EVOLUTION-MANAGER

Edit File: spectral_ops.py

# 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 operations (e.g. Short-time Fourier Transform).""" from __future__ import absolute_import from __future__ import division from __future__ import print_function import numpy as np from tensorflow.python.framework import constant_op from tensorflow.python.framework import dtypes from tensorflow.python.framework import ops from tensorflow.python.framework import tensor_util from tensorflow.python.ops import array_ops from tensorflow.python.ops import math_ops from tensorflow.python.ops.signal import dct_ops from tensorflow.python.ops.signal import fft_ops from tensorflow.python.ops.signal import reconstruction_ops from tensorflow.python.ops.signal import shape_ops from tensorflow.python.ops.signal import window_ops from tensorflow.python.util import dispatch from tensorflow.python.util.tf_export import tf_export @tf_export('signal.stft') @dispatch.add_dispatch_support 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]) @tf_export('signal.inverse_stft_window_fn') @dispatch.add_dispatch_support def inverse_stft_window_fn(frame_step, forward_window_fn=window_ops.hann_window, name=None): """Generates a window function that can be used in `inverse_stft`. Constructs a window that is equal to the forward window with a further pointwise amplitude correction. `inverse_stft_window_fn` is equivalent to `forward_window_fn` in the case where it would produce an exact inverse. See examples in `inverse_stft` documentation for usage. Args: frame_step: An integer scalar `Tensor`. The number of samples to step. forward_window_fn: window_fn used in the forward transform, `stft`. name: An optional name for the operation. Returns: A callable that takes a window length and a `dtype` keyword argument and returns a `[window_length]` `Tensor` of samples in the provided datatype. The returned window is suitable for reconstructing original waveform in inverse_stft. """ with ops.name_scope(name, 'inverse_stft_window_fn', [forward_window_fn]): frame_step = ops.convert_to_tensor(frame_step, name='frame_step') frame_step.shape.assert_has_rank(0) def inverse_stft_window_fn_inner(frame_length, dtype): """Computes a window that can be used in `inverse_stft`. Args: frame_length: An integer scalar `Tensor`. The window length in samples. dtype: Data type of waveform passed to `stft`. Returns: A window suitable for reconstructing original waveform in `inverse_stft`. Raises: ValueError: If `frame_length` is not scalar, `forward_window_fn` is not a callable that takes a window length and a `dtype` keyword argument and returns a `[window_length]` `Tensor` of samples in the provided datatype `frame_step` is not scalar, or `frame_step` is not scalar. """ with ops.name_scope(name, 'inverse_stft_window_fn', [forward_window_fn]): frame_length = ops.convert_to_tensor(frame_length, name='frame_length') frame_length.shape.assert_has_rank(0) # Use equation 7 from Griffin + Lim. forward_window = forward_window_fn(frame_length, dtype=dtype) denom = math_ops.square(forward_window) overlaps = -(-frame_length // frame_step) # Ceiling division. denom = array_ops.pad(denom, [(0, overlaps * frame_step - frame_length)]) denom = array_ops.reshape(denom, [overlaps, frame_step]) denom = math_ops.reduce_sum(denom, 0, keepdims=True) denom = array_ops.tile(denom, [overlaps, 1]) denom = array_ops.reshape(denom, [overlaps * frame_step]) return forward_window / denom[:frame_length] return inverse_stft_window_fn_inner @tf_export('signal.inverse_stft') @dispatch.add_dispatch_support def inverse_stft(stfts, frame_length, frame_step, fft_length=None, window_fn=window_ops.hann_window, name=None): """Computes the inverse [Short-time Fourier Transform][stft] of `stfts`. To reconstruct an original waveform, a complementary window function should be used with `inverse_stft`. Such a window function can be constructed with `tf.signal.inverse_stft_window_fn`. Example: ```python frame_length = 400 frame_step = 160 waveform = tf.random.normal(dtype=tf.float32, shape=[1000]) stft = tf.signal.stft(waveform, frame_length, frame_step) inverse_stft = tf.signal.inverse_stft( stft, frame_length, frame_step, window_fn=tf.signal.inverse_stft_window_fn(frame_step)) ``` If a custom `window_fn` is used with `tf.signal.stft`, it must be passed to `tf.signal.inverse_stft_window_fn`: ```python frame_length = 400 frame_step = 160 window_fn = tf.signal.hamming_window waveform = tf.random.normal(dtype=tf.float32, shape=[1000]) stft = tf.signal.stft( waveform, frame_length, frame_step, window_fn=window_fn) inverse_stft = tf.signal.inverse_stft( stft, frame_length, frame_step, window_fn=tf.signal.inverse_stft_window_fn( frame_step, forward_window_fn=window_fn)) ``` Implemented with TPU/GPU-compatible ops and supports gradients. Args: stfts: A `complex64`/`complex128` `[..., frames, fft_unique_bins]` `Tensor` of STFT bins representing a batch of `fft_length`-point STFTs where `fft_unique_bins` is `fft_length // 2 + 1` 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 that produced `stfts`. 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. name: An optional name for the operation. Returns: A `[..., samples]` `Tensor` of `float32`/`float64` signals representing the inverse STFT for each input STFT in `stfts`. Raises: ValueError: If `stfts` is not at least rank 2, `frame_length` is not scalar, `frame_step` is not scalar, or `fft_length` is not scalar. [stft]: https://en.wikipedia.org/wiki/Short-time_Fourier_transform """ with ops.name_scope(name, 'inverse_stft', [stfts]): stfts = ops.convert_to_tensor(stfts, name='stfts') stfts.shape.with_rank_at_least(2) 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') fft_length.shape.assert_has_rank(0) real_frames = fft_ops.irfft(stfts, [fft_length]) # frame_length may be larger or smaller than fft_length, so we pad or # truncate real_frames to frame_length. frame_length_static = tensor_util.constant_value(frame_length) # If we don't know the shape of real_frames's inner dimension, pad and # truncate to frame_length. if (frame_length_static is None or real_frames.shape.ndims is None or real_frames.shape.as_list()[-1] is None): real_frames = real_frames[..., :frame_length] real_frames_rank = array_ops.rank(real_frames) real_frames_shape = array_ops.shape(real_frames) paddings = array_ops.concat( [array_ops.zeros([real_frames_rank - 1, 2], dtype=frame_length.dtype), [[0, math_ops.maximum(0, frame_length - real_frames_shape[-1])]]], 0) real_frames = array_ops.pad(real_frames, paddings) # We know real_frames's last dimension and frame_length statically. If they # are different, then pad or truncate real_frames to frame_length. elif real_frames.shape.as_list()[-1] > frame_length_static: real_frames = real_frames[..., :frame_length_static] elif real_frames.shape.as_list()[-1] < frame_length_static: pad_amount = frame_length_static - real_frames.shape.as_list()[-1] real_frames = array_ops.pad(real_frames, [[0, 0]] * (real_frames.shape.ndims - 1) + [[0, pad_amount]]) # The above code pads the inner dimension of real_frames to frame_length, # but it does so in a way that may not be shape-inference friendly. # Restore shape information if we are able to. if frame_length_static is not None and real_frames.shape.ndims is not None: real_frames.set_shape([None] * (real_frames.shape.ndims - 1) + [frame_length_static]) # Optionally window and overlap-add the inner 2 dimensions of real_frames # into a single [samples] dimension. if window_fn is not None: window = window_fn(frame_length, dtype=stfts.dtype.real_dtype) real_frames *= window return reconstruction_ops.overlap_and_add(real_frames, frame_step) def _enclosing_power_of_two(value): """Return 2**N for integer N such that 2**N >= value.""" value_static = tensor_util.constant_value(value) if value_static is not None: return constant_op.constant( int(2**np.ceil(np.log(value_static) / np.log(2.0))), value.dtype) return math_ops.cast( math_ops.pow( 2.0, math_ops.ceil( math_ops.log(math_ops.cast(value, dtypes.float32)) / math_ops.log(2.0))), value.dtype) @tf_export('signal.mdct') @dispatch.add_dispatch_support def mdct(signals, frame_length, window_fn=window_ops.vorbis_window, pad_end=False, norm=None, name=None): """Computes the [Modified Discrete Cosine Transform][mdct] 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 which must be divisible by 4. window_fn: A callable that takes a frame_length and a `dtype` keyword argument and returns a `[frame_length]` `Tensor` of samples in the provided datatype. If set to `None`, a rectangular window with a scale of 1/sqrt(2) is used. For perfect reconstruction of a signal from `mdct` followed by `inverse_mdct`, please use `tf.signal.vorbis_window`, `tf.signal.kaiser_bessel_derived_window` or `None`. If using another window function, make sure that w[n]^2 + w[n + frame_length // 2]^2 = 1 and w[n] = w[frame_length - n - 1] for n = 0,...,frame_length // 2 - 1 to achieve perfect reconstruction. 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. norm: If it is None, unnormalized dct4 is used, if it is "ortho" orthonormal dct4 is used. name: An optional name for the operation. Returns: A `[..., frames, frame_length // 2]` `Tensor` of `float32`/`float64` MDCT values where `frames` is roughly `samples // (frame_length // 2)` when `pad_end=False`. Raises: ValueError: If `signals` is not at least rank 1, `frame_length` is not scalar, or `frame_length` is not a multiple of `4`. [mdct]: https://en.wikipedia.org/wiki/Modified_discrete_cosine_transform """ with ops.name_scope(name, 'mdct', [signals, frame_length]): 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) # Assert that frame_length is divisible by 4. frame_length_static = tensor_util.constant_value(frame_length) if frame_length_static is not None: if frame_length_static % 4 != 0: raise ValueError('The frame length must be a multiple of 4.') frame_step = ops.convert_to_tensor(frame_length_static // 2, dtype=frame_length.dtype) else: frame_step = frame_length // 2 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 else: framed_signals *= 1.0 / np.sqrt(2) split_frames = array_ops.split(framed_signals, 4, axis=-1) frame_firsthalf = -array_ops.reverse(split_frames[2], [-1]) - split_frames[3] frame_secondhalf = split_frames[0] - array_ops.reverse(split_frames[1], [-1]) frames_rearranged = array_ops.concat((frame_firsthalf, frame_secondhalf), axis=-1) # Below call produces the (frame_length // 2) unique components of the # type 4 orthonormal DCT of the real windowed signals in frames_rearranged. return dct_ops.dct(frames_rearranged, type=4, norm=norm) @tf_export('signal.inverse_mdct') @dispatch.add_dispatch_support def inverse_mdct(mdcts, window_fn=window_ops.vorbis_window, norm=None, name=None): """Computes the inverse modified DCT of `mdcts`. To reconstruct an original waveform, the same window function should be used with `mdct` and `inverse_mdct`. Example usage: >>> @tf.function ... def compare_round_trip(): ... samples = 1000 ... frame_length = 400 ... halflen = frame_length // 2 ... waveform = tf.random.normal(dtype=tf.float32, shape=[samples]) ... waveform_pad = tf.pad(waveform, [[halflen, 0],]) ... mdct = tf.signal.mdct(waveform_pad, frame_length, pad_end=True, ... window_fn=tf.signal.vorbis_window) ... inverse_mdct = tf.signal.inverse_mdct(mdct, ... window_fn=tf.signal.vorbis_window) ... inverse_mdct = inverse_mdct[halflen: halflen + samples] ... return waveform, inverse_mdct >>> waveform, inverse_mdct = compare_round_trip() >>> np.allclose(waveform.numpy(), inverse_mdct.numpy(), rtol=1e-3, atol=1e-4) True Implemented with TPU/GPU-compatible ops and supports gradients. Args: mdcts: A `float32`/`float64` `[..., frames, frame_length // 2]` `Tensor` of MDCT bins representing a batch of `frame_length // 2`-point MDCTs. window_fn: A callable that takes a frame_length and a `dtype` keyword argument and returns a `[frame_length]` `Tensor` of samples in the provided datatype. If set to `None`, a rectangular window with a scale of 1/sqrt(2) is used. For perfect reconstruction of a signal from `mdct` followed by `inverse_mdct`, please use `tf.signal.vorbis_window`, `tf.signal.kaiser_bessel_derived_window` or `None`. If using another window function, make sure that w[n]^2 + w[n + frame_length // 2]^2 = 1 and w[n] = w[frame_length - n - 1] for n = 0,...,frame_length // 2 - 1 to achieve perfect reconstruction. norm: If "ortho", orthonormal inverse DCT4 is performed, if it is None, a regular dct4 followed by scaling of `1/frame_length` is performed. name: An optional name for the operation. Returns: A `[..., samples]` `Tensor` of `float32`/`float64` signals representing the inverse MDCT for each input MDCT in `mdcts` where `samples` is `(frames - 1) * (frame_length // 2) + frame_length`. Raises: ValueError: If `mdcts` is not at least rank 2. [mdct]: https://en.wikipedia.org/wiki/Modified_discrete_cosine_transform """ with ops.name_scope(name, 'inverse_mdct', [mdcts]): mdcts = ops.convert_to_tensor(mdcts, name='mdcts') mdcts.shape.with_rank_at_least(2) half_len = math_ops.cast(mdcts.shape[-1], dtype=dtypes.int32) if norm is None: half_len_float = math_ops.cast(half_len, dtype=mdcts.dtype) result_idct4 = (0.5 / half_len_float) * dct_ops.dct(mdcts, type=4) elif norm == 'ortho': result_idct4 = dct_ops.dct(mdcts, type=4, norm='ortho') split_result = array_ops.split(result_idct4, 2, axis=-1) real_frames = array_ops.concat((split_result[1], -array_ops.reverse(split_result[1], [-1]), -array_ops.reverse(split_result[0], [-1]), -split_result[0]), axis=-1) # Optionally window and overlap-add the inner 2 dimensions of real_frames # into a single [samples] dimension. if window_fn is not None: window = window_fn(2 * half_len, dtype=mdcts.dtype) real_frames *= window else: real_frames *= 1.0 / np.sqrt(2) return reconstruction_ops.overlap_and_add(real_frames, half_len)