Modules/stft.py

"""

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

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(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS

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"""

import torch
import numpy as np
import torch.nn.functional as F
from torch.autograd import Variable
from scipy.signal import get_window
from librosa.util import pad_center, tiny
import librosa.util as librosa_util


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


def stft(x, fft_size, hop_size, win_length, window):
    """Perform STFT and convert to magnitude spectrogram.

    Args:

        x (Tensor): Input signal tensor (B, T).

        fft_size (int): FFT size.

        hop_size (int): Hop size.

        win_length (int): Window length.

        window (str): Window function type.

    Returns:

        Tensor: Magnitude spectrogram (B, #frames, fft_size // 2 + 1).

    """
    x_stft = torch.stft(x, fft_size, hop_size, win_length, window, return_complex=False)
    real = x_stft[..., 0]
    imag = x_stft[..., 1]

    # NOTE(kan-bayashi): clamp is needed to avoid nan or inf
    return torch.sqrt(torch.clamp(real**2 + imag**2, min=1e-7)).transpose(2, 1)


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, 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.to(inverse_transform.device())
                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


class TorchSTFT(torch.nn.Module):
    def __init__(

        self, device, filter_length=800, hop_length=200, win_length=800, window="hann"

    ):
        super().__init__()
        self.filter_length = filter_length
        self.hop_length = hop_length
        self.win_length = win_length
        self.device = device
        self.window = torch.from_numpy(
            get_window(window, win_length, fftbins=True).astype(np.float32)
        ).to(device)

    def transform(self, input_data):
        forward_transform = torch.stft(
            input_data,
            self.filter_length,
            self.hop_length,
            self.win_length,
            window=self.window,
            return_complex=True,
        )

        return torch.abs(forward_transform), torch.angle(forward_transform)

    def inverse(self, magnitude, phase):
        inverse_transform = torch.istft(
            magnitude * torch.exp(phase * 1j),
            self.filter_length,
            self.hop_length,
            self.win_length,
            window=self.window,
        )

        return inverse_transform.unsqueeze(
            -2
        )  # unsqueeze to stay consistent with conv_transpose1d implementation

    def forward(self, input_data):
        self.magnitude, self.phase = self.transform(input_data)
        reconstruction = self.inverse(self.magnitude, self.phase)
        return reconstruction