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"""
BSD 3-Clause License
Copyright (c) 2017, Prem Seetharaman
All rights reserved.
* Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are met:
* Redistributions of source code must retain the above copyright notice,
this list of conditions and the following disclaimer.
* Redistributions in binary form must reproduce the above copyright notice, this
list of conditions and the following disclaimer in the
documentation and/or other materials provided with the distribution.
* Neither the name of the copyright holder nor the names of its
contributors may be used to endorse or promote products derived from this
software without specific prior written permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR
ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
"""
import librosa.util as librosa_util
import numpy as np
import torch
import torch.nn.functional as F
from librosa.util import pad_center, tiny
from scipy.signal import get_window
from torch.autograd import Variable
def window_sumsquare(
window,
n_frames,
hop_length=200,
win_length=800,
n_fft=800,
dtype=np.float32,
norm=None,
):
"""
# from librosa 0.6
Compute the sum-square envelope of a window function at a given hop length.
This is used to estimate modulation effects induced by windowing
observations in short-time fourier transforms.
Parameters
----------
window : string, tuple, number, callable, or list-like
Window specification, as in `get_window`
n_frames : int > 0
The number of analysis frames
hop_length : int > 0
The number of samples to advance between frames
win_length : [optional]
The length of the window function. By default, this matches `n_fft`.
n_fft : int > 0
The length of each analysis frame.
dtype : np.dtype
The data type of the output
Returns
-------
wss : np.ndarray, shape=`(n_fft + hop_length * (n_frames - 1))`
The sum-squared envelope of the window function
"""
if win_length is None:
win_length = n_fft
n = n_fft + hop_length * (n_frames - 1)
x = np.zeros(n, dtype=dtype)
# Compute the squared window at the desired length
win_sq = get_window(window, win_length, fftbins=True)
win_sq = librosa_util.normalize(win_sq, norm=norm) ** 2
win_sq = librosa_util.pad_center(win_sq, n_fft)
# Fill the envelope
for i in range(n_frames):
sample = i * hop_length
x[sample : min(n, sample + n_fft)] += win_sq[: max(0, min(n_fft, n - sample))]
return x
class STFT(torch.nn.Module):
"""adapted from Prem Seetharaman's https://github.com/pseeth/pytorch-stft"""
def __init__(
self, filter_length=800, hop_length=200, win_length=800, window="hann"
):
super(STFT, self).__init__()
self.filter_length = filter_length
self.hop_length = hop_length
self.win_length = win_length
self.window = window
self.forward_transform = None
scale = self.filter_length / self.hop_length
fourier_basis = np.fft.fft(np.eye(self.filter_length))
cutoff = int((self.filter_length / 2 + 1))
fourier_basis = np.vstack(
[np.real(fourier_basis[:cutoff, :]), np.imag(fourier_basis[:cutoff, :])]
)
forward_basis = torch.FloatTensor(fourier_basis[:, None, :])
inverse_basis = torch.FloatTensor(
np.linalg.pinv(scale * fourier_basis).T[:, None, :]
)
if window is not None:
assert filter_length >= win_length
# get window and zero center pad it to filter_length
fft_window = get_window(window, win_length, fftbins=True)
fft_window = pad_center(fft_window, size=filter_length)
fft_window = torch.from_numpy(fft_window).float()
# window the bases
forward_basis *= fft_window
inverse_basis *= fft_window
self.register_buffer("forward_basis", forward_basis.float())
self.register_buffer("inverse_basis", inverse_basis.float())
def transform(self, input_data):
num_batches = input_data.size(0)
num_samples = input_data.size(1)
self.num_samples = num_samples
# similar to librosa, reflect-pad the input
input_data = input_data.view(num_batches, 1, num_samples)
input_data = F.pad(
input_data.unsqueeze(1),
(int(self.filter_length / 2), int(self.filter_length / 2), 0, 0),
mode="reflect",
)
input_data = input_data.squeeze(1)
forward_transform = F.conv1d(
input_data,
Variable(self.forward_basis, requires_grad=False),
stride=self.hop_length,
padding=0,
)
cutoff = int((self.filter_length / 2) + 1)
real_part = forward_transform[:, :cutoff, :]
imag_part = forward_transform[:, cutoff:, :]
magnitude = torch.sqrt(real_part**2 + imag_part**2)
phase = torch.autograd.Variable(torch.atan2(imag_part.data, real_part.data))
return magnitude, phase
def inverse(self, magnitude, phase):
recombine_magnitude_phase = torch.cat(
[magnitude * torch.cos(phase), magnitude * torch.sin(phase)], dim=1
)
inverse_transform = F.conv_transpose1d(
recombine_magnitude_phase,
Variable(self.inverse_basis, requires_grad=False),
stride=self.hop_length,
padding=0,
)
if self.window is not None:
window_sum = window_sumsquare(
self.window,
magnitude.size(-1),
hop_length=self.hop_length,
win_length=self.win_length,
n_fft=self.filter_length,
dtype=np.float32,
)
# remove modulation effects
approx_nonzero_indices = torch.from_numpy(
np.where(window_sum > tiny(window_sum))[0]
)
window_sum = torch.autograd.Variable(
torch.from_numpy(window_sum), requires_grad=False
)
window_sum = window_sum.cuda() if magnitude.is_cuda else window_sum
inverse_transform[:, :, approx_nonzero_indices] /= window_sum[
approx_nonzero_indices
]
# scale by hop ratio
inverse_transform *= float(self.filter_length) / self.hop_length
inverse_transform = inverse_transform[:, :, int(self.filter_length / 2) :]
inverse_transform = inverse_transform[:, :, : -int(self.filter_length / 2) :]
return inverse_transform
def forward(self, input_data):
self.magnitude, self.phase = self.transform(input_data)
reconstruction = self.inverse(self.magnitude, self.phase)
return reconstruction
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