def _dct2_1d(signals, name=None):
"""Computes the type II 1D Discrete Cosine Transform (DCT) of `signals`.
Args:
signals: A `[..., samples]` `float32` `Tensor` containing the signals to
take the DCT of.
name: An optional name for the operation.
Returns:
A `[..., samples]` `float32` `Tensor` containing the DCT of `signals`.
"""
with ops.name_scope(name, 'dct', [signals]):
# We use the FFT to compute the DCT and TensorFlow only supports float32 for
# FFTs at the moment.
signals = ops.convert_to_tensor(signals, dtype=dtypes.float32)
axis_dim = signals.shape[-1].value or array_ops.shape(signals)[-1]
axis_dim_float = math_ops.to_float(axis_dim)
scale = 2.0 * math_ops.exp(math_ops.complex(
0.0, -math.pi * math_ops.range(axis_dim_float) /
(2.0 * axis_dim_float)))
rfft = spectral_ops.rfft(signals, fft_length=[2 * axis_dim])[..., :axis_dim]
dct2 = math_ops.real(rfft * scale)
return dct2
def stft(signals, frame_length, frame_step, fft_length=None,
window_fn=functools.partial(window_ops.hann_window, periodic=True),
pad_end=False, name=None):
"""Computes the [Short-time Fourier Transform][stft] of `signals`.
Implemented with GPU-compatible ops and supports gradients.
Args:
signals: A `[..., samples]` `float32` `Tensor` of real-valued signals.
frame_length: An integer scalar `Tensor`. The window length in samples.
frame_step: An integer scalar `Tensor`. The number of samples to step.
fft_length: An integer scalar `Tensor`. The size of the FFT to apply.
If not provided, uses the smallest power of 2 enclosing `frame_length`.
window_fn: A callable that takes a window length and a `dtype` keyword
argument and returns a `[window_length]` `Tensor` of samples in the
provided datatype. If set to `None`, no windowing is used.
pad_end: Whether to pad the end of `signals` with zeros when the provided
frame length and step produces a frame that lies partially past its end.
name: An optional name for the operation.
Returns:
A `[..., frames, fft_unique_bins]` `Tensor` of `complex64` STFT values where
`fft_unique_bins` is `fft_length // 2 + 1` (the unique components of the
FFT).
Raises:
ValueError: If `signals` is not at least rank 1, `frame_length` is
not scalar, or `frame_step` is not scalar.
[stft]: https://en.wikipedia.org/wiki/Short-time_Fourier_transform
"""
with ops.name_scope(name, 'stft', [signals, frame_length,
frame_step]):
signals = ops.convert_to_tensor(signals, name='signals')
signals.shape.with_rank_at_least(1)
frame_length = ops.convert_to_tensor(frame_length, name='frame_length')
frame_length.shape.assert_has_rank(0)
frame_step = ops.convert_to_tensor(frame_step, name='frame_step')
frame_step.shape.assert_has_rank(0)
if fft_length is None:
fft_length = _enclosing_power_of_two(frame_length)
else:
fft_length = ops.convert_to_tensor(fft_length, name='fft_length')
framed_signals = shape_ops.frame(
signals, frame_length, frame_step, pad_end=pad_end)
# Optionally window the framed signals.
if window_fn is not None:
window = window_fn(frame_length, dtype=framed_signals.dtype)
framed_signals *= window
# spectral_ops.rfft produces the (fft_length/2 + 1) unique components of the
# FFT of the real windowed signals in framed_signals.
return spectral_ops.rfft(framed_signals, [fft_length])
def testRFFT(self):
self._VerifyFftMethod(
INNER_DIMS_1D, np.real, lambda x: np.fft.rfft(x, n=x.shape[-1]),
lambda x: spectral_ops.rfft(x, fft_length=[x.shape[-1].value]))
def testRFFT(self):
self._VerifyFftMethod(
INNER_DIMS_1D, np.real, lambda x: np.fft.rfft(x, n=x.shape[-1]),
lambda x: spectral_ops.rfft(x, fft_length=[x.shape[-1].value]))
def stft(signals,
frame_length,
frame_step,
fft_length=None,
window_fn=functools.partial(window_ops.hann_window, periodic=True),
pad_end=False,
name=None):
"""Computes the [Short-time Fourier Transform][stft] of `signals`.
Implemented with GPU-compatible ops and supports gradients.
Args:
signals: A `[..., samples]` `float32` `Tensor` of real-valued signals.
frame_length: An integer scalar `Tensor`. The window length in samples.
frame_step: An integer scalar `Tensor`. The number of samples to step.
fft_length: An integer scalar `Tensor`. The size of the FFT to apply.
If not provided, uses the smallest power of 2 enclosing `frame_length`.
window_fn: A callable that takes a window length and a `dtype` keyword
argument and returns a `[window_length]` `Tensor` of samples in the
provided datatype. If set to `None`, no windowing is used.
pad_end: Whether to pad the end of `signals` with zeros when the provided
frame length and step produces a frame that lies partially past its end.
name: An optional name for the operation.
Returns:
A `[..., frames, fft_unique_bins]` `Tensor` of `complex64` STFT values where
`fft_unique_bins` is `fft_length // 2 + 1` (the unique components of the
FFT).
Raises:
ValueError: If `signals` is not at least rank 1, `frame_length` is
not scalar, or `frame_step` is not scalar.
[stft]: https://en.wikipedia.org/wiki/Short-time_Fourier_transform
"""
with ops.name_scope(name, 'stft', [signals, frame_length, frame_step]):
signals = ops.convert_to_tensor(signals, name='signals')
signals.shape.with_rank_at_least(1)
frame_length = ops.convert_to_tensor(frame_length, name='frame_length')
frame_length.shape.assert_has_rank(0)
frame_step = ops.convert_to_tensor(frame_step, name='frame_step')
frame_step.shape.assert_has_rank(0)
if fft_length is None:
fft_length = _enclosing_power_of_two(frame_length)
else:
fft_length = ops.convert_to_tensor(fft_length, name='fft_length')
framed_signals = shape_ops.frame(signals,
frame_length,
frame_step,
pad_end=pad_end)
# Optionally window the framed signals.
if window_fn is not None:
window = window_fn(frame_length, dtype=framed_signals.dtype)
framed_signals *= window
# spectral_ops.rfft produces the (fft_length/2 + 1) unique components of the
# FFT of the real windowed signals in framed_signals.
return spectral_ops.rfft(framed_signals, [fft_length])