 512
+        >>> # (channel, freq, time)
+        >>> complex_specgrams = torch.randn(2, freq, 300, dtype=torch.cfloat)
+        >>> rate = 1.3 # Speed up by 30%
+        >>> phase_advance = torch.linspace(
+        >>>    0, math.pi * hop_length, freq)[..., None]
+        >>> x = phase_vocoder(complex_specgrams, rate, phase_advance)
+        >>> x.shape # with 231 == ceil(300 / 1.3)
+        torch.Size([2, 1025, 231])
+
+    Example - With Tensor of real dtype and extra dimension for complex field
         >>> freq, hop_length = 1025, 512
         >>> # (channel, freq, time, complex=2)
         >>> complex_specgrams = torch.randn(2, freq, 300, 2)
@@ -583,32 +598,48 @@ def phase_vocoder(
         >>> x.shape # with 231 == ceil(300 / 1.3)
         torch.Size([2, 1025, 231, 2])
     """
+    if rate == 1.0:
+        return complex_specgrams
+
+    if not complex_specgrams.is_complex() and complex_specgrams.size(-1) != 2:
+        raise ValueError(
+            "complex_specgrams must be either native complex tensors or "
+            "real valued tensors with shape (..., 2)")
+
+    is_complex = complex_specgrams.is_complex()
+
+    if not is_complex:
+        complex_specgrams = torch.view_as_complex(complex_specgrams)
 
     # pack batch
     shape = complex_specgrams.size()
-    complex_specgrams = complex_specgrams.reshape([-1] + list(shape[-3:]))
-
-    time_steps = torch.arange(0,
-                              complex_specgrams.size(-2),
-                              rate,
-                              device=complex_specgrams.device,
-                              dtype=complex_specgrams.dtype)
+    complex_specgrams = complex_specgrams.reshape([-1] + list(shape[-2:]))
+
+    # Figures out the corresponding real dtype, i.e. complex128 -> float64, complex64 -> float32
+    # Note torch.real is a view so it does not incur any memory copy.
+    real_dtype = torch.real(complex_specgrams).dtype
+    time_steps = torch.arange(
+        0,
+        complex_specgrams.size(-1),
+        rate,
+        device=complex_specgrams.device,
+        dtype=real_dtype)
 
     alphas = time_steps % 1.0
-    phase_0 = angle(complex_specgrams[..., :1, :])
+    phase_0 = complex_specgrams[..., :1].angle()
 
     # Time Padding
-    complex_specgrams = torch.nn.functional.pad(complex_specgrams, [0, 0, 0, 2])
+    complex_specgrams = torch.nn.functional.pad(complex_specgrams, [0, 2])
 
     # (new_bins, freq, 2)
-    complex_specgrams_0 = complex_specgrams.index_select(-2, time_steps.long())
-    complex_specgrams_1 = complex_specgrams.index_select(-2, (time_steps + 1).long())
+    complex_specgrams_0 = complex_specgrams.index_select(-1, time_steps.long())
+    complex_specgrams_1 = complex_specgrams.index_select(-1, (time_steps + 1).long())
 
-    angle_0 = angle(complex_specgrams_0)
-    angle_1 = angle(complex_specgrams_1)
+    angle_0 = complex_specgrams_0.angle()
+    angle_1 = complex_specgrams_1.angle()
 
-    norm_0 = torch.norm(complex_specgrams_0, p=2, dim=-1)
-    norm_1 = torch.norm(complex_specgrams_1, p=2, dim=-1)
+    norm_0 = complex_specgrams_0.abs()
+    norm_1 = complex_specgrams_1.abs()
 
     phase = angle_1 - angle_0 - phase_advance
     phase = phase - 2 * math.pi * torch.round(phase / (2 * math.pi))
@@ -620,14 +651,13 @@ def phase_vocoder(
 
     mag = alphas * norm_1 + (1 - alphas) * norm_0
 
-    real_stretch = mag * torch.cos(phase_acc)
-    imag_stretch = mag * torch.sin(phase_acc)
-
-    complex_specgrams_stretch = torch.stack([real_stretch, imag_stretch], dim=-1)
+    complex_specgrams_stretch = torch.polar(mag, phase_acc)
 
     # unpack batch
-    complex_specgrams_stretch = complex_specgrams_stretch.reshape(shape[:-3] + complex_specgrams_stretch.shape[1:])
+    complex_specgrams_stretch = complex_specgrams_stretch.reshape(shape[:-2] + complex_specgrams_stretch.shape[1:])
 
+    if not is_complex:
+        return torch.view_as_real(complex_specgrams_stretch)
     return complex_specgrams_stretch
 
 
diff --git a/torchaudio/transforms.py b/torchaudio/transforms.py
index 6f3ea1b6e1..e5dd5b2210 100644
--- a/torchaudio/transforms.py
+++ b/torchaudio/transforms.py
@@ -729,26 +729,24 @@ def __init__(self,
     def forward(self, complex_specgrams: Tensor, overriding_rate: Optional[float] = None) -> Tensor:
         r"""
         Args:
-            complex_specgrams (Tensor): complex spectrogram (..., freq, time, complex=2).
+            complex_specgrams (Tensor):
+                Either a real tensor of dimension of ``(..., freq, num_frame, complex=2)``
+                or a tensor of dimension ``(..., freq, num_frame)`` with complex dtype.
             overriding_rate (float or None, optional): speed up to apply to this batch.
                 If no rate is passed, use ``self.fixed_rate``. (Default: ``None``)
 
         Returns:
-            Tensor: Stretched complex spectrogram of dimension (..., freq, ceil(time/rate), complex=2).
+            Tensor:
+                Stretched spectrogram. The resulting tensor is of the same dtype as the input
+                spectrogram, but the number of frames is changed to ``ceil(num_frame / rate)``.
         """
-        assert complex_specgrams.size(-1) == 2, "complex_specgrams should be a complex tensor, shape (..., complex=2)"
-
         if overriding_rate is None:
+            if self.fixed_rate is None:
+                raise ValueError(
+                    "If no fixed_rate is specified, must pass a valid rate to the forward method.")
             rate = self.fixed_rate
-            if rate is None:
-                raise ValueError("If no fixed_rate is specified"
-                                 ", must pass a valid rate to the forward method.")
         else:
             rate = overriding_rate
-
-        if rate == 1.0:
-            return complex_specgrams
-
         return F.phase_vocoder(complex_specgrams, rate, self.phase_advance)