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"""
Low level signal processing utilities
Authors
* Peter Plantinga 2020
* Francois Grondin 2020
* William Aris 2020
* Samuele Cornell 2020
* Sarthak Yadav 2022
"""
import math
import torch
def compute_amplitude(waveforms, lengths=None, amp_type="avg", scale="linear"):
"""Compute amplitude of a batch of waveforms.
Arguments
---------
waveforms : tensor
The waveforms used for computing amplitude.
Shape should be `[time]` or `[batch, time]` or
`[batch, time, channels]`.
lengths : tensor
The lengths of the waveforms excluding the padding.
Shape should be a single dimension, `[batch]`.
amp_type : str
Whether to compute "avg" average or "peak" amplitude.
Choose between ["avg", "peak"].
scale : str
Whether to compute amplitude in "dB" or "linear" scale.
Choose between ["linear", "dB"].
Returns
-------
The average amplitude of the waveforms.
Example
-------
>>> signal = torch.sin(torch.arange(16000.0)).unsqueeze(0)
>>> compute_amplitude(signal, signal.size(1))
tensor([[0.6366]])
"""
if len(waveforms.shape) == 1:
waveforms = waveforms.unsqueeze(0)
assert amp_type in ["avg", "rms", "peak"]
assert scale in ["linear", "dB"]
if amp_type == "avg":
if lengths is None:
out = torch.mean(torch.abs(waveforms), dim=1, keepdim=True)
else:
wav_sum = torch.sum(input=torch.abs(waveforms), dim=1, keepdim=True)
# Manage multi-channel waveforms
if len(wav_sum.shape) == 3 and isinstance(lengths, torch.Tensor):
lengths = lengths.unsqueeze(2)
out = wav_sum / lengths
elif amp_type == "rms":
if lengths is None:
out = torch.sqrt(torch.mean(waveforms**2, dim=1, keepdim=True))
else:
wav_sum = torch.sum(
input=torch.pow(waveforms, 2), dim=1, keepdim=True
)
if len(wav_sum.shape) == 3 and isinstance(lengths, torch.Tensor):
lengths = lengths.unsqueeze(2)
out = torch.sqrt(wav_sum / lengths)
elif amp_type == "peak":
out = torch.max(torch.abs(waveforms), dim=1, keepdim=True)[0]
else:
raise NotImplementedError
if scale == "linear":
return out
elif scale == "dB":
return torch.clamp(20 * torch.log10(out), min=-80) # clamp zeros
else:
raise NotImplementedError
def normalize(waveforms, lengths=None, amp_type="avg", eps=1e-14):
"""This function normalizes a signal to unitary average or peak amplitude.
Arguments
---------
waveforms : tensor
The waveforms to normalize.
Shape should be `[batch, time]` or `[batch, time, channels]`.
lengths : tensor
The lengths of the waveforms excluding the padding.
Shape should be a single dimension, `[batch]`.
amp_type : str
Whether one wants to normalize with respect to "avg" or "peak"
amplitude. Choose between ["avg", "peak"]. Note: for "avg" clipping
is not prevented and can occur.
eps : float
A small number to add to the denominator to prevent NaN.
Returns
-------
waveforms : tensor
Normalized level waveform.
"""
assert amp_type in ["avg", "peak"]
batch_added = False
if len(waveforms.shape) == 1:
batch_added = True
waveforms = waveforms.unsqueeze(0)
den = compute_amplitude(waveforms, lengths, amp_type) + eps
if batch_added:
waveforms = waveforms.squeeze(0)
return waveforms / den
def mean_std_norm(waveforms, dims=1, eps=1e-06):
"""This function normalizes the mean and std of the input
waveform (along the specified axis).
Arguments
---------
waveforms : tensor
The waveforms to normalize.
Shape should be `[batch, time]` or `[batch, time, channels]`.
dims : int or tuple
The dimension(s) on which mean and std are computed
eps : float
A small number to add to the denominator to prevent NaN.
Returns
-------
waveforms : tensor
Normalized level waveform.
"""
mean = waveforms.mean(dims, keepdim=True)
std = waveforms.std(dims, keepdim=True)
waveforms = (waveforms - mean) / (std + eps)
return waveforms
def rescale(waveforms, lengths, target_lvl, amp_type="avg", scale="linear"):
"""This functions performs signal rescaling to a target level.
Arguments
---------
waveforms : tensor
The waveforms to normalize.
Shape should be `[batch, time]` or `[batch, time, channels]`.
lengths : tensor
The lengths of the waveforms excluding the padding.
Shape should be a single dimension, `[batch]`.
target_lvl : float
Target lvl in dB or linear scale.
amp_type : str
Whether one wants to rescale with respect to "avg" or "peak" amplitude.
Choose between ["avg", "peak"].
scale : str
whether target_lvl belongs to linear or dB scale.
Choose between ["linear", "dB"].
Returns
-------
waveforms : tensor
Rescaled waveforms.
"""
assert amp_type in ["peak", "avg"]
assert scale in ["linear", "dB"]
batch_added = False
if len(waveforms.shape) == 1:
batch_added = True
waveforms = waveforms.unsqueeze(0)
waveforms = normalize(waveforms, lengths, amp_type)
if scale == "linear":
out = target_lvl * waveforms
elif scale == "dB":
out = dB_to_amplitude(target_lvl) * waveforms
else:
raise NotImplementedError("Invalid scale, choose between dB and linear")
if batch_added:
out = out.squeeze(0)
return out
def convolve1d(
waveform,
kernel,
padding=0,
pad_type="constant",
stride=1,
groups=1,
use_fft=False,
rotation_index=0,
):
"""Use torch.nn.functional to perform 1d padding and conv.
Arguments
---------
waveform : tensor
The tensor to perform operations on.
kernel : tensor
The filter to apply during convolution.
padding : int or tuple
The padding (pad_left, pad_right) to apply.
If an integer is passed instead, this is passed
to the conv1d function and pad_type is ignored.
pad_type : str
The type of padding to use. Passed directly to
`torch.nn.functional.pad`, see PyTorch documentation
for available options.
stride : int
The number of units to move each time convolution is applied.
Passed to conv1d. Has no effect if `use_fft` is True.
groups : int
This option is passed to `conv1d` to split the input into groups for
convolution. Input channels should be divisible by the number of groups.
use_fft : bool
When `use_fft` is passed `True`, then compute the convolution in the
spectral domain using complex multiply. This is more efficient on CPU
when the size of the kernel is large (e.g. reverberation). WARNING:
Without padding, circular convolution occurs. This makes little
difference in the case of reverberation, but may make more difference
with different kernels.
rotation_index : int
This option only applies if `use_fft` is true. If so, the kernel is
rolled by this amount before convolution to shift the output location.
Returns
-------
The convolved waveform.
Example
-------
>>> from speechbrain.dataio.dataio import read_audio
>>> signal = read_audio("tests/samples/single-mic/example1.wav")
>>> signal = signal.unsqueeze(0).unsqueeze(2)
>>> kernel = torch.rand(1, 10, 1)
>>> signal = convolve1d(signal, kernel, padding=(9, 0))
"""
if len(waveform.shape) != 3:
raise ValueError("Convolve1D expects a 3-dimensional tensor")
# Move time dimension last, which pad and fft and conv expect.
waveform = waveform.transpose(2, 1)
kernel = kernel.transpose(2, 1)
# Padding can be a tuple (left_pad, right_pad) or an int
if isinstance(padding, tuple):
waveform = torch.nn.functional.pad(
input=waveform, pad=padding, mode=pad_type
)
# This approach uses FFT, which is more efficient if the kernel is large
if use_fft:
# Pad kernel to same length as signal, ensuring correct alignment
zero_length = waveform.size(-1) - kernel.size(-1)
# Handle case where signal is shorter
if zero_length < 0:
kernel = kernel[..., :zero_length]
zero_length = 0
# Perform rotation to ensure alignment
zeros = torch.zeros(
kernel.size(0), kernel.size(1), zero_length, device=kernel.device
)
after_index = kernel[..., rotation_index:]
before_index = kernel[..., :rotation_index]
kernel = torch.cat((after_index, zeros, before_index), dim=-1)
# Multiply in frequency domain to convolve in time domain
import torch.fft as fft
# cuFFT does not support half precision for non-power-of-2 sizes
orig_dtype = waveform.dtype
if orig_dtype == torch.float16 or orig_dtype == torch.bfloat16:
waveform = waveform.float()
kernel = kernel.float()
result = fft.rfft(waveform) * fft.rfft(kernel)
convolved = fft.irfft(result, n=waveform.size(-1))
if convolved.dtype != orig_dtype:
convolved = convolved.to(orig_dtype)
# Use the implementation given by torch, which should be efficient on GPU
else:
convolved = torch.nn.functional.conv1d(
input=waveform,
weight=kernel,
stride=stride,
groups=groups,
padding=padding if not isinstance(padding, tuple) else 0,
)
# Return time dimension to the second dimension.
return convolved.transpose(2, 1)
def reverberate(waveforms, rir_waveform, rescale_amp="avg"):
"""
General function to contaminate a given signal with reverberation given a
Room Impulse Response (RIR).
It performs convolution between RIR and signal, but without changing
the original amplitude of the signal.
Arguments
---------
waveforms : tensor
The waveforms to normalize.
Shape should be `[batch, time]` or `[batch, time, channels]`.
rir_waveform : tensor
RIR tensor, shape should be [time, channels].
rescale_amp : str or None
Whether reverberated signal is rescaled (None to avoid) and with respect either
to original signal "peak" amplitude or "avg" average amplitude.
Choose between [None, "avg", "peak"].
Returns
-------
waveforms: tensor
Reverberated signal.
"""
orig_shape = waveforms.shape
if len(waveforms.shape) > 3 or len(rir_waveform.shape) > 3:
raise NotImplementedError
# if inputs are mono tensors we reshape to 1, samples
if len(waveforms.shape) == 1:
waveforms = waveforms.unsqueeze(0).unsqueeze(-1)
elif len(waveforms.shape) == 2:
waveforms = waveforms.unsqueeze(-1)
if len(rir_waveform.shape) == 1: # convolve1d expects a 3d tensor !
rir_waveform = rir_waveform.unsqueeze(0).unsqueeze(-1)
elif len(rir_waveform.shape) == 2:
rir_waveform = rir_waveform.unsqueeze(-1)
if rescale_amp is not None:
# Compute the average amplitude of the clean
orig_amplitude = compute_amplitude(
waveforms, waveforms.size(1), rescale_amp
)
# Compute index of the direct signal, so we can preserve alignment
value_max, direct_index = rir_waveform.abs().max(axis=1, keepdim=True)
# Making sure the max is always positive (if not, flip)
# mask = torch.logical_and(rir_waveform == value_max, rir_waveform < 0)
# rir_waveform[mask] = -rir_waveform[mask]
# Use FFT to compute convolution, because of long reverberation filter
waveforms = convolve1d(
waveform=waveforms,
kernel=rir_waveform,
use_fft=True,
rotation_index=direct_index,
)
if rescale_amp is not None:
# Rescale to the peak amplitude of the clean waveform
waveforms = rescale(
waveforms, waveforms.size(1), orig_amplitude, rescale_amp
)
if len(orig_shape) == 1:
waveforms = waveforms.squeeze(0).squeeze(-1)
if len(orig_shape) == 2:
waveforms = waveforms.squeeze(-1)
return waveforms
def dB_to_amplitude(SNR):
"""Returns the amplitude ratio, converted from decibels.
Arguments
---------
SNR : float
The ratio in decibels to convert.
Returns
-------
The amplitude ratio
Example
-------
>>> round(dB_to_amplitude(SNR=10), 3)
3.162
>>> dB_to_amplitude(SNR=0)
1.0
"""
return 10 ** (SNR / 20)
def notch_filter(notch_freq, filter_width=101, notch_width=0.05):
"""Returns a notch filter constructed from a high-pass and low-pass filter.
(from https://tomroelandts.com/articles/
how-to-create-simple-band-pass-and-band-reject-filters)
Arguments
---------
notch_freq : float
frequency to put notch as a fraction of the
sampling rate / 2. The range of possible inputs is 0 to 1.
filter_width : int
Filter width in samples. Longer filters have
smaller transition bands, but are more inefficient.
notch_width : float
Width of the notch, as a fraction of the sampling_rate / 2.
Returns
-------
The computed filter
Example
-------
>>> from speechbrain.dataio.dataio import read_audio
>>> signal = read_audio("tests/samples/single-mic/example1.wav")
>>> signal = signal.unsqueeze(0).unsqueeze(2)
>>> kernel = notch_filter(0.25)
>>> notched_signal = convolve1d(signal, kernel)
"""
# Check inputs
assert 0 < notch_freq <= 1
assert filter_width % 2 != 0
pad = filter_width // 2
inputs = torch.arange(filter_width) - pad
# Avoid frequencies that are too low
notch_freq += notch_width
# Define sinc function, avoiding division by zero
def sinc(x):
"""Computes the sinc function."""
def _sinc(x):
return torch.sin(x) / x
# The zero is at the middle index
return torch.cat([_sinc(x[:pad]), torch.ones(1), _sinc(x[pad + 1 :])])
# Compute a low-pass filter with cutoff frequency notch_freq.
hlpf = sinc(3 * (notch_freq - notch_width) * inputs)
hlpf *= torch.blackman_window(filter_width)
hlpf /= torch.sum(hlpf)
# Compute a high-pass filter with cutoff frequency notch_freq.
hhpf = sinc(3 * (notch_freq + notch_width) * inputs)
hhpf *= torch.blackman_window(filter_width)
hhpf /= -torch.sum(hhpf)
hhpf[pad] += 1
# Adding filters creates notch filter
return (hlpf + hhpf).view(1, -1, 1)
def overlap_and_add(signal, frame_step):
"""Taken from https://github.com/kaituoxu/Conv-TasNet/blob/master/src/utils.py
Reconstructs a signal from a framed representation.
Adds potentially overlapping frames of a signal with shape
`[..., frames, frame_length]`, offsetting subsequent frames by `frame_step`.
The resulting tensor has shape `[..., output_size]` where
output_size = (frames - 1) * frame_step + frame_length
Arguments
---------
signal: A [..., frames, frame_length] torch.Tensor.
All dimensions may be unknown, and rank must be at least 2.
frame_step: int
An integer denoting overlap offsets. Must be less than or equal to frame_length.
Returns
-------
A Tensor with shape [..., output_size] containing the overlap-added frames of signal's inner-most two dimensions.
output_size = (frames - 1) * frame_step + frame_length
Based on
https://github.com/tensorflow/tensorflow/blob/r1.12/tensorflow/contrib/signal/python/ops/reconstruction_ops.py
Example
-------
>>> signal = torch.randn(5, 20)
>>> overlapped = overlap_and_add(signal, 20)
>>> overlapped.shape
torch.Size([100])
"""
outer_dimensions = signal.size()[:-2]
frames, frame_length = signal.size()[-2:]
subframe_length = math.gcd(
frame_length, frame_step
) # gcd=Greatest Common Divisor
subframe_step = frame_step // subframe_length
subframes_per_frame = frame_length // subframe_length
output_size = frame_step * (frames - 1) + frame_length
output_subframes = output_size // subframe_length
subframe_signal = signal.view(*outer_dimensions, -1, subframe_length)
frame = torch.arange(0, output_subframes).unfold(
0, subframes_per_frame, subframe_step
)
# frame_old = signal.new_tensor(frame).long() # signal may in GPU or CPU
frame = frame.clone().detach().to(signal.device.type)
# print((frame - frame_old).sum())
frame = frame.contiguous().view(-1)
result = signal.new_zeros(
*outer_dimensions, output_subframes, subframe_length
)
result.index_add_(-2, frame, subframe_signal)
result = result.view(*outer_dimensions, -1)
return result
def resynthesize(enhanced_mag, noisy_inputs, stft, istft, normalize_wavs=True):
"""Function for resynthesizing waveforms from enhanced mags.
Arguments
---------
enhanced_mag : torch.Tensor
Predicted spectral magnitude, should be three dimensional.
noisy_inputs : torch.Tensor
The noisy waveforms before any processing, to extract phase.
stft : torch.nn.Module
Module for computing the STFT for extracting phase.
istft : torch.nn.Module
Module for computing the iSTFT for resynthesis.
normalize_wavs : bool
Whether to normalize the output wavs before returning them.
Returns
-------
enhanced_wav : torch.Tensor
The resynthesized waveforms of the enhanced magnitudes with noisy phase.
"""
# Extract noisy phase from inputs
noisy_feats = stft(noisy_inputs)
noisy_phase = torch.atan2(noisy_feats[:, :, :, 1], noisy_feats[:, :, :, 0])
# Combine with enhanced magnitude
complex_predictions = torch.mul(
torch.unsqueeze(enhanced_mag, -1),
torch.cat(
(
torch.unsqueeze(torch.cos(noisy_phase), -1),
torch.unsqueeze(torch.sin(noisy_phase), -1),
),
-1,
),
)
pred_wavs = istft(complex_predictions, sig_length=noisy_inputs.shape[1])
# Normalize. Since we're using peak amplitudes, ignore lengths
if normalize_wavs:
pred_wavs = normalize(pred_wavs, amp_type="peak")
return pred_wavs
def gabor_impulse_response(t, center, fwhm):
"""
Function for generating gabor impulse responses
as used by GaborConv1d proposed in
Neil Zeghidour, Olivier Teboul, F{\'e}lix de Chaumont Quitry & Marco Tagliasacchi, "LEAF: A LEARNABLE FRONTEND
FOR AUDIO CLASSIFICATION", in Proc of ICLR 2021 (https://arxiv.org/abs/2101.08596)
"""
denominator = 1.0 / (torch.sqrt(torch.tensor(2.0) * math.pi) * fwhm)
gaussian = torch.exp(
torch.tensordot(
1.0 / (2.0 * fwhm.unsqueeze(1) ** 2),
(-(t**2.0)).unsqueeze(0),
dims=1,
)
)
center_frequency_complex = center.type(torch.complex64)
t_complex = t.type(torch.complex64)
sinusoid = torch.exp(
torch.complex(torch.tensor(0.0), torch.tensor(1.0))
* torch.tensordot(
center_frequency_complex.unsqueeze(1),
t_complex.unsqueeze(0),
dims=1,
)
)
denominator = denominator.type(torch.complex64).unsqueeze(1)
gaussian = gaussian.type(torch.complex64)
return denominator * sinusoid * gaussian
def gabor_impulse_response_legacy_complex(t, center, fwhm):
"""
Function for generating gabor impulse responses, but without using complex64 dtype
as used by GaborConv1d proposed in
Neil Zeghidour, Olivier Teboul, F{\'e}lix de Chaumont Quitry & Marco Tagliasacchi, "LEAF: A LEARNABLE FRONTEND
FOR AUDIO CLASSIFICATION", in Proc of ICLR 2021 (https://arxiv.org/abs/2101.08596)
"""
denominator = 1.0 / (torch.sqrt(torch.tensor(2.0) * math.pi) * fwhm)
gaussian = torch.exp(
torch.tensordot(
1.0 / (2.0 * fwhm.unsqueeze(1) ** 2),
(-(t**2.0)).unsqueeze(0),
dims=1,
)
)
temp = torch.tensordot(center.unsqueeze(1), t.unsqueeze(0), dims=1)
temp2 = torch.zeros(*temp.shape + (2,), device=temp.device)
# since output of torch.tensordot(..) is multiplied by 0+j
# output can simply be written as flipping real component of torch.tensordot(..) to the imag component
temp2[:, :, 0] *= -1 * temp2[:, :, 0]
temp2[:, :, 1] = temp[:, :]
# exponent of complex number c is
# o.real = exp(c.real) * cos(c.imag)
# o.imag = exp(c.real) * sin(c.imag)
sinusoid = torch.zeros_like(temp2, device=temp.device)
sinusoid[:, :, 0] = torch.exp(temp2[:, :, 0]) * torch.cos(temp2[:, :, 1])
sinusoid[:, :, 1] = torch.exp(temp2[:, :, 0]) * torch.sin(temp2[:, :, 1])
# multiplication of two complex numbers c1 and c2 -> out:
# out.real = c1.real * c2.real - c1.imag * c2.imag
# out.imag = c1.real * c2.imag + c1.imag * c2.real
denominator_sinusoid = torch.zeros(*temp.shape + (2,), device=temp.device)
denominator_sinusoid[:, :, 0] = (
denominator.view(-1, 1) * sinusoid[:, :, 0]
) - (torch.zeros_like(denominator).view(-1, 1) * sinusoid[:, :, 1])
denominator_sinusoid[:, :, 1] = (
denominator.view(-1, 1) * sinusoid[:, :, 1]
) + (torch.zeros_like(denominator).view(-1, 1) * sinusoid[:, :, 0])
output = torch.zeros(*temp.shape + (2,), device=temp.device)
output[:, :, 0] = (denominator_sinusoid[:, :, 0] * gaussian) - (
denominator_sinusoid[:, :, 1] * torch.zeros_like(gaussian)
)
output[:, :, 1] = (
denominator_sinusoid[:, :, 0] * torch.zeros_like(gaussian)
) + (denominator_sinusoid[:, :, 1] * gaussian)
return output