# Copyright 2017 The TensorFlow Authors. All Rights Reserved. # # Licensed under the Apache License, Version 2.0 (the "License"); # you may not use this file except in compliance with the License. # You may obtain a copy of the License at # # http://www.apache.org/licenses/LICENSE-2.0 # # Unless required by applicable law or agreed to in writing, software # distributed under the License is distributed on an "AS IS" BASIS, # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. # See the License for the specific language governing permissions and # limitations under the License. # ============================================================================== """Spectral operators (e.g. DCT, FFT, RFFT).""" from __future__ import absolute_import from __future__ import division from __future__ import print_function import math as _math from tensorflow.python.framework import dtypes as _dtypes from tensorflow.python.framework import ops as _ops from tensorflow.python.framework import tensor_util as _tensor_util from tensorflow.python.ops import array_ops as _array_ops from tensorflow.python.ops import gen_spectral_ops from tensorflow.python.ops import math_ops as _math_ops from tensorflow.python.util.tf_export import tf_export def _infer_fft_length_for_rfft(input_tensor, fft_rank): """Infers the `fft_length` argument for a `rank` RFFT from `input_tensor`.""" # A TensorShape for the inner fft_rank dimensions. fft_shape = input_tensor.get_shape()[-fft_rank:] # If any dim is unknown, fall back to tensor-based math. if not fft_shape.is_fully_defined(): return _array_ops.shape(input_tensor)[-fft_rank:] # Otherwise, return a constant. return _ops.convert_to_tensor(fft_shape.as_list(), _dtypes.int32) def _infer_fft_length_for_irfft(input_tensor, fft_rank): """Infers the `fft_length` argument for a `rank` IRFFT from `input_tensor`.""" # A TensorShape for the inner fft_rank dimensions. fft_shape = input_tensor.get_shape()[-fft_rank:] # If any dim is unknown, fall back to tensor-based math. if not fft_shape.is_fully_defined(): fft_length = _array_ops.unstack(_array_ops.shape(input_tensor)[-fft_rank:]) fft_length[-1] = _math_ops.maximum(0, 2 * (fft_length[-1] - 1)) return _array_ops.stack(fft_length) # Otherwise, return a constant. fft_length = fft_shape.as_list() if fft_length: fft_length[-1] = max(0, 2 * (fft_length[-1] - 1)) return _ops.convert_to_tensor(fft_length, _dtypes.int32) def _maybe_pad_for_rfft(input_tensor, fft_rank, fft_length, is_reverse=False): """Pads `input_tensor` to `fft_length` on its inner-most `fft_rank` dims.""" fft_shape = _tensor_util.constant_value_as_shape(fft_length) # Edge case: skip padding empty tensors. if (input_tensor.shape.ndims is not None and any(dim.value == 0 for dim in input_tensor.shape)): return input_tensor # If we know the shapes ahead of time, we can either skip or pre-compute the # appropriate paddings. Otherwise, fall back to computing paddings in # TensorFlow. if fft_shape.is_fully_defined() and input_tensor.shape.ndims is not None: # Slice the last FFT-rank dimensions from input_tensor's shape. input_fft_shape = input_tensor.shape[-fft_shape.ndims:] if input_fft_shape.is_fully_defined(): # In reverse, we only pad the inner-most dimension to fft_length / 2 + 1. if is_reverse: fft_shape = fft_shape[:-1].concatenate(fft_shape[-1].value // 2 + 1) paddings = [[0, max(fft_dim.value - input_dim.value, 0)] for fft_dim, input_dim in zip(fft_shape, input_fft_shape)] if any(pad > 0 for _, pad in paddings): outer_paddings = [[0, 0]] * max((input_tensor.shape.ndims - fft_shape.ndims), 0) return _array_ops.pad(input_tensor, outer_paddings + paddings) return input_tensor # If we can't determine the paddings ahead of time, then we have to pad. If # the paddings end up as zero, tf.pad has a special-case that does no work. input_rank = _array_ops.rank(input_tensor) input_fft_shape = _array_ops.shape(input_tensor)[-fft_rank:] outer_dims = _math_ops.maximum(0, input_rank - fft_rank) outer_paddings = _array_ops.zeros([outer_dims], fft_length.dtype) # In reverse, we only pad the inner-most dimension to fft_length / 2 + 1. if is_reverse: fft_length = _array_ops.concat([fft_length[:-1], fft_length[-1:] // 2 + 1], 0) fft_paddings = _math_ops.maximum(0, fft_length - input_fft_shape) paddings = _array_ops.concat([outer_paddings, fft_paddings], 0) paddings = _array_ops.stack([_array_ops.zeros_like(paddings), paddings], axis=1) return _array_ops.pad(input_tensor, paddings) def _rfft_wrapper(fft_fn, fft_rank, default_name): """Wrapper around gen_spectral_ops.rfft* that infers fft_length argument.""" def _rfft(input_tensor, fft_length=None, name=None): with _ops.name_scope(name, default_name, [input_tensor, fft_length]) as name: input_tensor = _ops.convert_to_tensor(input_tensor, _dtypes.float32) input_tensor.shape.with_rank_at_least(fft_rank) if fft_length is None: fft_length = _infer_fft_length_for_rfft(input_tensor, fft_rank) else: fft_length = _ops.convert_to_tensor(fft_length, _dtypes.int32) input_tensor = _maybe_pad_for_rfft(input_tensor, fft_rank, fft_length) return fft_fn(input_tensor, fft_length, name) _rfft.__doc__ = fft_fn.__doc__ return _rfft def _irfft_wrapper(ifft_fn, fft_rank, default_name): """Wrapper around gen_spectral_ops.irfft* that infers fft_length argument.""" def _irfft(input_tensor, fft_length=None, name=None): with _ops.name_scope(name, default_name, [input_tensor, fft_length]) as name: input_tensor = _ops.convert_to_tensor(input_tensor, _dtypes.complex64) input_tensor.shape.with_rank_at_least(fft_rank) if fft_length is None: fft_length = _infer_fft_length_for_irfft(input_tensor, fft_rank) else: fft_length = _ops.convert_to_tensor(fft_length, _dtypes.int32) input_tensor = _maybe_pad_for_rfft(input_tensor, fft_rank, fft_length, is_reverse=True) return ifft_fn(input_tensor, fft_length, name) _irfft.__doc__ = ifft_fn.__doc__ return _irfft fft = gen_spectral_ops.fft ifft = gen_spectral_ops.ifft fft2d = gen_spectral_ops.fft2d ifft2d = gen_spectral_ops.ifft2d fft3d = gen_spectral_ops.fft3d ifft3d = gen_spectral_ops.ifft3d rfft = _rfft_wrapper(gen_spectral_ops.rfft, 1, "rfft") tf_export("spectral.rfft")(rfft) irfft = _irfft_wrapper(gen_spectral_ops.irfft, 1, "irfft") tf_export("spectral.irfft")(irfft) rfft2d = _rfft_wrapper(gen_spectral_ops.rfft2d, 2, "rfft2d") tf_export("spectral.rfft2d")(rfft2d) irfft2d = _irfft_wrapper(gen_spectral_ops.irfft2d, 2, "irfft2d") tf_export("spectral.irfft2d")(irfft2d) rfft3d = _rfft_wrapper(gen_spectral_ops.rfft3d, 3, "rfft3d") tf_export("spectral.rfft3d")(rfft3d) irfft3d = _irfft_wrapper(gen_spectral_ops.irfft3d, 3, "irfft3d") tf_export("spectral.irfft3d")(irfft3d) def _validate_dct_arguments(dct_type, n, axis, norm): if n is not None: raise NotImplementedError("The DCT length argument is not implemented.") if axis != -1: raise NotImplementedError("axis must be -1. Got: %s" % axis) 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) # TODO(rjryan): Implement `type`, `n` and `axis` parameters. @tf_export("spectral.dct") 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 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 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 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 `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 """ _validate_dct_arguments(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 = input.shape[-1].value or _array_ops.shape(input)[-1] axis_dim_float = _math_ops.to_float(axis_dim) 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)