def stft(signals, frame_length, frame_step, fft_length=None,
window_fn=window_ops.hann_window,
pad_end=False, name=None):
"""Computes the [Short-time Fourier Transform][stft] of `signals`.
Implemented with TPU/GPU-compatible ops and supports gradients.
Args:
signals: A `[..., samples]` `float32`/`float64` `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`/`complex128`
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
# fft_ops.rfft produces the (fft_length/2 + 1) unique components of the
# FFT of the real windowed signals in framed_signals.
return fft_ops.rfft(framed_signals, [fft_length])
def stft(signals, frame_length, frame_step, fft_length=None,
window_fn=window_ops.hann_window,
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
# fft_ops.rfft produces the (fft_length/2 + 1) unique components of the
# FFT of the real windowed signals in framed_signals.
return fft_ops.rfft(framed_signals, [fft_length])
def dct(input, type=2, n=None, axis=-1, norm=None, name=None): # pylint: disable=redefined-builtin
"""Computes the 1D [Discrete Cosine Transform (DCT)][dct] of `input`.
Types I, II, III and IV are supported.
Type I is implemented using a length `2N` padded `tf.signal.rfft`.
Type II is implemented using a length `2N` padded `tf.signal.rfft`, as
described here: [Type 2 DCT using 2N FFT padded (Makhoul)]
(https://dsp.stackexchange.com/a/10606).
Type III is a fairly straightforward inverse of Type II
(i.e. using a length `2N` padded `tf.signal.irfft`).
Type IV is calculated through 2N length DCT2 of padded signal and
picking the odd indices.
@compatibility(scipy)
Equivalent to [scipy.fftpack.dct]
(https://docs.scipy.org/doc/scipy-1.4.0/reference/generated/scipy.fftpack.dct.html)
for Type-I, Type-II, Type-III and Type-IV DCT.
@end_compatibility
Args:
input: A `[..., samples]` `float32`/`float64` `Tensor` containing the
signals to take the DCT of.
type: The DCT type to perform. Must be 1, 2, 3 or 4.
n: The length of the transform. If length is less than sequence length,
only the first n elements of the sequence are considered for the DCT.
If n is greater than the sequence length, zeros are padded and then
the DCT is computed as usual.
axis: For future expansion. The axis to compute the DCT along. Must be `-1`.
norm: The normalization to apply. `None` for no normalization or `'ortho'`
for orthonormal normalization.
name: An optional name for the operation.
Returns:
A `[..., samples]` `float32`/`float64` `Tensor` containing the DCT of
`input`.
Raises:
ValueError: If `type` is not `1`, `2`, `3` or `4`, `axis` is
not `-1`, `n` is not `None` or greater than 0,
or `norm` is not `None` or `'ortho'`.
ValueError: If `type` is `1` and `norm` is `ortho`.
[dct]: https://en.wikipedia.org/wiki/Discrete_cosine_transform
"""
_validate_dct_arguments(input, type, n, axis, norm)
with _ops.name_scope(name, "dct", [input]):
input = _ops.convert_to_tensor(input)
zero = _ops.convert_to_tensor(0.0, dtype=input.dtype)
seq_len = (tensor_shape.dimension_value(input.shape[-1])
or _array_ops.shape(input)[-1])
if n is not None:
if n <= seq_len:
input = input[..., 0:n]
else:
rank = len(input.shape)
padding = [[0, 0] for _ in range(rank)]
padding[rank - 1][1] = n - seq_len
padding = _ops.convert_to_tensor(padding, dtype=_dtypes.int32)
input = _array_ops.pad(input, paddings=padding)
axis_dim = (tensor_shape.dimension_value(input.shape[-1])
or _array_ops.shape(input)[-1])
axis_dim_float = _math_ops.cast(axis_dim, input.dtype)
if type == 1:
dct1_input = _array_ops.concat([input, input[..., -2:0:-1]],
axis=-1)
dct1 = _math_ops.real(fft_ops.rfft(dct1_input))
return dct1
if type == 2:
scale = 2.0 * _math_ops.exp(
_math_ops.complex(
zero, -_math_ops.range(axis_dim_float) * _math.pi * 0.5 /
axis_dim_float))
# TODO(rjryan): Benchmark performance and memory usage of the various
# approaches to computing a DCT via the RFFT.
dct2 = _math_ops.real(
fft_ops.rfft(input, fft_length=[2 * axis_dim])[..., :axis_dim]
* scale)
if norm == "ortho":
n1 = 0.5 * _math_ops.rsqrt(axis_dim_float)
n2 = n1 * _math.sqrt(2.0)
# Use tf.pad to make a vector of [n1, n2, n2, n2, ...].
weights = _array_ops.pad(_array_ops.expand_dims(n1, 0),
[[0, axis_dim - 1]],
constant_values=n2)
dct2 *= weights
return dct2
elif type == 3:
if norm == "ortho":
n1 = _math_ops.sqrt(axis_dim_float)
n2 = n1 * _math.sqrt(0.5)
# Use tf.pad to make a vector of [n1, n2, n2, n2, ...].
weights = _array_ops.pad(_array_ops.expand_dims(n1, 0),
[[0, axis_dim - 1]],
constant_values=n2)
input *= weights
else:
input *= axis_dim_float
scale = 2.0 * _math_ops.exp(
_math_ops.complex(
zero,
_math_ops.range(axis_dim_float) * _math.pi * 0.5 /
axis_dim_float))
dct3 = _math_ops.real(
fft_ops.irfft(scale * _math_ops.complex(input, zero),
fft_length=[2 * axis_dim]))[..., :axis_dim]
return dct3
elif type == 4:
# DCT-2 of 2N length zero-padded signal, unnormalized.
dct2 = dct(input, type=2, n=2 * axis_dim, axis=axis, norm=None)
# Get odd indices of DCT-2 of zero padded 2N signal to obtain
# DCT-4 of the original N length signal.
dct4 = dct2[..., 1::2]
if norm == "ortho":
dct4 *= _math.sqrt(0.5) * _math_ops.rsqrt(axis_dim_float)
return dct4
def rfft(input_tensor, fft_length=None, name=None):
return fft_ops.rfft(input_tensor, fft_length, name)
def dct(input, type=2, n=None, axis=-1, norm=None, name=None): # pylint: disable=redefined-builtin
"""Computes the 1D [Discrete Cosine Transform (DCT)][dct] of `input`.
Currently only Types I, II and III are supported.
Type I is implemented using a length `2N` padded `tf.spectral.rfft`.
Type II is implemented using a length `2N` padded `tf.spectral.rfft`, as
described here:
https://dsp.stackexchange.com/a/10606.
Type III is a fairly straightforward inverse of Type II
(i.e. using a length `2N` padded `tf.spectral.irfft`).
@compatibility(scipy)
Equivalent to scipy.fftpack.dct for Type-I, Type-II and Type-III DCT.
https://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.fftpack.dct.html
@end_compatibility
Args:
input: A `[..., samples]` `float32` `Tensor` containing the signals to
take the DCT of.
type: The DCT type to perform. Must be 1, 2 or 3.
n: For future expansion. The length of the transform. Must be `None`.
axis: For future expansion. The axis to compute the DCT along. Must be `-1`.
norm: The normalization to apply. `None` for no normalization or `'ortho'`
for orthonormal normalization.
name: An optional name for the operation.
Returns:
A `[..., samples]` `float32` `Tensor` containing the DCT of `input`.
Raises:
ValueError: If `type` is not `1`, `2` or `3`, `n` is not `None, `axis` is
not `-1`, or `norm` is not `None` or `'ortho'`.
ValueError: If `type` is `1` and `norm` is `ortho`.
[dct]: https://en.wikipedia.org/wiki/Discrete_cosine_transform
"""
_validate_dct_arguments(input, type, n, axis, norm)
with _ops.name_scope(name, "dct", [input]):
# We use the RFFT to compute the DCT and TensorFlow only supports float32
# for FFTs at the moment.
input = _ops.convert_to_tensor(input, dtype=_dtypes.float32)
axis_dim = (tensor_shape.dimension_value(input.shape[-1])
or _array_ops.shape(input)[-1])
axis_dim_float = _math_ops.to_float(axis_dim)
if type == 1:
dct1_input = _array_ops.concat([input, input[..., -2:0:-1]], axis=-1)
dct1 = _math_ops.real(fft_ops.rfft(dct1_input))
return dct1
if type == 2:
scale = 2.0 * _math_ops.exp(
_math_ops.complex(
0.0, -_math_ops.range(axis_dim_float) * _math.pi * 0.5 /
axis_dim_float))
# TODO(rjryan): Benchmark performance and memory usage of the various
# approaches to computing a DCT via the RFFT.
dct2 = _math_ops.real(
fft_ops.rfft(
input, fft_length=[2 * axis_dim])[..., :axis_dim] * scale)
if norm == "ortho":
n1 = 0.5 * _math_ops.rsqrt(axis_dim_float)
n2 = n1 * _math_ops.sqrt(2.0)
# Use tf.pad to make a vector of [n1, n2, n2, n2, ...].
weights = _array_ops.pad(
_array_ops.expand_dims(n1, 0), [[0, axis_dim - 1]],
constant_values=n2)
dct2 *= weights
return dct2
elif type == 3:
if norm == "ortho":
n1 = _math_ops.sqrt(axis_dim_float)
n2 = n1 * _math_ops.sqrt(0.5)
# Use tf.pad to make a vector of [n1, n2, n2, n2, ...].
weights = _array_ops.pad(
_array_ops.expand_dims(n1, 0), [[0, axis_dim - 1]],
constant_values=n2)
input *= weights
else:
input *= axis_dim_float
scale = 2.0 * _math_ops.exp(
_math_ops.complex(
0.0,
_math_ops.range(axis_dim_float) * _math.pi * 0.5 /
axis_dim_float))
dct3 = _math_ops.real(
fft_ops.irfft(
scale * _math_ops.complex(input, 0.0),
fft_length=[2 * axis_dim]))[..., :axis_dim]
return dct3
def dct(input, type=2, n=None, axis=-1, norm=None, name=None): # pylint: disable=redefined-builtin
"""Computes the 1D [Discrete Cosine Transform (DCT)][dct] of `input`.
Currently only Types I, II and III are supported.
Type I is implemented using a length `2N` padded `tf.spectral.rfft`.
Type II is implemented using a length `2N` padded `tf.spectral.rfft`, as
described here:
https://dsp.stackexchange.com/a/10606.
Type III is a fairly straightforward inverse of Type II
(i.e. using a length `2N` padded `tf.spectral.irfft`).
@compatibility(scipy)
Equivalent to scipy.fftpack.dct for Type-I, Type-II and Type-III DCT.
https://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.fftpack.dct.html
@end_compatibility
Args:
input: A `[..., samples]` `float32` `Tensor` containing the signals to
take the DCT of.
type: The DCT type to perform. Must be 1, 2 or 3.
n: For future expansion. The length of the transform. Must be `None`.
axis: For future expansion. The axis to compute the DCT along. Must be `-1`.
norm: The normalization to apply. `None` for no normalization or `'ortho'`
for orthonormal normalization.
name: An optional name for the operation.
Returns:
A `[..., samples]` `float32` `Tensor` containing the DCT of `input`.
Raises:
ValueError: If `type` is not `1`, `2` or `3`, `n` is not `None, `axis` is
not `-1`, or `norm` is not `None` or `'ortho'`.
ValueError: If `type` is `1` and `norm` is `ortho`.
[dct]: https://en.wikipedia.org/wiki/Discrete_cosine_transform
"""
_validate_dct_arguments(input, type, n, axis, norm)
with _ops.name_scope(name, "dct", [input]):
# We use the RFFT to compute the DCT and TensorFlow only supports float32
# for FFTs at the moment.
input = _ops.convert_to_tensor(input, dtype=_dtypes.float32)
axis_dim = (tensor_shape.dimension_value(input.shape[-1])
or _array_ops.shape(input)[-1])
axis_dim_float = _math_ops.to_float(axis_dim)
if type == 1:
dct1_input = _array_ops.concat([input, input[..., -2:0:-1]],
axis=-1)
dct1 = _math_ops.real(fft_ops.rfft(dct1_input))
return dct1
if type == 2:
scale = 2.0 * _math_ops.exp(
_math_ops.complex(
0.0, -_math_ops.range(axis_dim_float) * _math.pi * 0.5 /
axis_dim_float))
# TODO(rjryan): Benchmark performance and memory usage of the various
# approaches to computing a DCT via the RFFT.
dct2 = _math_ops.real(
fft_ops.rfft(input, fft_length=[2 * axis_dim])[..., :axis_dim]
* scale)
if norm == "ortho":
n1 = 0.5 * _math_ops.rsqrt(axis_dim_float)
n2 = n1 * _math_ops.sqrt(2.0)
# Use tf.pad to make a vector of [n1, n2, n2, n2, ...].
weights = _array_ops.pad(_array_ops.expand_dims(n1, 0),
[[0, axis_dim - 1]],
constant_values=n2)
dct2 *= weights
return dct2
elif type == 3:
if norm == "ortho":
n1 = _math_ops.sqrt(axis_dim_float)
n2 = n1 * _math_ops.sqrt(0.5)
# Use tf.pad to make a vector of [n1, n2, n2, n2, ...].
weights = _array_ops.pad(_array_ops.expand_dims(n1, 0),
[[0, axis_dim - 1]],
constant_values=n2)
input *= weights
else:
input *= axis_dim_float
scale = 2.0 * _math_ops.exp(
_math_ops.complex(
0.0,
_math_ops.range(axis_dim_float) * _math.pi * 0.5 /
axis_dim_float))
dct3 = _math_ops.real(
fft_ops.irfft(scale * _math_ops.complex(input, 0.0),
fft_length=[2 * axis_dim]))[..., :axis_dim]
return dct3
