diff options
Diffstat (limited to 'tensorflow/python/ops/spectral_ops.py')
| -rw-r--r-- | tensorflow/python/ops/spectral_ops.py | 125 |
1 files changed, 98 insertions, 27 deletions
diff --git a/tensorflow/python/ops/spectral_ops.py b/tensorflow/python/ops/spectral_ops.py index 28054f50ef..293aace728 100644 --- a/tensorflow/python/ops/spectral_ops.py +++ b/tensorflow/python/ops/spectral_ops.py @@ -167,8 +167,8 @@ def _validate_dct_arguments(dct_type, n, axis, norm): raise NotImplementedError("The DCT length argument is not implemented.") if axis != -1: raise NotImplementedError("axis must be -1. Got: %s" % axis) - if dct_type != 2: - raise ValueError("Only the Type II DCT is supported.") + if dct_type not in (2, 3): + raise ValueError("Only Types II and III (I)DCT are supported.") if norm not in (None, "ortho"): raise ValueError( "Unknown normalization. Expected None or 'ortho', got: %s" % norm) @@ -179,18 +179,20 @@ def _validate_dct_arguments(dct_type, n, axis, norm): 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 Type II is supported. Implemented using a length `2N` padded - @{tf.spectral.rfft}, as described here: https://dsp.stackexchange.com/a/10606 + Currently only Types II and III are supported. 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 the Type-II DCT. + Equivalent to scipy.fftpack.dct for 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 2. + type: The DCT type to perform. Must be 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'` @@ -201,8 +203,8 @@ def dct(input, type=2, n=None, axis=-1, norm=None, name=None): # pylint: disabl A `[..., samples]` `float32` `Tensor` containing the DCT of `input`. Raises: - ValueError: If `type` is not `2`, `n` is not `None, `axis` is not `-1`, or - `norm` is not `None` or `'ortho'`. + ValueError: If `type` is not `2` or `3`, `n` is not `None, `axis` is not + `-1`, or `norm` is not `None` or `'ortho'`. [dct]: https://en.wikipedia.org/wiki/Discrete_cosine_transform """ @@ -214,22 +216,91 @@ def dct(input, type=2, n=None, axis=-1, norm=None, name=None): # pylint: disabl axis_dim = input.shape[-1].value or _array_ops.shape(input)[-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))) - - # TODO(rjryan): Benchmark performance and memory usage of the various - # approaches to computing a DCT via the RFFT. - dct2 = _math_ops.real( - 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 + 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( + 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( + irfft( + scale * _math_ops.complex(input, 0.0), + fft_length=[2 * axis_dim]))[..., :axis_dim] + + return dct3 + + +# TODO(rjryan): Implement `type`, `n` and `axis` parameters. +@tf_export("spectral.idct") +def idct(input, type=2, n=None, axis=-1, norm=None, name=None): # pylint: disable=redefined-builtin + """Computes the 1D [Inverse Discrete Cosine Transform (DCT)][idct] of `input`. + + Currently only Types II and III are supported. Type III is the inverse of + Type II, and vice versa. + + Note that you must re-normalize by 1/(2n) to obtain an inverse if `norm` is + not `'ortho'`. That is: + `signal == idct(dct(signal)) * 0.5 / signal.shape[-1]`. + When `norm='ortho'`, we have: + `signal == idct(dct(signal, norm='ortho'), norm='ortho')`. + + @compatibility(scipy) + Equivalent to scipy.fftpack.idct for Type-II and Type-III DCT. + https://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.fftpack.idct.html + @end_compatibility + + Args: + input: A `[..., samples]` `float32` `Tensor` containing the signals to take + the DCT of. + type: The IDCT type to perform. Must be 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 IDCT of `input`. + + Raises: + ValueError: If `type` is not `2` or `3`, `n` is not `None, `axis` is not + `-1`, or `norm` is not `None` or `'ortho'`. + + [idct]: + https://en.wikipedia.org/wiki/Discrete_cosine_transform#Inverse_transforms + """ + _validate_dct_arguments(type, n, axis, norm) + inverse_type = {2: 3, 3: 2}[type] + return dct(input, type=inverse_type, n=n, axis=axis, norm=norm, name=name) |