import math
import torch
import torch.nn as nn
class Deltas(torch.nn.Module):
"""Computes delta coefficients (time derivatives).
Arguments
---------
win_length : int
Length of the window used to compute the time derivatives.
Example
-------
>>> inputs = torch.randn([10, 101, 20])
>>> compute_deltas = Deltas(input_size=inputs.size(-1))
>>> features = compute_deltas(inputs)
>>> features.shape
torch.Size([10, 101, 20])
"""
def __init__(
self, input_size, window_length=5,
):
super().__init__()
self.n = (window_length - 1) // 2
self.denom = self.n * (self.n + 1) * (2 * self.n + 1) / 3
self.register_buffer(
"kernel",
torch.arange(-self.n, self.n + 1, dtype=torch.float32,).repeat(
input_size, 1, 1
),
)
def forward(self, x):
"""Returns the delta coefficients.
Arguments
---------
x : tensor
A batch of tensors.
"""
# Managing multi-channel deltas reshape tensor (batch*channel,time)
x = x.transpose(1, 2).transpose(2, -1)
or_shape = x.shape
if len(or_shape) == 4:
x = x.reshape(or_shape[0] * or_shape[2], or_shape[1], or_shape[3])
# Padding for time borders
x = torch.nn.functional.pad(x, (self.n, self.n), mode="replicate")
# Derivative estimation (with a fixed convolutional kernel)
delta_coeff = (
torch.nn.functional.conv1d(
x, self.kernel.to(x.device), groups=x.shape[1]
)
/ self.denom
)
# Retrieving the original dimensionality (for multi-channel case)
if len(or_shape) == 4:
delta_coeff = delta_coeff.reshape(
or_shape[0], or_shape[1], or_shape[2], or_shape[3],
)
delta_coeff = delta_coeff.transpose(1, -1).transpose(2, -1)
return delta_coeff
class Filterbank(torch.nn.Module):
"""computes filter bank (FBANK) features given spectral magnitudes.
Arguments
---------
n_mels : float
Number of Mel filters used to average the spectrogram.
log_mel : bool
If True, it computes the log of the FBANKs.
filter_shape : str
Shape of the filters ('triangular', 'rectangular', 'gaussian').
f_min : int
Lowest frequency for the Mel filters.
f_max : int
Highest frequency for the Mel filters.
n_fft : int
Number of fft points of the STFT. It defines the frequency resolution
(n_fft should be<= than win_len).
sample_rate : int
Sample rate of the input audio signal (e.g, 16000)
power_spectrogram : float
Exponent used for spectrogram computation.
amin : float
Minimum amplitude (used for numerical stability).
ref_value : float
Reference value used for the dB scale.
top_db : float
Minimum negative cut-off in decibels.
freeze : bool
If False, it the central frequency and the band of each filter are
added into nn.parameters. If True, the standard frozen features
are computed.
param_change_factor: bool
If freeze=False, this parameter affects the speed at which the filter
parameters (i.e., central_freqs and bands) can be changed. When high
(e.g., param_change_factor=1) the filters change a lot during training.
When low (e.g. param_change_factor=0.1) the filter parameters are more
stable during training
param_rand_factor: float
This parameter can be used to randomly change the filter parameters
(i.e, central frequencies and bands) during training. It is thus a
sort of regularization. param_rand_factor=0 does not affect, while
param_rand_factor=0.15 allows random variations within +-15% of the
standard values of the filter parameters (e.g., if the central freq
is 100 Hz, we can randomly change it from 85 Hz to 115 Hz).
Example
-------
>>> import torch
>>> compute_fbanks = Filterbank()
>>> inputs = torch.randn([10, 101, 201])
>>> features = compute_fbanks(inputs)
>>> features.shape
torch.Size([10, 101, 40])
"""
def __init__(
self,
n_mels=40,
log_mel=True,
filter_shape="triangular",
f_min=0,
f_max=8000,
n_fft=400,
sample_rate=16000,
power_spectrogram=2,
amin=1e-10,
ref_value=1.0,
top_db=80.0,
param_change_factor=1.0,
param_rand_factor=0.0,
freeze=True,
):
super().__init__()
self.n_mels = n_mels
self.log_mel = log_mel
self.filter_shape = filter_shape
self.f_min = f_min
self.f_max = f_max
self.n_fft = n_fft
self.sample_rate = sample_rate
self.power_spectrogram = power_spectrogram
self.amin = amin
self.ref_value = ref_value
self.top_db = top_db
self.freeze = freeze
self.n_stft = self.n_fft // 2 + 1
self.db_multiplier = math.log10(max(self.amin, self.ref_value))
self.device_inp = torch.device("cpu")
self.param_change_factor = param_change_factor
self.param_rand_factor = param_rand_factor
if self.power_spectrogram == 2:
self.multiplier = 10
else:
self.multiplier = 20
# Make sure f_min < f_max
if self.f_min >= self.f_max:
err_msg = "Require f_min: %f < f_max: %f" % (
self.f_min,
self.f_max,
)
print(err_msg)
# Filter definition
mel = torch.linspace(
self._to_mel(self.f_min), self._to_mel(self.f_max), self.n_mels + 2
)
hz = self._to_hz(mel)
# Computation of the filter bands
band = hz[1:] - hz[:-1]
self.band = band[:-1]
self.f_central = hz[1:-1]
# Adding the central frequency and the band to the list of nn param
if not self.freeze:
self.f_central = torch.nn.Parameter(
self.f_central / (self.sample_rate * self.param_change_factor)
)
self.band = torch.nn.Parameter(
self.band / (self.sample_rate * self.param_change_factor)
)
# Frequency axis
all_freqs = torch.linspace(0, self.sample_rate // 2, self.n_stft)
# Replicating for all the filters
self.all_freqs_mat = all_freqs.repeat(self.f_central.shape[0], 1)
def forward(self, spectrogram):
"""Returns the FBANks.
Arguments
---------
x : tensor
A batch of spectrogram tensors.
"""
# Computing central frequency and bandwidth of each filter
f_central_mat = self.f_central.repeat(
self.all_freqs_mat.shape[1], 1
).transpose(0, 1)
band_mat = self.band.repeat(self.all_freqs_mat.shape[1], 1).transpose(
0, 1
)
# Uncomment to print filter parameters
# print(self.f_central*self.sample_rate * self.param_change_factor)
# print(self.band*self.sample_rate* self.param_change_factor)
# Creation of the multiplication matrix. It is used to create
# the filters that average the computed spectrogram.
if not self.freeze:
f_central_mat = f_central_mat * (
self.sample_rate
* self.param_change_factor
* self.param_change_factor
)
band_mat = band_mat * (
self.sample_rate
* self.param_change_factor
* self.param_change_factor
)
# Regularization with random changes of filter central frequency and band
elif self.param_rand_factor != 0 and self.training:
rand_change = (
1.0
+ torch.rand(2) * 2 * self.param_rand_factor
- self.param_rand_factor
)
f_central_mat = f_central_mat * rand_change[0]
band_mat = band_mat * rand_change[1]
fbank_matrix = self._create_fbank_matrix(f_central_mat, band_mat).to(
spectrogram.device
)
sp_shape = spectrogram.shape
# Managing multi-channels case (batch, time, channels)
if len(sp_shape) == 4:
spectrogram = spectrogram.permute(0, 3, 1, 2)
spectrogram = spectrogram.reshape(
sp_shape[0] * sp_shape[3], sp_shape[1], sp_shape[2]
)
# FBANK computation
fbanks = torch.matmul(spectrogram, fbank_matrix)
if self.log_mel:
fbanks = self._amplitude_to_DB(fbanks)
# Reshaping in the case of multi-channel inputs
if len(sp_shape) == 4:
fb_shape = fbanks.shape
fbanks = fbanks.reshape(
sp_shape[0], sp_shape[3], fb_shape[1], fb_shape[2]
)
fbanks = fbanks.permute(0, 2, 3, 1)
return fbanks
@staticmethod
def _to_mel(hz):
"""Returns mel-frequency value corresponding to the input
frequency value in Hz.
Arguments
---------
x : float
The frequency point in Hz.
"""
return 2595 * math.log10(1 + hz / 700)
@staticmethod
def _to_hz(mel):
"""Returns hz-frequency value corresponding to the input
mel-frequency value.
Arguments
---------
x : float
The frequency point in the mel-scale.
"""
return 700 * (10 ** (mel / 2595) - 1)
def _triangular_filters(self, all_freqs, f_central, band):
"""Returns fbank matrix using triangular filters.
Arguments
---------
all_freqs : Tensor
Tensor gathering all the frequency points.
f_central : Tensor
Tensor gathering central frequencies of each filter.
band : Tensor
Tensor gathering the bands of each filter.
"""
# Computing the slops of the filters
slope = (all_freqs - f_central) / band
left_side = slope + 1.0
right_side = -slope + 1.0
# Adding zeros for negative values
zero = torch.zeros(1, device=self.device_inp)
fbank_matrix = torch.max(
zero, torch.min(left_side, right_side)
).transpose(0, 1)
return fbank_matrix
def _rectangular_filters(self, all_freqs, f_central, band):
"""Returns fbank matrix using rectangular filters.
Arguments
---------
all_freqs : Tensor
Tensor gathering all the frequency points.
f_central : Tensor
Tensor gathering central frequencies of each filter.
band : Tensor
Tensor gathering the bands of each filter.
"""
# cut-off frequencies of the filters
low_hz = f_central - band
high_hz = f_central + band
# Left/right parts of the filter
left_side = right_size = all_freqs.ge(low_hz)
right_size = all_freqs.le(high_hz)
fbank_matrix = (left_side * right_size).float().transpose(0, 1)
return fbank_matrix
def _gaussian_filters(
self, all_freqs, f_central, band, smooth_factor=torch.tensor(2)
):
"""Returns fbank matrix using gaussian filters.
Arguments
---------
all_freqs : Tensor
Tensor gathering all the frequency points.
f_central : Tensor
Tensor gathering central frequencies of each filter.
band : Tensor
Tensor gathering the bands of each filter.
smooth_factor: Tensor
Smoothing factor of the gaussian filter. It can be used to employ
sharper or flatter filters.
"""
fbank_matrix = torch.exp(
-0.5 * ((all_freqs - f_central) / (band / smooth_factor)) ** 2
).transpose(0, 1)
return fbank_matrix
def _create_fbank_matrix(self, f_central_mat, band_mat):
"""Returns fbank matrix to use for averaging the spectrum with
the set of filter-banks.
Arguments
---------
f_central : Tensor
Tensor gathering central frequencies of each filter.
band : Tensor
Tensor gathering the bands of each filter.
smooth_factor: Tensor
Smoothing factor of the gaussian filter. It can be used to employ
sharper or flatter filters.
"""
if self.filter_shape == "triangular":
fbank_matrix = self._triangular_filters(
self.all_freqs_mat, f_central_mat, band_mat
)
elif self.filter_shape == "rectangular":
fbank_matrix = self._rectangular_filters(
self.all_freqs_mat, f_central_mat, band_mat
)
else:
fbank_matrix = self._gaussian_filters(
self.all_freqs_mat, f_central_mat, band_mat
)
return fbank_matrix
def _amplitude_to_DB(self, x):
"""Converts linear-FBANKs to log-FBANKs.
Arguments
---------
x : Tensor
A batch of linear FBANK tensors.
"""
x_db = self.multiplier * torch.log10(torch.clamp(x, min=self.amin))
x_db -= self.multiplier * self.db_multiplier
# Setting up dB max. It is the max over time and frequency,
# Hence, of a whole sequence (sequence-dependent)
new_x_db_max = x_db.amax(dim=(-2, -1)) - self.top_db
# Clipping to dB max. The view is necessary as only a scalar is obtained
# per sequence.
x_db = torch.max(x_db, new_x_db_max.view(x_db.shape[0], 1, 1))
return x_db
class STFT(torch.nn.Module):
"""computes the Short-Term Fourier Transform (STFT).
This class computes the Short-Term Fourier Transform of an audio signal.
It supports multi-channel audio inputs (batch, time, channels).
Arguments
---------
sample_rate : int
Sample rate of the input audio signal (e.g 16000).
win_length : float
Length (in ms) of the sliding window used to compute the STFT.
hop_length : float
Length (in ms) of the hope of the sliding window used to compute
the STFT.
n_fft : int
Number of fft point of the STFT. It defines the frequency resolution
(n_fft should be <= than win_len).
window_fn : function
A function that takes an integer (number of samples) and outputs a
tensor to be multiplied with each window before fft.
normalized_stft : bool
If True, the function returns the normalized STFT results,
i.e., multiplied by win_length^-0.5 (default is False).
center : bool
If True (default), the input will be padded on both sides so that the
t-th frame is centered at time t×hop_length. Otherwise, the t-th frame
begins at time t×hop_length.
pad_mode : str
It can be 'constant','reflect','replicate', 'circular', 'reflect'
(default). 'constant' pads the input tensor boundaries with a
constant value. 'reflect' pads the input tensor using the reflection
of the input boundary. 'replicate' pads the input tensor using
replication of the input boundary. 'circular' pads using circular
replication.
onesided : True
If True (default) only returns nfft/2 values. Note that the other
samples are redundant due to the Fourier transform conjugate symmetry.
Example
-------
>>> import torch
>>> compute_STFT = STFT(
... sample_rate=16000, win_length=25, hop_length=10, n_fft=400
... )
>>> inputs = torch.randn([10, 16000])
>>> features = compute_STFT(inputs)
>>> features.shape
torch.Size([10, 101, 201, 2])
"""
def __init__(
self,
sample_rate,
win_length=25,
hop_length=10,
n_fft=400,
window_fn=torch.hamming_window,
normalized_stft=False,
center=True,
pad_mode="constant",
onesided=True,
):
super().__init__()
self.sample_rate = sample_rate
self.win_length = win_length
self.hop_length = hop_length
self.n_fft = n_fft
self.normalized_stft = normalized_stft
self.center = center
self.pad_mode = pad_mode
self.onesided = onesided
# Convert win_length and hop_length from ms to samples
self.win_length = int(
round((self.sample_rate / 1000.0) * self.win_length)
)
self.hop_length = int(
round((self.sample_rate / 1000.0) * self.hop_length)
)
self.window = window_fn(self.win_length)
def forward(self, x):
"""Returns the STFT generated from the input waveforms.
Arguments
---------
x : tensor
A batch of audio signals to transform.
"""
# Managing multi-channel stft
or_shape = x.shape
if len(or_shape) == 3:
x = x.transpose(1, 2)
x = x.reshape(or_shape[0] * or_shape[2], or_shape[1])
stft = torch.stft(
x,
self.n_fft,
self.hop_length,
self.win_length,
self.window.to(x.device),
self.center,
self.pad_mode,
self.normalized_stft,
self.onesided,
return_complex=True,
)
stft = torch.view_as_real(stft)
# Retrieving the original dimensionality (batch,time, channels)
if len(or_shape) == 3:
stft = stft.reshape(
or_shape[0],
or_shape[2],
stft.shape[1],
stft.shape[2],
stft.shape[3],
)
stft = stft.permute(0, 3, 2, 4, 1)
else:
# (batch, time, channels)
stft = stft.transpose(2, 1)
return stft
def spectral_magnitude(
stft, power: int = 1, log: bool = False, eps: float = 1e-14
):
"""Returns the magnitude of a complex spectrogram.
Arguments
---------
stft : torch.Tensor
A tensor, output from the stft function.
power : int
What power to use in computing the magnitude.
Use power=1 for the power spectrogram.
Use power=0.5 for the magnitude spectrogram.
log : bool
Whether to apply log to the spectral features.
Example
-------
>>> a = torch.Tensor([[3, 4]])
>>> spectral_magnitude(a, power=0.5)
tensor([5.])
"""
spectr = stft.pow(2).sum(-1)
# Add eps avoids NaN when spectr is zero
if power < 1:
spectr = spectr + eps
spectr = spectr.pow(power)
if log:
return torch.log(spectr + eps)
return spectr
class ContextWindow(torch.nn.Module):
"""Computes the context window.
This class applies a context window by gathering multiple time steps
in a single feature vector. The operation is performed with a
convolutional layer based on a fixed kernel designed for that.
Arguments
---------
left_frames : int
Number of left frames (i.e, past frames) to collect.
right_frames : int
Number of right frames (i.e, future frames) to collect.
Example
-------
>>> import torch
>>> compute_cw = ContextWindow(left_frames=5, right_frames=5)
>>> inputs = torch.randn([10, 101, 20])
>>> features = compute_cw(inputs)
>>> features.shape
torch.Size([10, 101, 220])
"""
def __init__(
self, left_frames=0, right_frames=0,
):
super().__init__()
self.left_frames = left_frames
self.right_frames = right_frames
self.context_len = self.left_frames + self.right_frames + 1
self.kernel_len = 2 * max(self.left_frames, self.right_frames) + 1
# Kernel definition
self.kernel = torch.eye(self.context_len, self.kernel_len)
if self.right_frames > self.left_frames:
lag = self.right_frames - self.left_frames
self.kernel = torch.roll(self.kernel, lag, 1)
self.first_call = True
def forward(self, x):
"""Returns the tensor with the surrounding context.
Arguments
---------
x : tensor
A batch of tensors.
"""
x = x.transpose(1, 2)
if self.first_call is True:
self.first_call = False
self.kernel = (
self.kernel.repeat(x.shape[1], 1, 1)
.view(x.shape[1] * self.context_len, self.kernel_len,)
.unsqueeze(1)
)
# Managing multi-channel case
or_shape = x.shape
if len(or_shape) == 4:
x = x.reshape(or_shape[0] * or_shape[2], or_shape[1], or_shape[3])
# Compute context (using the estimated convolutional kernel)
cw_x = torch.nn.functional.conv1d(
x,
self.kernel.to(x.device),
groups=x.shape[1],
padding=max(self.left_frames, self.right_frames),
)
# Retrieving the original dimensionality (for multi-channel case)
if len(or_shape) == 4:
cw_x = cw_x.reshape(
or_shape[0], cw_x.shape[1], or_shape[2], cw_x.shape[-1]
)
cw_x = cw_x.transpose(1, 2)
return cw_x
class Fbank(torch.nn.Module):
def __init__(
self,
deltas=False,
context=False,
requires_grad=False,
sample_rate=16000,
f_min=0,
f_max=None,
n_fft=400,
n_mels=40,
filter_shape="triangular",
param_change_factor=1.0,
param_rand_factor=0.0,
left_frames=5,
right_frames=5,
win_length=25,
hop_length=10,
):
super().__init__()
self.deltas = deltas
self.context = context
self.requires_grad = requires_grad
if f_max is None:
f_max = sample_rate / 2
self.compute_STFT = STFT(
sample_rate=sample_rate,
n_fft=n_fft,
win_length=win_length,
hop_length=hop_length,
)
self.compute_fbanks = Filterbank(
sample_rate=sample_rate,
n_fft=n_fft,
n_mels=n_mels,
f_min=f_min,
f_max=f_max,
freeze=not requires_grad,
filter_shape=filter_shape,
param_change_factor=param_change_factor,
param_rand_factor=param_rand_factor,
)
self.compute_deltas = Deltas(input_size=n_mels)
self.context_window = ContextWindow(
left_frames=left_frames, right_frames=right_frames,
)
def forward(self, wav):
"""Returns a set of features generated from the input waveforms.
Arguments
---------
wav : tensor
A batch of audio signals to transform to features.
"""
STFT = self.compute_STFT(wav)
mag = spectral_magnitude(STFT)
fbanks = self.compute_fbanks(mag)
if self.deltas:
delta1 = self.compute_deltas(fbanks)
delta2 = self.compute_deltas(delta1)
fbanks = torch.cat([fbanks, delta1, delta2], dim=2)
if self.context:
fbanks = self.context_window(fbanks)
return fbanks