from typing import Tuple
import math
import torch
import torchaudio
from torch import Tensor
__all__ = [
'get_mel_banks',
'inverse_mel_scale',
'inverse_mel_scale_scalar',
'mel_scale',
'mel_scale_scalar',
'spectrogram',
'fbank',
'mfcc',
'vtln_warp_freq',
'vtln_warp_mel_freq',
'resample_waveform',
]
# numeric_limits<float>::epsilon() 1.1920928955078125e-07
EPSILON = torch.tensor(torch.finfo(torch.float).eps)
# 1 milliseconds = 0.001 seconds
MILLISECONDS_TO_SECONDS = 0.001
# window types
HAMMING = 'hamming'
HANNING = 'hanning'
POVEY = 'povey'
RECTANGULAR = 'rectangular'
BLACKMAN = 'blackman'
WINDOWS = [HAMMING, HANNING, POVEY, RECTANGULAR, BLACKMAN]
def _next_power_of_2(x: int) -> int:
r"""Returns the smallest power of 2 that is greater than x
"""
return 1 if x == 0 else 2 ** (x - 1).bit_length()
def _get_strided(waveform: Tensor, window_size: int, window_shift: int, snip_edges: bool) -> Tensor:
r"""Given a waveform (1D tensor of size ``num_samples``), it returns a 2D tensor (m, ``window_size``)
representing how the window is shifted along the waveform. Each row is a frame.
Args:
waveform (Tensor): Tensor of size ``num_samples``
window_size (int): Frame length
window_shift (int): Frame shift
snip_edges (bool): If True, end effects will be handled by outputting only frames that completely fit
in the file, and the number of frames depends on the frame_length. If False, the number of frames
depends only on the frame_shift, and we reflect the data at the ends.
Returns:
Tensor: 2D tensor of size (m, ``window_size``) where each row is a frame
"""
assert waveform.dim() == 1
num_samples = waveform.size(0)
strides = (window_shift * waveform.stride(0), waveform.stride(0))
if snip_edges:
if num_samples < window_size:
return torch.empty((0, 0))
else:
m = 1 + (num_samples - window_size) // window_shift
else:
reversed_waveform = torch.flip(waveform, [0])
m = (num_samples + (window_shift // 2)) // window_shift
pad = window_size // 2 - window_shift // 2
pad_right = reversed_waveform
if pad > 0:
# torch.nn.functional.pad returns [2,1,0,1,2] for 'reflect'
# but we want [2, 1, 0, 0, 1, 2]
pad_left = reversed_waveform[-pad:]
waveform = torch.cat((pad_left, waveform, pad_right), dim=0)
else:
# pad is negative so we want to trim the waveform at the front
waveform = torch.cat((waveform[-pad:], pad_right), dim=0)
sizes = (m, window_size)
return waveform.as_strided(sizes, strides)
def _feature_window_function(window_type: str,
window_size: int,
blackman_coeff: float) -> Tensor:
r"""Returns a window function with the given type and size
"""
if window_type == HANNING:
return torch.hann_window(window_size, periodic=False)
elif window_type == HAMMING:
return torch.hamming_window(window_size, periodic=False, alpha=0.54, beta=0.46)
elif window_type == POVEY:
# like hanning but goes to zero at edges
return torch.hann_window(window_size, periodic=False).pow(0.85)
elif window_type == RECTANGULAR:
return torch.ones(window_size)
elif window_type == BLACKMAN:
a = 2 * math.pi / (window_size - 1)
window_function = torch.arange(window_size)
# can't use torch.blackman_window as they use different coefficients
return (blackman_coeff - 0.5 * torch.cos(a * window_function) +
(0.5 - blackman_coeff) * torch.cos(2 * a * window_function))
else:
raise Exception('Invalid window type ' + window_type)
def _get_log_energy(strided_input: Tensor,
epsilon: Tensor,
energy_floor: float) -> Tensor:
r"""Returns the log energy of size (m) for a strided_input (m,*)
"""
log_energy = torch.max(strided_input.pow(2).sum(1), epsilon).log() # size (m)
if energy_floor == 0.0:
return log_energy
else:
return torch.max(log_energy,
torch.tensor(math.log(energy_floor)))
def _get_waveform_and_window_properties(waveform: Tensor,
channel: int,
sample_frequency: float,
frame_shift: float,
frame_length: float,
round_to_power_of_two: bool,
preemphasis_coefficient: float) -> Tuple[Tensor, int, int, int]:
r"""Gets the waveform and window properties
"""
channel = max(channel, 0)
assert channel < waveform.size(0), ('Invalid channel %d for size %d' % (channel, waveform.size(0)))
waveform = waveform[channel, :] # size (n)
window_shift = int(sample_frequency * frame_shift * MILLISECONDS_TO_SECONDS)
window_size = int(sample_frequency * frame_length * MILLISECONDS_TO_SECONDS)
padded_window_size = _next_power_of_2(window_size) if round_to_power_of_two else window_size
assert 2 <= window_size <= len(waveform), ('choose a window size %d that is [2, %d]' % (window_size, len(waveform)))
assert 0 < window_shift, '`window_shift` must be greater than 0'
assert padded_window_size % 2 == 0, 'the padded `window_size` must be divisible by two.' \
' use `round_to_power_of_two` or change `frame_length`'
assert 0. <= preemphasis_coefficient <= 1.0, '`preemphasis_coefficient` must be between [0,1]'
assert sample_frequency > 0, '`sample_frequency` must be greater than zero'
return waveform, window_shift, window_size, padded_window_size
def _get_window(waveform: Tensor,
padded_window_size: int,
window_size: int,
window_shift: int,
window_type: str,
blackman_coeff: float,
snip_edges: bool,
raw_energy: bool,
energy_floor: float,
dither: float,
remove_dc_offset: bool,
preemphasis_coefficient: float) -> Tuple[Tensor, Tensor]:
r"""Gets a window and its log energy
Returns:
(Tensor, Tensor): strided_input of size (m, ``padded_window_size``) and signal_log_energy of size (m)
"""
# size (m, window_size)
strided_input = _get_strided(waveform, window_size, window_shift, snip_edges)
if dither != 0.0:
# Returns a random number strictly between 0 and 1
x = torch.max(EPSILON, torch.rand(strided_input.shape))
rand_gauss = torch.sqrt(-2 * x.log()) * torch.cos(2 * math.pi * x)
strided_input = strided_input + rand_gauss * dither
if remove_dc_offset:
# Subtract each row/frame by its mean
row_means = torch.mean(strided_input, dim=1).unsqueeze(1) # size (m, 1)
strided_input = strided_input - row_means
if raw_energy:
# Compute the log energy of each row/frame before applying preemphasis and
# window function
signal_log_energy = _get_log_energy(strided_input, EPSILON, energy_floor) # size (m)
if preemphasis_coefficient != 0.0:
# strided_input[i,j] -= preemphasis_coefficient * strided_input[i, max(0, j-1)] for all i,j
offset_strided_input = torch.nn.functional.pad(
strided_input.unsqueeze(0), (1, 0), mode='replicate').squeeze(0) # size (m, window_size + 1)
strided_input = strided_input - preemphasis_coefficient * offset_strided_input[:, :-1]
# Apply window_function to each row/frame
window_function = _feature_window_function(
window_type, window_size, blackman_coeff).unsqueeze(0) # size (1, window_size)
strided_input = strided_input * window_function # size (m, window_size)
# Pad columns with zero until we reach size (m, padded_window_size)
if padded_window_size != window_size:
padding_right = padded_window_size - window_size
strided_input = torch.nn.functional.pad(
strided_input.unsqueeze(0), (0, padding_right), mode='constant', value=0).squeeze(0)
# Compute energy after window function (not the raw one)
if not raw_energy:
signal_log_energy = _get_log_energy(strided_input, EPSILON, energy_floor) # size (m)
return strided_input, signal_log_energy
def _subtract_column_mean(tensor: Tensor, subtract_mean: bool) -> Tensor:
# subtracts the column mean of the tensor size (m, n) if subtract_mean=True
# it returns size (m, n)
if subtract_mean:
col_means = torch.mean(tensor, dim=0).unsqueeze(0)
tensor = tensor - col_means
return tensor
[docs]def spectrogram(waveform: Tensor,
blackman_coeff: float = 0.42,
channel: int = -1,
dither: float = 0.0,
energy_floor: float = 1.0,
frame_length: float = 25.0,
frame_shift: float = 10.0,
min_duration: float = 0.0,
preemphasis_coefficient: float = 0.97,
raw_energy: bool = True,
remove_dc_offset: bool = True,
round_to_power_of_two: bool = True,
sample_frequency: float = 16000.0,
snip_edges: bool = True,
subtract_mean: bool = False,
window_type: str = POVEY) -> Tensor:
r"""Create a spectrogram from a raw audio signal. This matches the input/output of Kaldi's
compute-spectrogram-feats.
Args:
waveform (Tensor): Tensor of audio of size (c, n) where c is in the range [0,2)
blackman_coeff (float, optional): Constant coefficient for generalized Blackman window. (Default: ``0.42``)
channel (int, optional): Channel to extract (-1 -> expect mono, 0 -> left, 1 -> right) (Default: ``-1``)
dither (float, optional): Dithering constant (0.0 means no dither). If you turn this off, you should set
the energy_floor option, e.g. to 1.0 or 0.1 (Default: ``0.0``)
energy_floor (float, optional): Floor on energy (absolute, not relative) in Spectrogram computation. Caution:
this floor is applied to the zeroth component, representing the total signal energy. The floor on the
individual spectrogram elements is fixed at std::numeric_limits<float>::epsilon(). (Default: ``1.0``)
frame_length (float, optional): Frame length in milliseconds (Default: ``25.0``)
frame_shift (float, optional): Frame shift in milliseconds (Default: ``10.0``)
min_duration (float, optional): Minimum duration of segments to process (in seconds). (Default: ``0.0``)
preemphasis_coefficient (float, optional): Coefficient for use in signal preemphasis (Default: ``0.97``)
raw_energy (bool, optional): If True, compute energy before preemphasis and windowing (Default: ``True``)
remove_dc_offset (bool, optional): Subtract mean from waveform on each frame (Default: ``True``)
round_to_power_of_two (bool, optional): If True, round window size to power of two by zero-padding input
to FFT. (Default: ``True``)
sample_frequency (float, optional): Waveform data sample frequency (must match the waveform file, if
specified there) (Default: ``16000.0``)
snip_edges (bool, optional): If True, end effects will be handled by outputting only frames that completely fit
in the file, and the number of frames depends on the frame_length. If False, the number of frames
depends only on the frame_shift, and we reflect the data at the ends. (Default: ``True``)
subtract_mean (bool, optional): Subtract mean of each feature file [CMS]; not recommended to do
it this way. (Default: ``False``)
window_type (str, optional): Type of window ('hamming'|'hanning'|'povey'|'rectangular'|'blackman')
(Default: ``'povey'``)
Returns:
Tensor: A spectrogram identical to what Kaldi would output. The shape is
(m, ``padded_window_size // 2 + 1``) where m is calculated in _get_strided
"""
waveform, window_shift, window_size, padded_window_size = _get_waveform_and_window_properties(
waveform, channel, sample_frequency, frame_shift, frame_length, round_to_power_of_two, preemphasis_coefficient)
if len(waveform) < min_duration * sample_frequency:
# signal is too short
return torch.empty(0)
strided_input, signal_log_energy = _get_window(
waveform, padded_window_size, window_size, window_shift, window_type, blackman_coeff,
snip_edges, raw_energy, energy_floor, dither, remove_dc_offset, preemphasis_coefficient)
# size (m, padded_window_size // 2 + 1, 2)
fft = torch.rfft(strided_input, 1, normalized=False, onesided=True)
# Convert the FFT into a power spectrum
power_spectrum = torch.max(fft.pow(2).sum(2), EPSILON).log() # size (m, padded_window_size // 2 + 1)
power_spectrum[:, 0] = signal_log_energy
power_spectrum = _subtract_column_mean(power_spectrum, subtract_mean)
return power_spectrum
def inverse_mel_scale_scalar(mel_freq: float) -> float:
return 700.0 * (math.exp(mel_freq / 1127.0) - 1.0)
def inverse_mel_scale(mel_freq: Tensor) -> Tensor:
return 700.0 * ((mel_freq / 1127.0).exp() - 1.0)
def mel_scale_scalar(freq: float) -> float:
return 1127.0 * math.log(1.0 + freq / 700.0)
def mel_scale(freq: Tensor) -> Tensor:
return 1127.0 * (1.0 + freq / 700.0).log()
def vtln_warp_freq(vtln_low_cutoff: float,
vtln_high_cutoff: float,
low_freq: float,
high_freq: float,
vtln_warp_factor: float,
freq: Tensor) -> Tensor:
r"""This computes a VTLN warping function that is not the same as HTK's one,
but has similar inputs (this function has the advantage of never producing
empty bins).
This function computes a warp function F(freq), defined between low_freq
and high_freq inclusive, with the following properties:
F(low_freq) == low_freq
F(high_freq) == high_freq
The function is continuous and piecewise linear with two inflection
points.
The lower inflection point (measured in terms of the unwarped
frequency) is at frequency l, determined as described below.
The higher inflection point is at a frequency h, determined as
described below.
If l <= f <= h, then F(f) = f/vtln_warp_factor.
If the higher inflection point (measured in terms of the unwarped
frequency) is at h, then max(h, F(h)) == vtln_high_cutoff.
Since (by the last point) F(h) == h/vtln_warp_factor, then
max(h, h/vtln_warp_factor) == vtln_high_cutoff, so
h = vtln_high_cutoff / max(1, 1/vtln_warp_factor).
= vtln_high_cutoff * min(1, vtln_warp_factor).
If the lower inflection point (measured in terms of the unwarped
frequency) is at l, then min(l, F(l)) == vtln_low_cutoff
This implies that l = vtln_low_cutoff / min(1, 1/vtln_warp_factor)
= vtln_low_cutoff * max(1, vtln_warp_factor)
Args:
vtln_low_cutoff (float): Lower frequency cutoffs for VTLN
vtln_high_cutoff (float): Upper frequency cutoffs for VTLN
low_freq (float): Lower frequency cutoffs in mel computation
high_freq (float): Upper frequency cutoffs in mel computation
vtln_warp_factor (float): Vtln warp factor
freq (Tensor): given frequency in Hz
Returns:
Tensor: Freq after vtln warp
"""
assert vtln_low_cutoff > low_freq, 'be sure to set the vtln_low option higher than low_freq'
assert vtln_high_cutoff < high_freq, 'be sure to set the vtln_high option lower than high_freq [or negative]'
l = vtln_low_cutoff * max(1.0, vtln_warp_factor)
h = vtln_high_cutoff * min(1.0, vtln_warp_factor)
scale = 1.0 / vtln_warp_factor
Fl = scale * l # F(l)
Fh = scale * h # F(h)
assert l > low_freq and h < high_freq
# slope of left part of the 3-piece linear function
scale_left = (Fl - low_freq) / (l - low_freq)
# [slope of center part is just "scale"]
# slope of right part of the 3-piece linear function
scale_right = (high_freq - Fh) / (high_freq - h)
res = torch.empty_like(freq)
outside_low_high_freq = torch.lt(freq, low_freq) | torch.gt(freq, high_freq) # freq < low_freq || freq > high_freq
before_l = torch.lt(freq, l) # freq < l
before_h = torch.lt(freq, h) # freq < h
after_h = torch.ge(freq, h) # freq >= h
# order of operations matter here (since there is overlapping frequency regions)
res[after_h] = high_freq + scale_right * (freq[after_h] - high_freq)
res[before_h] = scale * freq[before_h]
res[before_l] = low_freq + scale_left * (freq[before_l] - low_freq)
res[outside_low_high_freq] = freq[outside_low_high_freq]
return res
def vtln_warp_mel_freq(vtln_low_cutoff: float,
vtln_high_cutoff: float,
low_freq, high_freq: float,
vtln_warp_factor: float,
mel_freq: Tensor) -> Tensor:
r"""
Args:
vtln_low_cutoff (float): Lower frequency cutoffs for VTLN
vtln_high_cutoff (float): Upper frequency cutoffs for VTLN
low_freq (float): Lower frequency cutoffs in mel computation
high_freq (float): Upper frequency cutoffs in mel computation
vtln_warp_factor (float): Vtln warp factor
mel_freq (Tensor): Given frequency in Mel
Returns:
Tensor: ``mel_freq`` after vtln warp
"""
return mel_scale(vtln_warp_freq(vtln_low_cutoff, vtln_high_cutoff, low_freq, high_freq,
vtln_warp_factor, inverse_mel_scale(mel_freq)))
def get_mel_banks(num_bins: int,
window_length_padded: int,
sample_freq: float,
low_freq: float,
high_freq: float,
vtln_low: float,
vtln_high: float,
vtln_warp_factor: float) -> Tuple[Tensor, Tensor]:
"""
Returns:
(Tensor, Tensor): The tuple consists of ``bins`` (which is
melbank of size (``num_bins``, ``num_fft_bins``)) and ``center_freqs`` (which is
center frequencies of bins of size (``num_bins``)).
"""
assert num_bins > 3, 'Must have at least 3 mel bins'
assert window_length_padded % 2 == 0
num_fft_bins = window_length_padded / 2
nyquist = 0.5 * sample_freq
if high_freq <= 0.0:
high_freq += nyquist
assert (0.0 <= low_freq < nyquist) and (0.0 < high_freq <= nyquist) and (low_freq < high_freq), \
('Bad values in options: low-freq %f and high-freq %f vs. nyquist %f' % (low_freq, high_freq, nyquist))
# fft-bin width [think of it as Nyquist-freq / half-window-length]
fft_bin_width = sample_freq / window_length_padded
mel_low_freq = mel_scale_scalar(low_freq)
mel_high_freq = mel_scale_scalar(high_freq)
# divide by num_bins+1 in next line because of end-effects where the bins
# spread out to the sides.
mel_freq_delta = (mel_high_freq - mel_low_freq) / (num_bins + 1)
if vtln_high < 0.0:
vtln_high += nyquist
assert vtln_warp_factor == 1.0 or ((low_freq < vtln_low < high_freq) and
(0.0 < vtln_high < high_freq) and (vtln_low < vtln_high)), \
('Bad values in options: vtln-low %f and vtln-high %f, versus low-freq %f and high-freq %f' %
(vtln_low, vtln_high, low_freq, high_freq))
bin = torch.arange(num_bins).unsqueeze(1)
left_mel = mel_low_freq + bin * mel_freq_delta # size(num_bins, 1)
center_mel = mel_low_freq + (bin + 1.0) * mel_freq_delta # size(num_bins, 1)
right_mel = mel_low_freq + (bin + 2.0) * mel_freq_delta # size(num_bins, 1)
if vtln_warp_factor != 1.0:
left_mel = vtln_warp_mel_freq(vtln_low, vtln_high, low_freq, high_freq, vtln_warp_factor, left_mel)
center_mel = vtln_warp_mel_freq(vtln_low, vtln_high, low_freq, high_freq, vtln_warp_factor, center_mel)
right_mel = vtln_warp_mel_freq(vtln_low, vtln_high, low_freq, high_freq, vtln_warp_factor, right_mel)
center_freqs = inverse_mel_scale(center_mel) # size (num_bins)
# size(1, num_fft_bins)
mel = mel_scale(fft_bin_width * torch.arange(num_fft_bins)).unsqueeze(0)
# size (num_bins, num_fft_bins)
up_slope = (mel - left_mel) / (center_mel - left_mel)
down_slope = (right_mel - mel) / (right_mel - center_mel)
if vtln_warp_factor == 1.0:
# left_mel < center_mel < right_mel so we can min the two slopes and clamp negative values
bins = torch.max(torch.zeros(1), torch.min(up_slope, down_slope))
else:
# warping can move the order of left_mel, center_mel, right_mel anywhere
bins = torch.zeros_like(up_slope)
up_idx = torch.gt(mel, left_mel) & torch.le(mel, center_mel) # left_mel < mel <= center_mel
down_idx = torch.gt(mel, center_mel) & torch.lt(mel, right_mel) # center_mel < mel < right_mel
bins[up_idx] = up_slope[up_idx]
bins[down_idx] = down_slope[down_idx]
return bins, center_freqs
[docs]def fbank(waveform: Tensor,
blackman_coeff: float = 0.42,
channel: int = -1,
dither: float = 0.0,
energy_floor: float = 1.0,
frame_length: float = 25.0,
frame_shift: float = 10.0,
high_freq: float = 0.0,
htk_compat: bool = False,
low_freq: float = 20.0,
min_duration: float = 0.0,
num_mel_bins: int = 23,
preemphasis_coefficient: float = 0.97,
raw_energy: bool = True,
remove_dc_offset: bool = True,
round_to_power_of_two: bool = True,
sample_frequency: float = 16000.0,
snip_edges: bool = True,
subtract_mean: bool = False,
use_energy: bool = False,
use_log_fbank: bool = True,
use_power: bool = True,
vtln_high: float = -500.0,
vtln_low: float = 100.0,
vtln_warp: float = 1.0,
window_type: str = POVEY) -> Tensor:
r"""Create a fbank from a raw audio signal. This matches the input/output of Kaldi's
compute-fbank-feats.
Args:
waveform (Tensor): Tensor of audio of size (c, n) where c is in the range [0,2)
blackman_coeff (float, optional): Constant coefficient for generalized Blackman window. (Default: ``0.42``)
channel (int, optional): Channel to extract (-1 -> expect mono, 0 -> left, 1 -> right) (Default: ``-1``)
dither (float, optional): Dithering constant (0.0 means no dither). If you turn this off, you should set
the energy_floor option, e.g. to 1.0 or 0.1 (Default: ``0.0``)
energy_floor (float, optional): Floor on energy (absolute, not relative) in Spectrogram computation. Caution:
this floor is applied to the zeroth component, representing the total signal energy. The floor on the
individual spectrogram elements is fixed at std::numeric_limits<float>::epsilon(). (Default: ``1.0``)
frame_length (float, optional): Frame length in milliseconds (Default: ``25.0``)
frame_shift (float, optional): Frame shift in milliseconds (Default: ``10.0``)
high_freq (float, optional): High cutoff frequency for mel bins (if <= 0, offset from Nyquist)
(Default: ``0.0``)
htk_compat (bool, optional): If true, put energy last. Warning: not sufficient to get HTK compatible features
(need to change other parameters). (Default: ``False``)
low_freq (float, optional): Low cutoff frequency for mel bins (Default: ``20.0``)
min_duration (float, optional): Minimum duration of segments to process (in seconds). (Default: ``0.0``)
num_mel_bins (int, optional): Number of triangular mel-frequency bins (Default: ``23``)
preemphasis_coefficient (float, optional): Coefficient for use in signal preemphasis (Default: ``0.97``)
raw_energy (bool, optional): If True, compute energy before preemphasis and windowing (Default: ``True``)
remove_dc_offset (bool, optional): Subtract mean from waveform on each frame (Default: ``True``)
round_to_power_of_two (bool, optional): If True, round window size to power of two by zero-padding input
to FFT. (Default: ``True``)
sample_frequency (float, optional): Waveform data sample frequency (must match the waveform file, if
specified there) (Default: ``16000.0``)
snip_edges (bool, optional): If True, end effects will be handled by outputting only frames that completely fit
in the file, and the number of frames depends on the frame_length. If False, the number of frames
depends only on the frame_shift, and we reflect the data at the ends. (Default: ``True``)
subtract_mean (bool, optional): Subtract mean of each feature file [CMS]; not recommended to do
it this way. (Default: ``False``)
use_energy (bool, optional): Add an extra dimension with energy to the FBANK output. (Default: ``False``)
use_log_fbank (bool, optional):If true, produce log-filterbank, else produce linear. (Default: ``True``)
use_power (bool, optional): If true, use power, else use magnitude. (Default: ``True``)
vtln_high (float, optional): High inflection point in piecewise linear VTLN warping function (if
negative, offset from high-mel-freq (Default: ``-500.0``)
vtln_low (float, optional): Low inflection point in piecewise linear VTLN warping function (Default: ``100.0``)
vtln_warp (float, optional): Vtln warp factor (only applicable if vtln_map not specified) (Default: ``1.0``)
window_type (str, optional): Type of window ('hamming'|'hanning'|'povey'|'rectangular'|'blackman')
(Default: ``'povey'``)
Returns:
Tensor: A fbank identical to what Kaldi would output. The shape is (m, ``num_mel_bins + use_energy``)
where m is calculated in _get_strided
"""
waveform, window_shift, window_size, padded_window_size = _get_waveform_and_window_properties(
waveform, channel, sample_frequency, frame_shift, frame_length, round_to_power_of_two, preemphasis_coefficient)
if len(waveform) < min_duration * sample_frequency:
# signal is too short
return torch.empty(0)
# strided_input, size (m, padded_window_size) and signal_log_energy, size (m)
strided_input, signal_log_energy = _get_window(
waveform, padded_window_size, window_size, window_shift, window_type, blackman_coeff,
snip_edges, raw_energy, energy_floor, dither, remove_dc_offset, preemphasis_coefficient)
# size (m, padded_window_size // 2 + 1, 2)
fft = torch.rfft(strided_input, 1, normalized=False, onesided=True)
power_spectrum = fft.pow(2).sum(2).unsqueeze(1) # size (m, 1, padded_window_size // 2 + 1)
if not use_power:
power_spectrum = power_spectrum.pow(0.5)
# size (num_mel_bins, padded_window_size // 2)
mel_energies, _ = get_mel_banks(num_mel_bins, padded_window_size, sample_frequency,
low_freq, high_freq, vtln_low, vtln_high, vtln_warp)
# pad right column with zeros and add dimension, size (1, num_mel_bins, padded_window_size // 2 + 1)
mel_energies = torch.nn.functional.pad(mel_energies, (0, 1), mode='constant', value=0).unsqueeze(0)
# sum with mel fiterbanks over the power spectrum, size (m, num_mel_bins)
mel_energies = (power_spectrum * mel_energies).sum(dim=2)
if use_log_fbank:
# avoid log of zero (which should be prevented anyway by dithering)
mel_energies = torch.max(mel_energies, EPSILON).log()
# if use_energy then add it as the last column for htk_compat == true else first column
if use_energy:
signal_log_energy = signal_log_energy.unsqueeze(1) # size (m, 1)
# returns size (m, num_mel_bins + 1)
if htk_compat:
mel_energies = torch.cat((mel_energies, signal_log_energy), dim=1)
else:
mel_energies = torch.cat((signal_log_energy, mel_energies), dim=1)
mel_energies = _subtract_column_mean(mel_energies, subtract_mean)
return mel_energies
def _get_dct_matrix(num_ceps: int, num_mel_bins: int) -> Tensor:
# returns a dct matrix of size (num_mel_bins, num_ceps)
# size (num_mel_bins, num_mel_bins)
dct_matrix = torchaudio.functional.create_dct(num_mel_bins, num_mel_bins, 'ortho')
# kaldi expects the first cepstral to be weighted sum of factor sqrt(1/num_mel_bins)
# this would be the first column in the dct_matrix for torchaudio as it expects a
# right multiply (which would be the first column of the kaldi's dct_matrix as kaldi
# expects a left multiply e.g. dct_matrix * vector).
dct_matrix[:, 0] = math.sqrt(1 / float(num_mel_bins))
dct_matrix = dct_matrix[:, :num_ceps]
return dct_matrix
def _get_lifter_coeffs(num_ceps: int, cepstral_lifter: float) -> Tensor:
# returns size (num_ceps)
# Compute liftering coefficients (scaling on cepstral coeffs)
# coeffs are numbered slightly differently from HTK: the zeroth index is C0, which is not affected.
i = torch.arange(num_ceps)
return 1.0 + 0.5 * cepstral_lifter * torch.sin(math.pi * i / cepstral_lifter)
[docs]def mfcc(
waveform: Tensor,
blackman_coeff: float = 0.42,
cepstral_lifter: float = 22.0,
channel: int = -1,
dither: float = 0.0,
energy_floor: float = 1.0,
frame_length: float = 25.0,
frame_shift: float = 10.0,
high_freq: float = 0.0,
htk_compat: bool = False,
low_freq: float = 20.0,
num_ceps: int = 13,
min_duration: float = 0.0,
num_mel_bins: int = 23,
preemphasis_coefficient: float = 0.97,
raw_energy: bool = True,
remove_dc_offset: bool = True,
round_to_power_of_two: bool = True,
sample_frequency: float = 16000.0,
snip_edges: bool = True,
subtract_mean: bool = False,
use_energy: bool = False,
vtln_high: float = -500.0,
vtln_low: float = 100.0,
vtln_warp: float = 1.0,
window_type: str = POVEY) -> Tensor:
r"""Create a mfcc from a raw audio signal. This matches the input/output of Kaldi's
compute-mfcc-feats.
Args:
waveform (Tensor): Tensor of audio of size (c, n) where c is in the range [0,2)
blackman_coeff (float, optional): Constant coefficient for generalized Blackman window. (Default: ``0.42``)
cepstral_lifter (float, optional): Constant that controls scaling of MFCCs (Default: ``22.0``)
channel (int, optional): Channel to extract (-1 -> expect mono, 0 -> left, 1 -> right) (Default: ``-1``)
dither (float, optional): Dithering constant (0.0 means no dither). If you turn this off, you should set
the energy_floor option, e.g. to 1.0 or 0.1 (Default: ``0.0``)
energy_floor (float, optional): Floor on energy (absolute, not relative) in Spectrogram computation. Caution:
this floor is applied to the zeroth component, representing the total signal energy. The floor on the
individual spectrogram elements is fixed at std::numeric_limits<float>::epsilon(). (Default: ``1.0``)
frame_length (float, optional): Frame length in milliseconds (Default: ``25.0``)
frame_shift (float, optional): Frame shift in milliseconds (Default: ``10.0``)
high_freq (float, optional): High cutoff frequency for mel bins (if <= 0, offset from Nyquist)
(Default: ``0.0``)
htk_compat (bool, optional): If true, put energy last. Warning: not sufficient to get HTK compatible
features (need to change other parameters). (Default: ``False``)
low_freq (float, optional): Low cutoff frequency for mel bins (Default: ``20.0``)
num_ceps (int, optional): Number of cepstra in MFCC computation (including C0) (Default: ``13``)
min_duration (float, optional): Minimum duration of segments to process (in seconds). (Default: ``0.0``)
num_mel_bins (int, optional): Number of triangular mel-frequency bins (Default: ``23``)
preemphasis_coefficient (float, optional): Coefficient for use in signal preemphasis (Default: ``0.97``)
raw_energy (bool, optional): If True, compute energy before preemphasis and windowing (Default: ``True``)
remove_dc_offset (bool, optional): Subtract mean from waveform on each frame (Default: ``True``)
round_to_power_of_two (bool, optional): If True, round window size to power of two by zero-padding input
to FFT. (Default: ``True``)
sample_frequency (float, optional): Waveform data sample frequency (must match the waveform file, if
specified there) (Default: ``16000.0``)
snip_edges (bool, optional): If True, end effects will be handled by outputting only frames that completely fit
in the file, and the number of frames depends on the frame_length. If False, the number of frames
depends only on the frame_shift, and we reflect the data at the ends. (Default: ``True``)
subtract_mean (bool, optional): Subtract mean of each feature file [CMS]; not recommended to do
it this way. (Default: ``False``)
use_energy (bool, optional): Add an extra dimension with energy to the FBANK output. (Default: ``False``)
vtln_high (float, optional): High inflection point in piecewise linear VTLN warping function (if
negative, offset from high-mel-freq (Default: ``-500.0``)
vtln_low (float, optional): Low inflection point in piecewise linear VTLN warping function (Default: ``100.0``)
vtln_warp (float, optional): Vtln warp factor (only applicable if vtln_map not specified) (Default: ``1.0``)
window_type (str, optional): Type of window ('hamming'|'hanning'|'povey'|'rectangular'|'blackman')
(Default: ``"povey"``)
Returns:
Tensor: A mfcc identical to what Kaldi would output. The shape is (m, ``num_ceps``)
where m is calculated in _get_strided
"""
assert num_ceps <= num_mel_bins, 'num_ceps cannot be larger than num_mel_bins: %d vs %d' % (num_ceps, num_mel_bins)
# The mel_energies should not be squared (use_power=True), not have mean subtracted
# (subtract_mean=False), and use log (use_log_fbank=True).
# size (m, num_mel_bins + use_energy)
feature = fbank(waveform=waveform, blackman_coeff=blackman_coeff, channel=channel,
dither=dither, energy_floor=energy_floor, frame_length=frame_length,
frame_shift=frame_shift, high_freq=high_freq, htk_compat=htk_compat,
low_freq=low_freq, min_duration=min_duration, num_mel_bins=num_mel_bins,
preemphasis_coefficient=preemphasis_coefficient, raw_energy=raw_energy,
remove_dc_offset=remove_dc_offset, round_to_power_of_two=round_to_power_of_two,
sample_frequency=sample_frequency, snip_edges=snip_edges, subtract_mean=False,
use_energy=use_energy, use_log_fbank=True, use_power=True,
vtln_high=vtln_high, vtln_low=vtln_low, vtln_warp=vtln_warp, window_type=window_type)
if use_energy:
# size (m)
signal_log_energy = feature[:, num_mel_bins if htk_compat else 0]
# offset is 0 if htk_compat==True else 1
mel_offset = int(not htk_compat)
feature = feature[:, mel_offset:(num_mel_bins + mel_offset)]
# size (num_mel_bins, num_ceps)
dct_matrix = _get_dct_matrix(num_ceps, num_mel_bins)
# size (m, num_ceps)
feature = feature.matmul(dct_matrix)
if cepstral_lifter != 0.0:
# size (1, num_ceps)
lifter_coeffs = _get_lifter_coeffs(num_ceps, cepstral_lifter).unsqueeze(0)
feature *= lifter_coeffs
# if use_energy then replace the last column for htk_compat == true else first column
if use_energy:
feature[:, 0] = signal_log_energy
if htk_compat:
energy = feature[:, 0].unsqueeze(1) # size (m, 1)
feature = feature[:, 1:] # size (m, num_ceps - 1)
if not use_energy:
# scale on C0 (actually removing a scale we previously added that's
# part of one common definition of the cosine transform.)
energy *= math.sqrt(2)
feature = torch.cat((feature, energy), dim=1)
feature = _subtract_column_mean(feature, subtract_mean)
return feature
def _get_LR_indices_and_weights(orig_freq: float,
new_freq: float,
output_samples_in_unit: int,
window_width: float,
lowpass_cutoff: float,
lowpass_filter_width: int) -> Tuple[Tensor, Tensor]:
r"""Based on LinearResample::SetIndexesAndWeights where it retrieves the weights for
resampling as well as the indices in which they are valid. LinearResample (LR) means
that the output signal is at linearly spaced intervals (i.e the output signal has a
frequency of ``new_freq``). It uses sinc/bandlimited interpolation to upsample/downsample
the signal.
The reason why the same filter is not used for multiple convolutions is because the
sinc function could sampled at different points in time. For example, suppose
a signal is sampled at the timestamps (seconds)
0 16 32
and we want it to be sampled at the timestamps (seconds)
0 5 10 15 20 25 30 35
at the timestamp of 16, the delta timestamps are
16 11 6 1 4 9 14 19
at the timestamp of 32, the delta timestamps are
32 27 22 17 12 8 2 3
As we can see from deltas, the sinc function is sampled at different points of time
assuming the center of the sinc function is at 0, 16, and 32 (the deltas [..., 6, 1, 4, ....]
for 16 vs [...., 2, 3, ....] for 32)
Example, one case is when the ``orig_freq`` and ``new_freq`` are multiples of each other then
there needs to be one filter.
A windowed filter function (i.e. Hanning * sinc) because the ideal case of sinc function
has infinite support (non-zero for all values) so instead it is truncated and multiplied by
a window function which gives it less-than-perfect rolloff [1].
[1] Chapter 16: Windowed-Sinc Filters, https://www.dspguide.com/ch16/1.htm
Args:
orig_freq (float): The original frequency of the signal
new_freq (float): The desired frequency
output_samples_in_unit (int): The number of output samples in the smallest repeating unit:
num_samp_out = new_freq / Gcd(orig_freq, new_freq)
window_width (float): The width of the window which is nonzero
lowpass_cutoff (float): The filter cutoff in Hz. The filter cutoff needs to be less
than samp_rate_in_hz/2 and less than samp_rate_out_hz/2.
lowpass_filter_width (int): Controls the sharpness of the filter, more == sharper but less
efficient. We suggest around 4 to 10 for normal use
Returns:
(Tensor, Tensor): A tuple of ``min_input_index`` (which is the minimum indices
where the window is valid, size (``output_samples_in_unit``)) and ``weights`` (which is the weights
which correspond with min_input_index, size (``output_samples_in_unit``, ``max_weight_width``)).
"""
assert lowpass_cutoff < min(orig_freq, new_freq) / 2
output_t = torch.arange(0., output_samples_in_unit) / new_freq
min_t = output_t - window_width
max_t = output_t + window_width
min_input_index = torch.ceil(min_t * orig_freq) # size (output_samples_in_unit)
max_input_index = torch.floor(max_t * orig_freq) # size (output_samples_in_unit)
num_indices = max_input_index - min_input_index + 1 # size (output_samples_in_unit)
max_weight_width = num_indices.max()
# create a group of weights of size (output_samples_in_unit, max_weight_width)
j = torch.arange(max_weight_width).unsqueeze(0)
input_index = min_input_index.unsqueeze(1) + j
delta_t = (input_index / orig_freq) - output_t.unsqueeze(1)
weights = torch.zeros_like(delta_t)
inside_window_indices = delta_t.abs().lt(window_width)
# raised-cosine (Hanning) window with width `window_width`
weights[inside_window_indices] = 0.5 * (1 + torch.cos(2 * math.pi * lowpass_cutoff /
lowpass_filter_width * delta_t[inside_window_indices]))
t_eq_zero_indices = delta_t.eq(0.0)
t_not_eq_zero_indices = ~t_eq_zero_indices
# sinc filter function
weights[t_not_eq_zero_indices] *= torch.sin(
2 * math.pi * lowpass_cutoff * delta_t[t_not_eq_zero_indices]) / (math.pi * delta_t[t_not_eq_zero_indices])
# limit of the function at t = 0
weights[t_eq_zero_indices] *= 2 * lowpass_cutoff
weights /= orig_freq # size (output_samples_in_unit, max_weight_width)
return min_input_index, weights
def _lcm(a: int, b: int) -> int:
return abs(a * b) // math.gcd(a, b)
def _get_num_LR_output_samples(input_num_samp: int,
samp_rate_in: float,
samp_rate_out: float) -> int:
r"""Based on LinearResample::GetNumOutputSamples. LinearResample (LR) means that
the output signal is at linearly spaced intervals (i.e the output signal has a
frequency of ``new_freq``). It uses sinc/bandlimited interpolation to upsample/downsample
the signal.
Args:
input_num_samp (int): The number of samples in the input
samp_rate_in (float): The original frequency of the signal
samp_rate_out (float): The desired frequency
Returns:
int: The number of output samples
"""
# For exact computation, we measure time in "ticks" of 1.0 / tick_freq,
# where tick_freq is the least common multiple of samp_rate_in and
# samp_rate_out.
samp_rate_in = int(samp_rate_in)
samp_rate_out = int(samp_rate_out)
tick_freq = _lcm(samp_rate_in, samp_rate_out)
ticks_per_input_period = tick_freq // samp_rate_in
# work out the number of ticks in the time interval
# [ 0, input_num_samp/samp_rate_in ).
interval_length_in_ticks = input_num_samp * ticks_per_input_period
if interval_length_in_ticks <= 0:
return 0
ticks_per_output_period = tick_freq // samp_rate_out
# Get the last output-sample in the closed interval, i.e. replacing [ ) with
# [ ]. Note: integer division rounds down. See
# http://en.wikipedia.org/wiki/Interval_(mathematics) for an explanation of
# the notation.
last_output_samp = interval_length_in_ticks // ticks_per_output_period
# We need the last output-sample in the open interval, so if it takes us to
# the end of the interval exactly, subtract one.
if last_output_samp * ticks_per_output_period == interval_length_in_ticks:
last_output_samp -= 1
# First output-sample index is zero, so the number of output samples
# is the last output-sample plus one.
num_output_samp = last_output_samp + 1
return num_output_samp
