Source code for torchaudio.functional.functional
# -*- coding: utf-8 -*-
import io
import math
import warnings
from collections.abc import Sequence
from typing import List, Optional, Tuple, Union
import torch
import torchaudio
from torch import Tensor
from .filtering import highpass_biquad, treble_biquad
__all__ = [
"spectrogram",
"inverse_spectrogram",
"griffinlim",
"amplitude_to_DB",
"DB_to_amplitude",
"compute_deltas",
"compute_kaldi_pitch",
"melscale_fbanks",
"linear_fbanks",
"create_dct",
"compute_deltas",
"detect_pitch_frequency",
"DB_to_amplitude",
"mu_law_encoding",
"mu_law_decoding",
"phase_vocoder",
"mask_along_axis",
"mask_along_axis_iid",
"sliding_window_cmn",
"spectral_centroid",
"apply_codec",
"resample",
"edit_distance",
"loudness",
"pitch_shift",
"rnnt_loss",
"psd",
"mvdr_weights_souden",
"mvdr_weights_rtf",
"rtf_evd",
"rtf_power",
"apply_beamforming",
"fftconvolve",
"convolve",
"add_noise",
"speed",
"preemphasis",
"deemphasis",
]
[docs]def spectrogram(
waveform: Tensor,
pad: int,
window: Tensor,
n_fft: int,
hop_length: int,
win_length: int,
power: Optional[float],
normalized: Union[bool, str],
center: bool = True,
pad_mode: str = "reflect",
onesided: bool = True,
return_complex: Optional[bool] = None,
) -> Tensor:
r"""Create a spectrogram or a batch of spectrograms from a raw audio signal.
The spectrogram can be either magnitude-only or complex.
.. devices:: CPU CUDA
.. properties:: Autograd TorchScript
Args:
waveform (Tensor): Tensor of audio of dimension `(..., time)`
pad (int): Two sided padding of signal
window (Tensor): Window tensor that is applied/multiplied to each frame/window
n_fft (int): Size of FFT
hop_length (int): Length of hop between STFT windows
win_length (int): Window size
power (float or None): Exponent for the magnitude spectrogram,
(must be > 0) e.g., 1 for energy, 2 for power, etc.
If None, then the complex spectrum is returned instead.
normalized (bool or str): Whether to normalize by magnitude after stft. If input is str, choices are
``"window"`` and ``"frame_length"``, if specific normalization type is desirable. ``True`` maps to
``"window"``. When normalized on ``"window"``, waveform is normalized upon the window's L2 energy. If
normalized on ``"frame_length"``, waveform is normalized by dividing by
:math:`(\text{frame\_length})^{0.5}`.
center (bool, optional): whether to pad :attr:`waveform` on both sides so
that the :math:`t`-th frame is centered at time :math:`t \times \text{hop\_length}`.
Default: ``True``
pad_mode (string, optional): controls the padding method used when
:attr:`center` is ``True``. Default: ``"reflect"``
onesided (bool, optional): controls whether to return half of results to
avoid redundancy. Default: ``True``
return_complex (bool, optional):
Deprecated and not used.
Returns:
Tensor: Dimension `(..., freq, time)`, freq is
``n_fft // 2 + 1`` and ``n_fft`` is the number of
Fourier bins, and time is the number of window hops (n_frame).
"""
if return_complex is not None:
warnings.warn(
"`return_complex` argument is now deprecated and is not effective."
"`torchaudio.functional.spectrogram(power=None)` always returns a tensor with "
"complex dtype. Please remove the argument in the function call."
)
if pad > 0:
# TODO add "with torch.no_grad():" back when JIT supports it
waveform = torch.nn.functional.pad(waveform, (pad, pad), "constant")
frame_length_norm, window_norm = _get_spec_norms(normalized)
# pack batch
shape = waveform.size()
waveform = waveform.reshape(-1, shape[-1])
# default values are consistent with librosa.core.spectrum._spectrogram
spec_f = torch.stft(
input=waveform,
n_fft=n_fft,
hop_length=hop_length,
win_length=win_length,
window=window,
center=center,
pad_mode=pad_mode,
normalized=frame_length_norm,
onesided=onesided,
return_complex=True,
)
# unpack batch
spec_f = spec_f.reshape(shape[:-1] + spec_f.shape[-2:])
if window_norm:
spec_f /= window.pow(2.0).sum().sqrt()
if power is not None:
if power == 1.0:
return spec_f.abs()
return spec_f.abs().pow(power)
return spec_f
[docs]def inverse_spectrogram(
spectrogram: Tensor,
length: Optional[int],
pad: int,
window: Tensor,
n_fft: int,
hop_length: int,
win_length: int,
normalized: Union[bool, str],
center: bool = True,
pad_mode: str = "reflect",
onesided: bool = True,
) -> Tensor:
r"""Create an inverse spectrogram or a batch of inverse spectrograms from the provided
complex-valued spectrogram.
.. devices:: CPU CUDA
.. properties:: Autograd TorchScript
Args:
spectrogram (Tensor): Complex tensor of audio of dimension (..., freq, time).
length (int or None): The output length of the waveform.
pad (int): Two sided padding of signal. It is only effective when ``length`` is provided.
window (Tensor): Window tensor that is applied/multiplied to each frame/window
n_fft (int): Size of FFT
hop_length (int): Length of hop between STFT windows
win_length (int): Window size
normalized (bool or str): Whether the stft output was normalized by magnitude. If input is str, choices are
``"window"`` and ``"frame_length"``, dependent on normalization mode. ``True`` maps to
``"window"``.
center (bool, optional): whether the waveform was padded on both sides so
that the :math:`t`-th frame is centered at time :math:`t \times \text{hop\_length}`.
Default: ``True``
pad_mode (string, optional): controls the padding method used when
:attr:`center` is ``True``. This parameter is provided for compatibility with the
spectrogram function and is not used. Default: ``"reflect"``
onesided (bool, optional): controls whether spectrogram was done in onesided mode.
Default: ``True``
Returns:
Tensor: Dimension `(..., time)`. Least squares estimation of the original signal.
"""
frame_length_norm, window_norm = _get_spec_norms(normalized)
if not spectrogram.is_complex():
raise ValueError("Expected `spectrogram` to be complex dtype.")
if window_norm:
spectrogram = spectrogram * window.pow(2.0).sum().sqrt()
# pack batch
shape = spectrogram.size()
spectrogram = spectrogram.reshape(-1, shape[-2], shape[-1])
# default values are consistent with librosa.core.spectrum._spectrogram
waveform = torch.istft(
input=spectrogram,
n_fft=n_fft,
hop_length=hop_length,
win_length=win_length,
window=window,
center=center,
normalized=frame_length_norm,
onesided=onesided,
length=length + 2 * pad if length is not None else None,
return_complex=False,
)
if length is not None and pad > 0:
# remove padding from front and back
waveform = waveform[:, pad:-pad]
# unpack batch
waveform = waveform.reshape(shape[:-2] + waveform.shape[-1:])
return waveform
def _get_spec_norms(normalized: Union[str, bool]):
frame_length_norm, window_norm = False, False
if torch.jit.isinstance(normalized, str):
if normalized not in ["frame_length", "window"]:
raise ValueError("Invalid normalized parameter: {}".format(normalized))
if normalized == "frame_length":
frame_length_norm = True
elif normalized == "window":
window_norm = True
elif torch.jit.isinstance(normalized, bool):
if normalized:
window_norm = True
else:
raise TypeError("Input type not supported")
return frame_length_norm, window_norm
def _get_complex_dtype(real_dtype: torch.dtype):
if real_dtype == torch.double:
return torch.cdouble
if real_dtype == torch.float:
return torch.cfloat
if real_dtype == torch.half:
return torch.complex32
raise ValueError(f"Unexpected dtype {real_dtype}")
[docs]def griffinlim(
specgram: Tensor,
window: Tensor,
n_fft: int,
hop_length: int,
win_length: int,
power: float,
n_iter: int,
momentum: float,
length: Optional[int],
rand_init: bool,
) -> Tensor:
r"""Compute waveform from a linear scale magnitude spectrogram using the Griffin-Lim transformation.
.. devices:: CPU CUDA
.. properties:: Autograd TorchScript
Implementation ported from
*librosa* :cite:`brian_mcfee-proc-scipy-2015`, *A fast Griffin-Lim algorithm* :cite:`6701851`
and *Signal estimation from modified short-time Fourier transform* :cite:`1172092`.
Args:
specgram (Tensor): A magnitude-only STFT spectrogram of dimension `(..., freq, frames)`
where freq is ``n_fft // 2 + 1``.
window (Tensor): Window tensor that is applied/multiplied to each frame/window
n_fft (int): Size of FFT, creates ``n_fft // 2 + 1`` bins
hop_length (int): Length of hop between STFT windows. (
Default: ``win_length // 2``)
win_length (int): Window size. (Default: ``n_fft``)
power (float): Exponent for the magnitude spectrogram,
(must be > 0) e.g., 1 for energy, 2 for power, etc.
n_iter (int): Number of iteration for phase recovery process.
momentum (float): The momentum parameter for fast Griffin-Lim.
Setting this to 0 recovers the original Griffin-Lim method.
Values near 1 can lead to faster convergence, but above 1 may not converge.
length (int or None): Array length of the expected output.
rand_init (bool): Initializes phase randomly if True, to zero otherwise.
Returns:
Tensor: waveform of `(..., time)`, where time equals the ``length`` parameter if given.
"""
if not 0 <= momentum < 1:
raise ValueError("momentum must be in range [0, 1). Found: {}".format(momentum))
momentum = momentum / (1 + momentum)
# pack batch
shape = specgram.size()
specgram = specgram.reshape([-1] + list(shape[-2:]))
specgram = specgram.pow(1 / power)
# initialize the phase
if rand_init:
angles = torch.rand(specgram.size(), dtype=_get_complex_dtype(specgram.dtype), device=specgram.device)
else:
angles = torch.full(specgram.size(), 1, dtype=_get_complex_dtype(specgram.dtype), device=specgram.device)
# And initialize the previous iterate to 0
tprev = torch.tensor(0.0, dtype=specgram.dtype, device=specgram.device)
for _ in range(n_iter):
# Invert with our current estimate of the phases
inverse = torch.istft(
specgram * angles, n_fft=n_fft, hop_length=hop_length, win_length=win_length, window=window, length=length
)
# Rebuild the spectrogram
rebuilt = torch.stft(
input=inverse,
n_fft=n_fft,
hop_length=hop_length,
win_length=win_length,
window=window,
center=True,
pad_mode="reflect",
normalized=False,
onesided=True,
return_complex=True,
)
# Update our phase estimates
angles = rebuilt
if momentum:
angles = angles - tprev.mul_(momentum)
angles = angles.div(angles.abs().add(1e-16))
# Store the previous iterate
tprev = rebuilt
# Return the final phase estimates
waveform = torch.istft(
specgram * angles, n_fft=n_fft, hop_length=hop_length, win_length=win_length, window=window, length=length
)
# unpack batch
waveform = waveform.reshape(shape[:-2] + waveform.shape[-1:])
return waveform
[docs]def amplitude_to_DB(
x: Tensor, multiplier: float, amin: float, db_multiplier: float, top_db: Optional[float] = None
) -> Tensor:
r"""Turn a spectrogram from the power/amplitude scale to the decibel scale.
.. devices:: CPU CUDA
.. properties:: Autograd TorchScript
The output of each tensor in a batch depends on the maximum value of that tensor,
and so may return different values for an audio clip split into snippets vs. a full clip.
Args:
x (Tensor): Input spectrogram(s) before being converted to decibel scale. Input should take
the form `(..., freq, time)`. Batched inputs should include a channel dimension and
have the form `(batch, channel, freq, time)`.
multiplier (float): Use 10. for power and 20. for amplitude
amin (float): Number to clamp ``x``
db_multiplier (float): Log10(max(reference value and amin))
top_db (float or None, optional): Minimum negative cut-off in decibels. A reasonable number
is 80. (Default: ``None``)
Returns:
Tensor: Output tensor in decibel scale
"""
x_db = multiplier * torch.log10(torch.clamp(x, min=amin))
x_db -= multiplier * db_multiplier
if top_db is not None:
# Expand batch
shape = x_db.size()
packed_channels = shape[-3] if x_db.dim() > 2 else 1
x_db = x_db.reshape(-1, packed_channels, shape[-2], shape[-1])
x_db = torch.max(x_db, (x_db.amax(dim=(-3, -2, -1)) - top_db).view(-1, 1, 1, 1))
# Repack batch
x_db = x_db.reshape(shape)
return x_db
[docs]def DB_to_amplitude(x: Tensor, ref: float, power: float) -> Tensor:
r"""Turn a tensor from the decibel scale to the power/amplitude scale.
.. devices:: CPU CUDA
.. properties:: TorchScript
Args:
x (Tensor): Input tensor before being converted to power/amplitude scale.
ref (float): Reference which the output will be scaled by.
power (float): If power equals 1, will compute DB to power. If 0.5, will compute DB to amplitude.
Returns:
Tensor: Output tensor in power/amplitude scale.
"""
return ref * torch.pow(torch.pow(10.0, 0.1 * x), power)
def _hz_to_mel(freq: float, mel_scale: str = "htk") -> float:
r"""Convert Hz to Mels.
Args:
freqs (float): Frequencies in Hz
mel_scale (str, optional): Scale to use: ``htk`` or ``slaney``. (Default: ``htk``)
Returns:
mels (float): Frequency in Mels
"""
if mel_scale not in ["slaney", "htk"]:
raise ValueError('mel_scale should be one of "htk" or "slaney".')
if mel_scale == "htk":
return 2595.0 * math.log10(1.0 + (freq / 700.0))
# Fill in the linear part
f_min = 0.0
f_sp = 200.0 / 3
mels = (freq - f_min) / f_sp
# Fill in the log-scale part
min_log_hz = 1000.0
min_log_mel = (min_log_hz - f_min) / f_sp
logstep = math.log(6.4) / 27.0
if freq >= min_log_hz:
mels = min_log_mel + math.log(freq / min_log_hz) / logstep
return mels
def _mel_to_hz(mels: Tensor, mel_scale: str = "htk") -> Tensor:
"""Convert mel bin numbers to frequencies.
Args:
mels (Tensor): Mel frequencies
mel_scale (str, optional): Scale to use: ``htk`` or ``slaney``. (Default: ``htk``)
Returns:
freqs (Tensor): Mels converted in Hz
"""
if mel_scale not in ["slaney", "htk"]:
raise ValueError('mel_scale should be one of "htk" or "slaney".')
if mel_scale == "htk":
return 700.0 * (10.0 ** (mels / 2595.0) - 1.0)
# Fill in the linear scale
f_min = 0.0
f_sp = 200.0 / 3
freqs = f_min + f_sp * mels
# And now the nonlinear scale
min_log_hz = 1000.0
min_log_mel = (min_log_hz - f_min) / f_sp
logstep = math.log(6.4) / 27.0
log_t = mels >= min_log_mel
freqs[log_t] = min_log_hz * torch.exp(logstep * (mels[log_t] - min_log_mel))
return freqs
def _create_triangular_filterbank(
all_freqs: Tensor,
f_pts: Tensor,
) -> Tensor:
"""Create a triangular filter bank.
Args:
all_freqs (Tensor): STFT freq points of size (`n_freqs`).
f_pts (Tensor): Filter mid points of size (`n_filter`).
Returns:
fb (Tensor): The filter bank of size (`n_freqs`, `n_filter`).
"""
# Adopted from Librosa
# calculate the difference between each filter mid point and each stft freq point in hertz
f_diff = f_pts[1:] - f_pts[:-1] # (n_filter + 1)
slopes = f_pts.unsqueeze(0) - all_freqs.unsqueeze(1) # (n_freqs, n_filter + 2)
# create overlapping triangles
zero = torch.zeros(1)
down_slopes = (-1.0 * slopes[:, :-2]) / f_diff[:-1] # (n_freqs, n_filter)
up_slopes = slopes[:, 2:] / f_diff[1:] # (n_freqs, n_filter)
fb = torch.max(zero, torch.min(down_slopes, up_slopes))
return fb
[docs]def melscale_fbanks(
n_freqs: int,
f_min: float,
f_max: float,
n_mels: int,
sample_rate: int,
norm: Optional[str] = None,
mel_scale: str = "htk",
) -> Tensor:
r"""Create a frequency bin conversion matrix.
.. devices:: CPU
.. properties:: TorchScript
Note:
For the sake of the numerical compatibility with librosa, not all the coefficients
in the resulting filter bank has magnitude of 1.
.. image:: https://download.pytorch.org/torchaudio/doc-assets/mel_fbanks.png
:alt: Visualization of generated filter bank
Args:
n_freqs (int): Number of frequencies to highlight/apply
f_min (float): Minimum frequency (Hz)
f_max (float): Maximum frequency (Hz)
n_mels (int): Number of mel filterbanks
sample_rate (int): Sample rate of the audio waveform
norm (str or None, optional): If "slaney", divide the triangular mel weights by the width of the mel band
(area normalization). (Default: ``None``)
mel_scale (str, optional): Scale to use: ``htk`` or ``slaney``. (Default: ``htk``)
Returns:
Tensor: Triangular filter banks (fb matrix) of size (``n_freqs``, ``n_mels``)
meaning number of frequencies to highlight/apply to x the number of filterbanks.
Each column is a filterbank so that assuming there is a matrix A of
size (..., ``n_freqs``), the applied result would be
``A * melscale_fbanks(A.size(-1), ...)``.
"""
if norm is not None and norm != "slaney":
raise ValueError('norm must be one of None or "slaney"')
# freq bins
all_freqs = torch.linspace(0, sample_rate // 2, n_freqs)
# calculate mel freq bins
m_min = _hz_to_mel(f_min, mel_scale=mel_scale)
m_max = _hz_to_mel(f_max, mel_scale=mel_scale)
m_pts = torch.linspace(m_min, m_max, n_mels + 2)
f_pts = _mel_to_hz(m_pts, mel_scale=mel_scale)
# create filterbank
fb = _create_triangular_filterbank(all_freqs, f_pts)
if norm is not None and norm == "slaney":
# Slaney-style mel is scaled to be approx constant energy per channel
enorm = 2.0 / (f_pts[2 : n_mels + 2] - f_pts[:n_mels])
fb *= enorm.unsqueeze(0)
if (fb.max(dim=0).values == 0.0).any():
warnings.warn(
"At least one mel filterbank has all zero values. "
f"The value for `n_mels` ({n_mels}) may be set too high. "
f"Or, the value for `n_freqs` ({n_freqs}) may be set too low."
)
return fb
[docs]def linear_fbanks(
n_freqs: int,
f_min: float,
f_max: float,
n_filter: int,
sample_rate: int,
) -> Tensor:
r"""Creates a linear triangular filterbank.
.. devices:: CPU
.. properties:: TorchScript
Note:
For the sake of the numerical compatibility with librosa, not all the coefficients
in the resulting filter bank has magnitude of 1.
.. image:: https://download.pytorch.org/torchaudio/doc-assets/lin_fbanks.png
:alt: Visualization of generated filter bank
Args:
n_freqs (int): Number of frequencies to highlight/apply
f_min (float): Minimum frequency (Hz)
f_max (float): Maximum frequency (Hz)
n_filter (int): Number of (linear) triangular filter
sample_rate (int): Sample rate of the audio waveform
Returns:
Tensor: Triangular filter banks (fb matrix) of size (``n_freqs``, ``n_filter``)
meaning number of frequencies to highlight/apply to x the number of filterbanks.
Each column is a filterbank so that assuming there is a matrix A of
size (..., ``n_freqs``), the applied result would be
``A * linear_fbanks(A.size(-1), ...)``.
"""
# freq bins
all_freqs = torch.linspace(0, sample_rate // 2, n_freqs)
# filter mid-points
f_pts = torch.linspace(f_min, f_max, n_filter + 2)
# create filterbank
fb = _create_triangular_filterbank(all_freqs, f_pts)
return fb
[docs]def create_dct(n_mfcc: int, n_mels: int, norm: Optional[str]) -> Tensor:
r"""Create a DCT transformation matrix with shape (``n_mels``, ``n_mfcc``),
normalized depending on norm.
.. devices:: CPU
.. properties:: TorchScript
Args:
n_mfcc (int): Number of mfc coefficients to retain
n_mels (int): Number of mel filterbanks
norm (str or None): Norm to use (either "ortho" or None)
Returns:
Tensor: The transformation matrix, to be right-multiplied to
row-wise data of size (``n_mels``, ``n_mfcc``).
"""
if norm is not None and norm != "ortho":
raise ValueError('norm must be either "ortho" or None')
# http://en.wikipedia.org/wiki/Discrete_cosine_transform#DCT-II
n = torch.arange(float(n_mels))
k = torch.arange(float(n_mfcc)).unsqueeze(1)
dct = torch.cos(math.pi / float(n_mels) * (n + 0.5) * k) # size (n_mfcc, n_mels)
if norm is None:
dct *= 2.0
else:
dct[0] *= 1.0 / math.sqrt(2.0)
dct *= math.sqrt(2.0 / float(n_mels))
return dct.t()
[docs]def mu_law_encoding(x: Tensor, quantization_channels: int) -> Tensor:
r"""Encode signal based on mu-law companding.
.. devices:: CPU CUDA
.. properties:: TorchScript
For more info see the
`Wikipedia Entry <https://en.wikipedia.org/wiki/%CE%9C-law_algorithm>`_
This algorithm expects the signal has been scaled to between -1 and 1 and
returns a signal encoded with values from 0 to quantization_channels - 1.
Args:
x (Tensor): Input tensor
quantization_channels (int): Number of channels
Returns:
Tensor: Input after mu-law encoding
"""
mu = quantization_channels - 1.0
if not x.is_floating_point():
warnings.warn(
"The input Tensor must be of floating type. \
This will be an error in the v0.12 release."
)
x = x.to(torch.float)
mu = torch.tensor(mu, dtype=x.dtype)
x_mu = torch.sign(x) * torch.log1p(mu * torch.abs(x)) / torch.log1p(mu)
x_mu = ((x_mu + 1) / 2 * mu + 0.5).to(torch.int64)
return x_mu
[docs]def mu_law_decoding(x_mu: Tensor, quantization_channels: int) -> Tensor:
r"""Decode mu-law encoded signal.
.. devices:: CPU CUDA
.. properties:: TorchScript
For more info see the
`Wikipedia Entry <https://en.wikipedia.org/wiki/%CE%9C-law_algorithm>`_
This expects an input with values between 0 and quantization_channels - 1
and returns a signal scaled between -1 and 1.
Args:
x_mu (Tensor): Input tensor
quantization_channels (int): Number of channels
Returns:
Tensor: Input after mu-law decoding
"""
mu = quantization_channels - 1.0
if not x_mu.is_floating_point():
x_mu = x_mu.to(torch.float)
mu = torch.tensor(mu, dtype=x_mu.dtype)
x = ((x_mu) / mu) * 2 - 1.0
x = torch.sign(x) * (torch.exp(torch.abs(x) * torch.log1p(mu)) - 1.0) / mu
return x
[docs]def phase_vocoder(complex_specgrams: Tensor, rate: float, phase_advance: Tensor) -> Tensor:
r"""Given a STFT tensor, speed up in time without modifying pitch by a factor of ``rate``.
.. devices:: CPU CUDA
.. properties:: Autograd TorchScript
Args:
complex_specgrams (Tensor):
A tensor of dimension `(..., freq, num_frame)` with complex dtype.
rate (float): Speed-up factor
phase_advance (Tensor): Expected phase advance in each bin. Dimension of `(freq, 1)`
Returns:
Tensor:
Stretched spectrogram. The resulting tensor is of the same dtype as the input
spectrogram, but the number of frames is changed to ``ceil(num_frame / rate)``.
Example
>>> freq, hop_length = 1025, 512
>>> # (channel, freq, time)
>>> complex_specgrams = torch.randn(2, freq, 300, dtype=torch.cfloat)
>>> rate = 1.3 # Speed up by 30%
>>> phase_advance = torch.linspace(
>>> 0, math.pi * hop_length, freq)[..., None]
>>> x = phase_vocoder(complex_specgrams, rate, phase_advance)
>>> x.shape # with 231 == ceil(300 / 1.3)
torch.Size([2, 1025, 231])
"""
if rate == 1.0:
return complex_specgrams
# pack batch
shape = complex_specgrams.size()
complex_specgrams = complex_specgrams.reshape([-1] + list(shape[-2:]))
# Figures out the corresponding real dtype, i.e. complex128 -> float64, complex64 -> float32
# Note torch.real is a view so it does not incur any memory copy.
real_dtype = torch.real(complex_specgrams).dtype
time_steps = torch.arange(0, complex_specgrams.size(-1), rate, device=complex_specgrams.device, dtype=real_dtype)
alphas = time_steps % 1.0
phase_0 = complex_specgrams[..., :1].angle()
# Time Padding
complex_specgrams = torch.nn.functional.pad(complex_specgrams, [0, 2])
# (new_bins, freq, 2)
complex_specgrams_0 = complex_specgrams.index_select(-1, time_steps.long())
complex_specgrams_1 = complex_specgrams.index_select(-1, (time_steps + 1).long())
angle_0 = complex_specgrams_0.angle()
angle_1 = complex_specgrams_1.angle()
norm_0 = complex_specgrams_0.abs()
norm_1 = complex_specgrams_1.abs()
phase = angle_1 - angle_0 - phase_advance
phase = phase - 2 * math.pi * torch.round(phase / (2 * math.pi))
# Compute Phase Accum
phase = phase + phase_advance
phase = torch.cat([phase_0, phase[..., :-1]], dim=-1)
phase_acc = torch.cumsum(phase, -1)
mag = alphas * norm_1 + (1 - alphas) * norm_0
complex_specgrams_stretch = torch.polar(mag, phase_acc)
# unpack batch
complex_specgrams_stretch = complex_specgrams_stretch.reshape(shape[:-2] + complex_specgrams_stretch.shape[1:])
return complex_specgrams_stretch
def _get_mask_param(mask_param: int, p: float, axis_length: int) -> int:
if p == 1.0:
return mask_param
else:
return min(mask_param, int(axis_length * p))
[docs]def mask_along_axis_iid(
specgrams: Tensor,
mask_param: int,
mask_value: float,
axis: int,
p: float = 1.0,
) -> Tensor:
r"""Apply a mask along ``axis``.
.. devices:: CPU CUDA
.. properties:: Autograd TorchScript
Mask will be applied from indices ``[v_0, v_0 + v)``,
where ``v`` is sampled from ``uniform(0, max_v)`` and
``v_0`` from ``uniform(0, specgrams.size(axis) - v)``,
with ``max_v = mask_param`` when ``p = 1.0`` and
``max_v = min(mask_param, floor(specgrams.size(axis) * p))`` otherwise.
Args:
specgrams (Tensor): Real spectrograms `(batch, channel, freq, time)`
mask_param (int): Number of columns to be masked will be uniformly sampled from [0, mask_param]
mask_value (float): Value to assign to the masked columns
axis (int): Axis to apply masking on (2 -> frequency, 3 -> time)
p (float, optional): maximum proportion of columns that can be masked. (Default: 1.0)
Returns:
Tensor: Masked spectrograms of dimensions `(batch, channel, freq, time)`
"""
if axis not in [2, 3]:
raise ValueError("Only Frequency and Time masking are supported")
if not 0.0 <= p <= 1.0:
raise ValueError(f"The value of p must be between 0.0 and 1.0 ({p} given).")
mask_param = _get_mask_param(mask_param, p, specgrams.shape[axis])
if mask_param < 1:
return specgrams
device = specgrams.device
dtype = specgrams.dtype
value = torch.rand(specgrams.shape[:2], device=device, dtype=dtype) * mask_param
min_value = torch.rand(specgrams.shape[:2], device=device, dtype=dtype) * (specgrams.size(axis) - value)
# Create broadcastable mask
mask_start = min_value.long()[..., None, None]
mask_end = (min_value.long() + value.long())[..., None, None]
mask = torch.arange(0, specgrams.size(axis), device=device, dtype=dtype)
# Per batch example masking
specgrams = specgrams.transpose(axis, -1)
specgrams = specgrams.masked_fill((mask >= mask_start) & (mask < mask_end), mask_value)
specgrams = specgrams.transpose(axis, -1)
return specgrams
[docs]def mask_along_axis(
specgram: Tensor,
mask_param: int,
mask_value: float,
axis: int,
p: float = 1.0,
) -> Tensor:
r"""Apply a mask along ``axis``.
.. devices:: CPU CUDA
.. properties:: Autograd TorchScript
Mask will be applied from indices ``[v_0, v_0 + v)``,
where ``v`` is sampled from ``uniform(0, max_v)`` and
``v_0`` from ``uniform(0, specgrams.size(axis) - v)``, with
``max_v = mask_param`` when ``p = 1.0`` and
``max_v = min(mask_param, floor(specgrams.size(axis) * p))``
otherwise.
All examples will have the same mask interval.
Args:
specgram (Tensor): Real spectrogram `(channel, freq, time)`
mask_param (int): Number of columns to be masked will be uniformly sampled from [0, mask_param]
mask_value (float): Value to assign to the masked columns
axis (int): Axis to apply masking on (1 -> frequency, 2 -> time)
p (float, optional): maximum proportion of columns that can be masked. (Default: 1.0)
Returns:
Tensor: Masked spectrogram of dimensions `(channel, freq, time)`
"""
if axis not in [1, 2]:
raise ValueError("Only Frequency and Time masking are supported")
if not 0.0 <= p <= 1.0:
raise ValueError(f"The value of p must be between 0.0 and 1.0 ({p} given).")
mask_param = _get_mask_param(mask_param, p, specgram.shape[axis])
if mask_param < 1:
return specgram
# pack batch
shape = specgram.size()
specgram = specgram.reshape([-1] + list(shape[-2:]))
value = torch.rand(1) * mask_param
min_value = torch.rand(1) * (specgram.size(axis) - value)
mask_start = (min_value.long()).squeeze()
mask_end = (min_value.long() + value.long()).squeeze()
mask = torch.arange(0, specgram.shape[axis], device=specgram.device, dtype=specgram.dtype)
mask = (mask >= mask_start) & (mask < mask_end)
if axis == 1:
mask = mask.unsqueeze(-1)
if mask_end - mask_start >= mask_param:
raise ValueError("Number of columns to be masked should be less than mask_param")
specgram = specgram.masked_fill(mask, mask_value)
# unpack batch
specgram = specgram.reshape(shape[:-2] + specgram.shape[-2:])
return specgram
[docs]def compute_deltas(specgram: Tensor, win_length: int = 5, mode: str = "replicate") -> Tensor:
r"""Compute delta coefficients of a tensor, usually a spectrogram:
.. devices:: CPU CUDA
.. properties:: TorchScript
.. math::
d_t = \frac{\sum_{n=1}^{\text{N}} n (c_{t+n} - c_{t-n})}{2 \sum_{n=1}^{\text{N}} n^2}
where :math:`d_t` is the deltas at time :math:`t`,
:math:`c_t` is the spectrogram coeffcients at time :math:`t`,
:math:`N` is ``(win_length-1)//2``.
Args:
specgram (Tensor): Tensor of audio of dimension `(..., freq, time)`
win_length (int, optional): The window length used for computing delta (Default: ``5``)
mode (str, optional): Mode parameter passed to padding (Default: ``"replicate"``)
Returns:
Tensor: Tensor of deltas of dimension `(..., freq, time)`
Example
>>> specgram = torch.randn(1, 40, 1000)
>>> delta = compute_deltas(specgram)
>>> delta2 = compute_deltas(delta)
"""
device = specgram.device
dtype = specgram.dtype
# pack batch
shape = specgram.size()
specgram = specgram.reshape(1, -1, shape[-1])
if win_length < 3:
raise ValueError(f"Window length should be greater than or equal to 3. Found win_length {win_length}")
n = (win_length - 1) // 2
# twice sum of integer squared
denom = n * (n + 1) * (2 * n + 1) / 3
specgram = torch.nn.functional.pad(specgram, (n, n), mode=mode)
kernel = torch.arange(-n, n + 1, 1, device=device, dtype=dtype).repeat(specgram.shape[1], 1, 1)
output = torch.nn.functional.conv1d(specgram, kernel, groups=specgram.shape[1]) / denom
# unpack batch
output = output.reshape(shape)
return output
def _compute_nccf(waveform: Tensor, sample_rate: int, frame_time: float, freq_low: int) -> Tensor:
r"""
Compute Normalized Cross-Correlation Function (NCCF).
.. math::
\phi_i(m) = \frac{\sum_{n=b_i}^{b_i + N-1} w(n) w(m+n)}{\sqrt{E(b_i) E(m+b_i)}},
where
:math:`\phi_i(m)` is the NCCF at frame :math:`i` with lag :math:`m`,
:math:`w` is the waveform,
:math:`N` is the length of a frame,
:math:`b_i` is the beginning of frame :math:`i`,
:math:`E(j)` is the energy :math:`\sum_{n=j}^{j+N-1} w^2(n)`.
"""
EPSILON = 10 ** (-9)
# Number of lags to check
lags = int(math.ceil(sample_rate / freq_low))
frame_size = int(math.ceil(sample_rate * frame_time))
waveform_length = waveform.size()[-1]
num_of_frames = int(math.ceil(waveform_length / frame_size))
p = lags + num_of_frames * frame_size - waveform_length
waveform = torch.nn.functional.pad(waveform, (0, p))
# Compute lags
output_lag = []
for lag in range(1, lags + 1):
s1 = waveform[..., :-lag].unfold(-1, frame_size, frame_size)[..., :num_of_frames, :]
s2 = waveform[..., lag:].unfold(-1, frame_size, frame_size)[..., :num_of_frames, :]
output_frames = (
(s1 * s2).sum(-1)
/ (EPSILON + torch.norm(s1, p=2, dim=-1)).pow(2)
/ (EPSILON + torch.norm(s2, p=2, dim=-1)).pow(2)
)
output_lag.append(output_frames.unsqueeze(-1))
nccf = torch.cat(output_lag, -1)
return nccf
def _combine_max(a: Tuple[Tensor, Tensor], b: Tuple[Tensor, Tensor], thresh: float = 0.99) -> Tuple[Tensor, Tensor]:
"""
Take value from first if bigger than a multiplicative factor of the second, elementwise.
"""
mask = a[0] > thresh * b[0]
values = mask * a[0] + ~mask * b[0]
indices = mask * a[1] + ~mask * b[1]
return values, indices
def _find_max_per_frame(nccf: Tensor, sample_rate: int, freq_high: int) -> Tensor:
r"""
For each frame, take the highest value of NCCF,
apply centered median smoothing, and convert to frequency.
Note: If the max among all the lags is very close
to the first half of lags, then the latter is taken.
"""
lag_min = int(math.ceil(sample_rate / freq_high))
# Find near enough max that is smallest
best = torch.max(nccf[..., lag_min:], -1)
half_size = nccf.shape[-1] // 2
half = torch.max(nccf[..., lag_min:half_size], -1)
best = _combine_max(half, best)
indices = best[1]
# Add back minimal lag
indices += lag_min
# Add 1 empirical calibration offset
indices += 1
return indices
def _median_smoothing(indices: Tensor, win_length: int) -> Tensor:
r"""
Apply median smoothing to the 1D tensor over the given window.
"""
# Centered windowed
pad_length = (win_length - 1) // 2
# "replicate" padding in any dimension
indices = torch.nn.functional.pad(indices, (pad_length, 0), mode="constant", value=0.0)
indices[..., :pad_length] = torch.cat(pad_length * [indices[..., pad_length].unsqueeze(-1)], dim=-1)
roll = indices.unfold(-1, win_length, 1)
values, _ = torch.median(roll, -1)
return values
[docs]def detect_pitch_frequency(
waveform: Tensor,
sample_rate: int,
frame_time: float = 10 ** (-2),
win_length: int = 30,
freq_low: int = 85,
freq_high: int = 3400,
) -> Tensor:
r"""Detect pitch frequency.
.. devices:: CPU CUDA
.. properties:: TorchScript
It is implemented using normalized cross-correlation function and median smoothing.
Args:
waveform (Tensor): Tensor of audio of dimension `(..., freq, time)`
sample_rate (int): The sample rate of the waveform (Hz)
frame_time (float, optional): Duration of a frame (Default: ``10 ** (-2)``).
win_length (int, optional): The window length for median smoothing (in number of frames) (Default: ``30``).
freq_low (int, optional): Lowest frequency that can be detected (Hz) (Default: ``85``).
freq_high (int, optional): Highest frequency that can be detected (Hz) (Default: ``3400``).
Returns:
Tensor: Tensor of freq of dimension `(..., frame)`
"""
# pack batch
shape = list(waveform.size())
waveform = waveform.reshape([-1] + shape[-1:])
nccf = _compute_nccf(waveform, sample_rate, frame_time, freq_low)
indices = _find_max_per_frame(nccf, sample_rate, freq_high)
indices = _median_smoothing(indices, win_length)
# Convert indices to frequency
EPSILON = 10 ** (-9)
freq = sample_rate / (EPSILON + indices.to(torch.float))
# unpack batch
freq = freq.reshape(shape[:-1] + list(freq.shape[-1:]))
return freq
[docs]def sliding_window_cmn(
specgram: Tensor,
cmn_window: int = 600,
min_cmn_window: int = 100,
center: bool = False,
norm_vars: bool = False,
) -> Tensor:
r"""
Apply sliding-window cepstral mean (and optionally variance) normalization per utterance.
.. devices:: CPU CUDA
.. properties:: TorchScript
Args:
specgram (Tensor): Tensor of spectrogram of dimension `(..., time, freq)`
cmn_window (int, optional): Window in frames for running average CMN computation (int, default = 600)
min_cmn_window (int, optional): Minimum CMN window used at start of decoding (adds latency only at start).
Only applicable if center == false, ignored if center==true (int, default = 100)
center (bool, optional): If true, use a window centered on the current frame
(to the extent possible, modulo end effects). If false, window is to the left. (bool, default = false)
norm_vars (bool, optional): If true, normalize variance to one. (bool, default = false)
Returns:
Tensor: Tensor matching input shape `(..., freq, time)`
"""
input_shape = specgram.shape
num_frames, num_feats = input_shape[-2:]
specgram = specgram.view(-1, num_frames, num_feats)
num_channels = specgram.shape[0]
dtype = specgram.dtype
device = specgram.device
last_window_start = last_window_end = -1
cur_sum = torch.zeros(num_channels, num_feats, dtype=dtype, device=device)
cur_sumsq = torch.zeros(num_channels, num_feats, dtype=dtype, device=device)
cmn_specgram = torch.zeros(num_channels, num_frames, num_feats, dtype=dtype, device=device)
for t in range(num_frames):
window_start = 0
window_end = 0
if center:
window_start = t - cmn_window // 2
window_end = window_start + cmn_window
else:
window_start = t - cmn_window
window_end = t + 1
if window_start < 0:
window_end -= window_start
window_start = 0
if not center:
if window_end > t:
window_end = max(t + 1, min_cmn_window)
if window_end > num_frames:
window_start -= window_end - num_frames
window_end = num_frames
if window_start < 0:
window_start = 0
if last_window_start == -1:
input_part = specgram[:, window_start : window_end - window_start, :]
cur_sum += torch.sum(input_part, 1)
if norm_vars:
cur_sumsq += torch.cumsum(input_part**2, 1)[:, -1, :]
else:
if window_start > last_window_start:
frame_to_remove = specgram[:, last_window_start, :]
cur_sum -= frame_to_remove
if norm_vars:
cur_sumsq -= frame_to_remove**2
if window_end > last_window_end:
frame_to_add = specgram[:, last_window_end, :]
cur_sum += frame_to_add
if norm_vars:
cur_sumsq += frame_to_add**2
window_frames = window_end - window_start
last_window_start = window_start
last_window_end = window_end
cmn_specgram[:, t, :] = specgram[:, t, :] - cur_sum / window_frames
if norm_vars:
if window_frames == 1:
cmn_specgram[:, t, :] = torch.zeros(num_channels, num_feats, dtype=dtype, device=device)
else:
variance = cur_sumsq
variance = variance / window_frames
variance -= (cur_sum**2) / (window_frames**2)
variance = torch.pow(variance, -0.5)
cmn_specgram[:, t, :] *= variance
cmn_specgram = cmn_specgram.view(input_shape[:-2] + (num_frames, num_feats))
if len(input_shape) == 2:
cmn_specgram = cmn_specgram.squeeze(0)
return cmn_specgram
[docs]def spectral_centroid(
waveform: Tensor,
sample_rate: int,
pad: int,
window: Tensor,
n_fft: int,
hop_length: int,
win_length: int,
) -> Tensor:
r"""Compute the spectral centroid for each channel along the time axis.
.. devices:: CPU CUDA
.. properties:: Autograd TorchScript
The spectral centroid is defined as the weighted average of the
frequency values, weighted by their magnitude.
Args:
waveform (Tensor): Tensor of audio of dimension `(..., time)`
sample_rate (int): Sample rate of the audio waveform
pad (int): Two sided padding of signal
window (Tensor): Window tensor that is applied/multiplied to each frame/window
n_fft (int): Size of FFT
hop_length (int): Length of hop between STFT windows
win_length (int): Window size
Returns:
Tensor: Dimension `(..., time)`
"""
specgram = spectrogram(
waveform,
pad=pad,
window=window,
n_fft=n_fft,
hop_length=hop_length,
win_length=win_length,
power=1.0,
normalized=False,
)
freqs = torch.linspace(0, sample_rate // 2, steps=1 + n_fft // 2, device=specgram.device).reshape((-1, 1))
freq_dim = -2
return (freqs * specgram).sum(dim=freq_dim) / specgram.sum(dim=freq_dim)
[docs]@torchaudio._extension.fail_if_no_sox
def apply_codec(
waveform: Tensor,
sample_rate: int,
format: str,
channels_first: bool = True,
compression: Optional[float] = None,
encoding: Optional[str] = None,
bits_per_sample: Optional[int] = None,
) -> Tensor:
r"""
Apply codecs as a form of augmentation.
.. devices:: CPU
Args:
waveform (Tensor): Audio data. Must be 2 dimensional. See also ```channels_first```.
sample_rate (int): Sample rate of the audio waveform.
format (str): File format.
channels_first (bool, optional):
When True, both the input and output Tensor have dimension `(channel, time)`.
Otherwise, they have dimension `(time, channel)`.
compression (float or None, optional): Used for formats other than WAV.
For more details see :py:func:`torchaudio.backend.sox_io_backend.save`.
encoding (str or None, optional): Changes the encoding for the supported formats.
For more details see :py:func:`torchaudio.backend.sox_io_backend.save`.
bits_per_sample (int or None, optional): Changes the bit depth for the supported formats.
For more details see :py:func:`torchaudio.backend.sox_io_backend.save`.
Returns:
Tensor: Resulting Tensor.
If ``channels_first=True``, it has `(channel, time)` else `(time, channel)`.
"""
bytes = io.BytesIO()
torchaudio.backend.sox_io_backend.save(
bytes, waveform, sample_rate, channels_first, compression, format, encoding, bits_per_sample
)
bytes.seek(0)
augmented, sr = torchaudio.backend.sox_io_backend.load(bytes, channels_first=channels_first, format=format)
if sr != sample_rate:
augmented = resample(augmented, sr, sample_rate)
return augmented
[docs]@torchaudio._extension.fail_if_no_kaldi
def compute_kaldi_pitch(
waveform: torch.Tensor,
sample_rate: float,
frame_length: float = 25.0,
frame_shift: float = 10.0,
min_f0: float = 50,
max_f0: float = 400,
soft_min_f0: float = 10.0,
penalty_factor: float = 0.1,
lowpass_cutoff: float = 1000,
resample_frequency: float = 4000,
delta_pitch: float = 0.005,
nccf_ballast: float = 7000,
lowpass_filter_width: int = 1,
upsample_filter_width: int = 5,
max_frames_latency: int = 0,
frames_per_chunk: int = 0,
simulate_first_pass_online: bool = False,
recompute_frame: int = 500,
snip_edges: bool = True,
) -> torch.Tensor:
"""Extract pitch based on method described in *A pitch extraction algorithm tuned
for automatic speech recognition* :cite:`6854049`.
.. devices:: CPU
.. properties:: TorchScript
This function computes the equivalent of `compute-kaldi-pitch-feats` from Kaldi.
Args:
waveform (Tensor):
The input waveform of shape `(..., time)`.
sample_rate (float):
Sample rate of `waveform`.
frame_length (float, optional):
Frame length in milliseconds. (default: 25.0)
frame_shift (float, optional):
Frame shift in milliseconds. (default: 10.0)
min_f0 (float, optional):
Minimum F0 to search for (Hz) (default: 50.0)
max_f0 (float, optional):
Maximum F0 to search for (Hz) (default: 400.0)
soft_min_f0 (float, optional):
Minimum f0, applied in soft way, must not exceed min-f0 (default: 10.0)
penalty_factor (float, optional):
Cost factor for FO change. (default: 0.1)
lowpass_cutoff (float, optional):
Cutoff frequency for LowPass filter (Hz) (default: 1000)
resample_frequency (float, optional):
Frequency that we down-sample the signal to. Must be more than twice lowpass-cutoff.
(default: 4000)
delta_pitch( float, optional):
Smallest relative change in pitch that our algorithm measures. (default: 0.005)
nccf_ballast (float, optional):
Increasing this factor reduces NCCF for quiet frames (default: 7000)
lowpass_filter_width (int, optional):
Integer that determines filter width of lowpass filter, more gives sharper filter.
(default: 1)
upsample_filter_width (int, optional):
Integer that determines filter width when upsampling NCCF. (default: 5)
max_frames_latency (int, optional):
Maximum number of frames of latency that we allow pitch tracking to introduce into
the feature processing (affects output only if ``frames_per_chunk > 0`` and
``simulate_first_pass_online=True``) (default: 0)
frames_per_chunk (int, optional):
The number of frames used for energy normalization. (default: 0)
simulate_first_pass_online (bool, optional):
If true, the function will output features that correspond to what an online decoder
would see in the first pass of decoding -- not the final version of the features,
which is the default. (default: False)
Relevant if ``frames_per_chunk > 0``.
recompute_frame (int, optional):
Only relevant for compatibility with online pitch extraction.
A non-critical parameter; the frame at which we recompute some of the forward pointers,
after revising our estimate of the signal energy.
Relevant if ``frames_per_chunk > 0``. (default: 500)
snip_edges (bool, optional):
If this is set to false, the incomplete frames near the ending edge won't be snipped,
so that the number of frames is the file size divided by the frame-shift.
This makes different types of features give the same number of frames. (default: True)
Returns:
Tensor: Pitch feature. Shape: `(batch, frames 2)` where the last dimension
corresponds to pitch and NCCF.
"""
shape = waveform.shape
waveform = waveform.reshape(-1, shape[-1])
result = torch.ops.torchaudio.kaldi_ComputeKaldiPitch(
waveform,
sample_rate,
frame_length,
frame_shift,
min_f0,
max_f0,
soft_min_f0,
penalty_factor,
lowpass_cutoff,
resample_frequency,
delta_pitch,
nccf_ballast,
lowpass_filter_width,
upsample_filter_width,
max_frames_latency,
frames_per_chunk,
simulate_first_pass_online,
recompute_frame,
snip_edges,
)
result = result.reshape(shape[:-1] + result.shape[-2:])
return result
def _get_sinc_resample_kernel(
orig_freq: int,
new_freq: int,
gcd: int,
lowpass_filter_width: int = 6,
rolloff: float = 0.99,
resampling_method: str = "sinc_interp_hann",
beta: Optional[float] = None,
device: torch.device = torch.device("cpu"),
dtype: Optional[torch.dtype] = None,
):
if not (int(orig_freq) == orig_freq and int(new_freq) == new_freq):
raise Exception(
"Frequencies must be of integer type to ensure quality resampling computation. "
"To work around this, manually convert both frequencies to integer values "
"that maintain their resampling rate ratio before passing them into the function. "
"Example: To downsample a 44100 hz waveform by a factor of 8, use "
"`orig_freq=8` and `new_freq=1` instead of `orig_freq=44100` and `new_freq=5512.5`. "
"For more information, please refer to https://github.com/pytorch/audio/issues/1487."
)
if resampling_method in ["sinc_interpolation", "kaiser_window"]:
method_map = {
"sinc_interpolation": "sinc_interp_hann",
"kaiser_window": "sinc_interp_kaiser",
}
warnings.warn(
f'"{resampling_method}" resampling method name is being deprecated and replaced by '
f'"{method_map[resampling_method]}" in the next release. '
"The default behavior remains unchanged."
)
elif resampling_method not in ["sinc_interp_hann", "sinc_interp_kaiser"]:
raise ValueError("Invalid resampling method: {}".format(resampling_method))
orig_freq = int(orig_freq) // gcd
new_freq = int(new_freq) // gcd
if lowpass_filter_width <= 0:
raise ValueError("Low pass filter width should be positive.")
base_freq = min(orig_freq, new_freq)
# This will perform antialiasing filtering by removing the highest frequencies.
# At first I thought I only needed this when downsampling, but when upsampling
# you will get edge artifacts without this, as the edge is equivalent to zero padding,
# which will add high freq artifacts.
base_freq *= rolloff
# The key idea of the algorithm is that x(t) can be exactly reconstructed from x[i] (tensor)
# using the sinc interpolation formula:
# x(t) = sum_i x[i] sinc(pi * orig_freq * (i / orig_freq - t))
# We can then sample the function x(t) with a different sample rate:
# y[j] = x(j / new_freq)
# or,
# y[j] = sum_i x[i] sinc(pi * orig_freq * (i / orig_freq - j / new_freq))
# We see here that y[j] is the convolution of x[i] with a specific filter, for which
# we take an FIR approximation, stopping when we see at least `lowpass_filter_width` zeros crossing.
# But y[j+1] is going to have a different set of weights and so on, until y[j + new_freq].
# Indeed:
# y[j + new_freq] = sum_i x[i] sinc(pi * orig_freq * ((i / orig_freq - (j + new_freq) / new_freq))
# = sum_i x[i] sinc(pi * orig_freq * ((i - orig_freq) / orig_freq - j / new_freq))
# = sum_i x[i + orig_freq] sinc(pi * orig_freq * (i / orig_freq - j / new_freq))
# so y[j+new_freq] uses the same filter as y[j], but on a shifted version of x by `orig_freq`.
# This will explain the F.conv1d after, with a stride of orig_freq.
width = math.ceil(lowpass_filter_width * orig_freq / base_freq)
# If orig_freq is still big after GCD reduction, most filters will be very unbalanced, i.e.,
# they will have a lot of almost zero values to the left or to the right...
# There is probably a way to evaluate those filters more efficiently, but this is kept for
# future work.
idx_dtype = dtype if dtype is not None else torch.float64
idx = torch.arange(-width, width + orig_freq, dtype=idx_dtype, device=device)[None, None] / orig_freq
t = torch.arange(0, -new_freq, -1, dtype=dtype, device=device)[:, None, None] / new_freq + idx
t *= base_freq
t = t.clamp_(-lowpass_filter_width, lowpass_filter_width)
# we do not use built in torch windows here as we need to evaluate the window
# at specific positions, not over a regular grid.
if resampling_method == "sinc_interp_hann":
window = torch.cos(t * math.pi / lowpass_filter_width / 2) ** 2
else:
# sinc_interp_kaiser
if beta is None:
beta = 14.769656459379492
beta_tensor = torch.tensor(float(beta))
window = torch.i0(beta_tensor * torch.sqrt(1 - (t / lowpass_filter_width) ** 2)) / torch.i0(beta_tensor)
t *= math.pi
scale = base_freq / orig_freq
kernels = torch.where(t == 0, torch.tensor(1.0).to(t), t.sin() / t)
kernels *= window * scale
if dtype is None:
kernels = kernels.to(dtype=torch.float32)
return kernels, width
def _apply_sinc_resample_kernel(
waveform: Tensor,
orig_freq: int,
new_freq: int,
gcd: int,
kernel: Tensor,
width: int,
):
if not waveform.is_floating_point():
raise TypeError(f"Expected floating point type for waveform tensor, but received {waveform.dtype}.")
orig_freq = int(orig_freq) // gcd
new_freq = int(new_freq) // gcd
# pack batch
shape = waveform.size()
waveform = waveform.view(-1, shape[-1])
num_wavs, length = waveform.shape
waveform = torch.nn.functional.pad(waveform, (width, width + orig_freq))
resampled = torch.nn.functional.conv1d(waveform[:, None], kernel, stride=orig_freq)
resampled = resampled.transpose(1, 2).reshape(num_wavs, -1)
target_length = int(math.ceil(new_freq * length / orig_freq))
resampled = resampled[..., :target_length]
# unpack batch
resampled = resampled.view(shape[:-1] + resampled.shape[-1:])
return resampled
[docs]def resample(
waveform: Tensor,
orig_freq: int,
new_freq: int,
lowpass_filter_width: int = 6,
rolloff: float = 0.99,
resampling_method: str = "sinc_interp_hann",
beta: Optional[float] = None,
) -> Tensor:
r"""Resamples the waveform at the new frequency using bandlimited interpolation. :cite:`RESAMPLE`.
.. devices:: CPU CUDA
.. properties:: Autograd TorchScript
Note:
``transforms.Resample`` precomputes and reuses the resampling kernel, so using it will result in
more efficient computation if resampling multiple waveforms with the same resampling parameters.
Args:
waveform (Tensor): The input signal of dimension `(..., time)`
orig_freq (int): The original frequency of the signal
new_freq (int): The desired frequency
lowpass_filter_width (int, optional): Controls the sharpness of the filter, more == sharper
but less efficient. (Default: ``6``)
rolloff (float, optional): The roll-off frequency of the filter, as a fraction of the Nyquist.
Lower values reduce anti-aliasing, but also reduce some of the highest frequencies. (Default: ``0.99``)
resampling_method (str, optional): The resampling method to use.
Options: [``"sinc_interp_hann"``, ``"sinc_interp_kaiser"``] (Default: ``"sinc_interp_hann"``)
beta (float or None, optional): The shape parameter used for kaiser window.
Returns:
Tensor: The waveform at the new frequency of dimension `(..., time).`
"""
if orig_freq <= 0.0 or new_freq <= 0.0:
raise ValueError("Original frequency and desired frequecy should be positive")
if orig_freq == new_freq:
return waveform
gcd = math.gcd(int(orig_freq), int(new_freq))
kernel, width = _get_sinc_resample_kernel(
orig_freq,
new_freq,
gcd,
lowpass_filter_width,
rolloff,
resampling_method,
beta,
waveform.device,
waveform.dtype,
)
resampled = _apply_sinc_resample_kernel(waveform, orig_freq, new_freq, gcd, kernel, width)
return resampled
[docs]@torch.jit.unused
def edit_distance(seq1: Sequence, seq2: Sequence) -> int:
"""
Calculate the word level edit (Levenshtein) distance between two sequences.
.. devices:: CPU
The function computes an edit distance allowing deletion, insertion and
substitution. The result is an integer.
For most applications, the two input sequences should be the same type. If
two strings are given, the output is the edit distance between the two
strings (character edit distance). If two lists of strings are given, the
output is the edit distance between sentences (word edit distance). Users
may want to normalize the output by the length of the reference sequence.
Args:
seq1 (Sequence): the first sequence to compare.
seq2 (Sequence): the second sequence to compare.
Returns:
int: The distance between the first and second sequences.
"""
len_sent2 = len(seq2)
dold = list(range(len_sent2 + 1))
dnew = [0 for _ in range(len_sent2 + 1)]
for i in range(1, len(seq1) + 1):
dnew[0] = i
for j in range(1, len_sent2 + 1):
if seq1[i - 1] == seq2[j - 1]:
dnew[j] = dold[j - 1]
else:
substitution = dold[j - 1] + 1
insertion = dnew[j - 1] + 1
deletion = dold[j] + 1
dnew[j] = min(substitution, insertion, deletion)
dnew, dold = dold, dnew
return int(dold[-1])
[docs]def loudness(waveform: Tensor, sample_rate: int):
r"""Measure audio loudness according to the ITU-R BS.1770-4 recommendation.
.. devices:: CPU CUDA
.. properties:: TorchScript
Args:
waveform(torch.Tensor): audio waveform of dimension `(..., channels, time)`
sample_rate (int): sampling rate of the waveform
Returns:
Tensor: loudness estimates (LKFS)
Reference:
- https://www.itu.int/rec/R-REC-BS.1770-4-201510-I/en
"""
if waveform.size(-2) > 5:
raise ValueError("Only up to 5 channels are supported.")
gate_duration = 0.4
overlap = 0.75
gamma_abs = -70.0
kweight_bias = -0.691
gate_samples = int(round(gate_duration * sample_rate))
step = int(round(gate_samples * (1 - overlap)))
# Apply K-weighting
waveform = treble_biquad(waveform, sample_rate, 4.0, 1500.0, 1 / math.sqrt(2))
waveform = highpass_biquad(waveform, sample_rate, 38.0, 0.5)
# Compute the energy for each block
energy = torch.square(waveform).unfold(-1, gate_samples, step)
energy = torch.mean(energy, dim=-1)
# Compute channel-weighted summation
g = torch.tensor([1.0, 1.0, 1.0, 1.41, 1.41], dtype=waveform.dtype, device=waveform.device)
g = g[: energy.size(-2)]
energy_weighted = torch.sum(g.unsqueeze(-1) * energy, dim=-2)
loudness = -0.691 + 10 * torch.log10(energy_weighted)
# Apply absolute gating of the blocks
gated_blocks = loudness > gamma_abs
gated_blocks = gated_blocks.unsqueeze(-2)
energy_filtered = torch.sum(gated_blocks * energy, dim=-1) / torch.count_nonzero(gated_blocks, dim=-1)
energy_weighted = torch.sum(g * energy_filtered, dim=-1)
gamma_rel = kweight_bias + 10 * torch.log10(energy_weighted) - 10
# Apply relative gating of the blocks
gated_blocks = torch.logical_and(gated_blocks.squeeze(-2), loudness > gamma_rel.unsqueeze(-1))
gated_blocks = gated_blocks.unsqueeze(-2)
energy_filtered = torch.sum(gated_blocks * energy, dim=-1) / torch.count_nonzero(gated_blocks, dim=-1)
energy_weighted = torch.sum(g * energy_filtered, dim=-1)
LKFS = kweight_bias + 10 * torch.log10(energy_weighted)
return LKFS
[docs]def pitch_shift(
waveform: Tensor,
sample_rate: int,
n_steps: int,
bins_per_octave: int = 12,
n_fft: int = 512,
win_length: Optional[int] = None,
hop_length: Optional[int] = None,
window: Optional[Tensor] = None,
) -> Tensor:
"""
Shift the pitch of a waveform by ``n_steps`` steps.
.. devices:: CPU CUDA
.. properties:: TorchScript
Args:
waveform (Tensor): The input waveform of shape `(..., time)`.
sample_rate (int): Sample rate of `waveform`.
n_steps (int): The (fractional) steps to shift `waveform`.
bins_per_octave (int, optional): The number of steps per octave (Default: ``12``).
n_fft (int, optional): Size of FFT, creates ``n_fft // 2 + 1`` bins (Default: ``512``).
win_length (int or None, optional): Window size. If None, then ``n_fft`` is used. (Default: ``None``).
hop_length (int or None, optional): Length of hop between STFT windows. If None, then
``win_length // 4`` is used (Default: ``None``).
window (Tensor or None, optional): Window tensor that is applied/multiplied to each frame/window.
If None, then ``torch.hann_window(win_length)`` is used (Default: ``None``).
Returns:
Tensor: The pitch-shifted audio waveform of shape `(..., time)`.
"""
waveform_stretch = _stretch_waveform(
waveform,
n_steps,
bins_per_octave,
n_fft,
win_length,
hop_length,
window,
)
rate = 2.0 ** (-float(n_steps) / bins_per_octave)
waveform_shift = resample(waveform_stretch, int(sample_rate / rate), sample_rate)
return _fix_waveform_shape(waveform_shift, waveform.size())
def _stretch_waveform(
waveform: Tensor,
n_steps: int,
bins_per_octave: int = 12,
n_fft: int = 512,
win_length: Optional[int] = None,
hop_length: Optional[int] = None,
window: Optional[Tensor] = None,
) -> Tensor:
"""
Pitch shift helper function to preprocess and stretch waveform before resampling step.
Args:
See pitch_shift arg descriptions.
Returns:
Tensor: The preprocessed waveform stretched prior to resampling.
"""
if hop_length is None:
hop_length = n_fft // 4
if win_length is None:
win_length = n_fft
if window is None:
window = torch.hann_window(window_length=win_length, device=waveform.device)
# pack batch
shape = waveform.size()
waveform = waveform.reshape(-1, shape[-1])
ori_len = shape[-1]
rate = 2.0 ** (-float(n_steps) / bins_per_octave)
spec_f = torch.stft(
input=waveform,
n_fft=n_fft,
hop_length=hop_length,
win_length=win_length,
window=window,
center=True,
pad_mode="reflect",
normalized=False,
onesided=True,
return_complex=True,
)
phase_advance = torch.linspace(0, math.pi * hop_length, spec_f.shape[-2], device=spec_f.device)[..., None]
spec_stretch = phase_vocoder(spec_f, rate, phase_advance)
len_stretch = int(round(ori_len / rate))
waveform_stretch = torch.istft(
spec_stretch, n_fft=n_fft, hop_length=hop_length, win_length=win_length, window=window, length=len_stretch
)
return waveform_stretch
def _fix_waveform_shape(
waveform_shift: Tensor,
shape: List[int],
) -> Tensor:
"""
PitchShift helper function to process after resampling step to fix the shape back.
Args:
waveform_shift(Tensor): The waveform after stretch and resample
shape (List[int]): The shape of initial waveform
Returns:
Tensor: The pitch-shifted audio waveform of shape `(..., time)`.
"""
ori_len = shape[-1]
shift_len = waveform_shift.size()[-1]
if shift_len > ori_len:
waveform_shift = waveform_shift[..., :ori_len]
else:
waveform_shift = torch.nn.functional.pad(waveform_shift, [0, ori_len - shift_len])
# unpack batch
waveform_shift = waveform_shift.view(shape[:-1] + waveform_shift.shape[-1:])
return waveform_shift
[docs]def rnnt_loss(
logits: Tensor,
targets: Tensor,
logit_lengths: Tensor,
target_lengths: Tensor,
blank: int = -1,
clamp: float = -1,
reduction: str = "mean",
fused_log_softmax: bool = True,
):
"""Compute the RNN Transducer loss from *Sequence Transduction with Recurrent Neural Networks*
:cite:`graves2012sequence`.
.. devices:: CPU CUDA
.. properties:: Autograd TorchScript
The RNN Transducer loss extends the CTC loss by defining a distribution over output
sequences of all lengths, and by jointly modelling both input-output and output-output
dependencies.
Args:
logits (Tensor): Tensor of dimension `(batch, max seq length, max target length + 1, class)`
containing output from joiner
targets (Tensor): Tensor of dimension `(batch, max target length)` containing targets with zero padded
logit_lengths (Tensor): Tensor of dimension `(batch)` containing lengths of each sequence from encoder
target_lengths (Tensor): Tensor of dimension `(batch)` containing lengths of targets for each sequence
blank (int, optional): blank label (Default: ``-1``)
clamp (float, optional): clamp for gradients (Default: ``-1``)
reduction (string, optional): Specifies the reduction to apply to the output:
``"none"`` | ``"mean"`` | ``"sum"``. (Default: ``"mean"``)
fused_log_softmax (bool): set to False if calling log_softmax outside of loss (Default: ``True``)
Returns:
Tensor: Loss with the reduction option applied. If ``reduction`` is ``"none"``, then size `(batch)`,
otherwise scalar.
"""
if reduction not in ["none", "mean", "sum"]:
raise ValueError('reduction should be one of "none", "mean", or "sum"')
if blank < 0: # reinterpret blank index if blank < 0.
blank = logits.shape[-1] + blank
costs, _ = torch.ops.torchaudio.rnnt_loss(
logits=logits,
targets=targets,
logit_lengths=logit_lengths,
target_lengths=target_lengths,
blank=blank,
clamp=clamp,
fused_log_softmax=fused_log_softmax,
)
if reduction == "mean":
return costs.mean()
elif reduction == "sum":
return costs.sum()
return costs
[docs]def psd(
specgram: Tensor,
mask: Optional[Tensor] = None,
normalize: bool = True,
eps: float = 1e-10,
) -> Tensor:
"""Compute cross-channel power spectral density (PSD) matrix.
.. devices:: CPU CUDA
.. properties:: Autograd TorchScript
Args:
specgram (torch.Tensor): Multi-channel complex-valued spectrum.
Tensor with dimensions `(..., channel, freq, time)`.
mask (torch.Tensor or None, optional): Time-Frequency mask for normalization.
Tensor with dimensions `(..., freq, time)`. (Default: ``None``)
normalize (bool, optional): If ``True``, normalize the mask along the time dimension. (Default: ``True``)
eps (float, optional): Value to add to the denominator in mask normalization. (Default: ``1e-15``)
Returns:
torch.Tensor: The complex-valued PSD matrix of the input spectrum.
Tensor with dimensions `(..., freq, channel, channel)`
"""
specgram = specgram.transpose(-3, -2) # shape (freq, channel, time)
# outer product:
# (..., ch_1, time) x (..., ch_2, time) -> (..., time, ch_1, ch_2)
psd = torch.einsum("...ct,...et->...tce", [specgram, specgram.conj()])
if mask is not None:
if mask.shape[:-1] != specgram.shape[:-2] or mask.shape[-1] != specgram.shape[-1]:
raise ValueError(
"The dimensions of mask except the channel dimension should be the same as specgram."
f"Found {mask.shape} for mask and {specgram.shape} for specgram."
)
# Normalized mask along time dimension:
if normalize:
mask = mask / (mask.sum(dim=-1, keepdim=True) + eps)
psd = psd * mask[..., None, None]
psd = psd.sum(dim=-3)
return psd
def _compute_mat_trace(input: torch.Tensor, dim1: int = -1, dim2: int = -2) -> torch.Tensor:
r"""Compute the trace of a Tensor along ``dim1`` and ``dim2`` dimensions.
Args:
input (torch.Tensor): Tensor with dimensions `(..., channel, channel)`.
dim1 (int, optional): The first dimension of the diagonal matrix.
(Default: ``-1``)
dim2 (int, optional): The second dimension of the diagonal matrix.
(Default: ``-2``)
Returns:
Tensor: The trace of the input Tensor.
"""
if input.ndim < 2:
raise ValueError("The dimension of the tensor must be at least 2.")
if input.shape[dim1] != input.shape[dim2]:
raise ValueError("The size of ``dim1`` and ``dim2`` must be the same.")
input = torch.diagonal(input, 0, dim1=dim1, dim2=dim2)
return input.sum(dim=-1)
def _tik_reg(mat: torch.Tensor, reg: float = 1e-7, eps: float = 1e-8) -> torch.Tensor:
"""Perform Tikhonov regularization (only modifying real part).
Args:
mat (torch.Tensor): Input matrix with dimensions `(..., channel, channel)`.
reg (float, optional): Regularization factor. (Default: 1e-8)
eps (float, optional): Value to avoid the correlation matrix is all-zero. (Default: ``1e-8``)
Returns:
Tensor: Regularized matrix with dimensions `(..., channel, channel)`.
"""
# Add eps
C = mat.size(-1)
eye = torch.eye(C, dtype=mat.dtype, device=mat.device)
epsilon = _compute_mat_trace(mat).real[..., None, None] * reg
# in case that correlation_matrix is all-zero
epsilon = epsilon + eps
mat = mat + epsilon * eye[..., :, :]
return mat
def _assert_psd_matrices(psd_s: torch.Tensor, psd_n: torch.Tensor) -> None:
"""Assertion checks of the PSD matrices of target speech and noise.
Args:
psd_s (torch.Tensor): The complex-valued power spectral density (PSD) matrix of target speech.
Tensor with dimensions `(..., freq, channel, channel)`.
psd_n (torch.Tensor): The complex-valued power spectral density (PSD) matrix of noise.
Tensor with dimensions `(..., freq, channel, channel)`.
"""
if psd_s.ndim < 3 or psd_n.ndim < 3:
raise ValueError(
"Expected at least 3D Tensor (..., freq, channel, channel) for psd_s and psd_n. "
f"Found {psd_s.shape} for psd_s and {psd_n.shape} for psd_n."
)
if not (psd_s.is_complex() and psd_n.is_complex()):
raise TypeError(
"The type of psd_s and psd_n must be ``torch.cfloat`` or ``torch.cdouble``. "
f"Found {psd_s.dtype} for psd_s and {psd_n.dtype} for psd_n."
)
if psd_s.shape != psd_n.shape:
raise ValueError(
f"The dimensions of psd_s and psd_n should be the same. Found {psd_s.shape} and {psd_n.shape}."
)
if psd_s.shape[-1] != psd_s.shape[-2]:
raise ValueError(f"The last two dimensions of psd_s should be the same. Found {psd_s.shape}.")
[docs]def mvdr_weights_souden(
psd_s: Tensor,
psd_n: Tensor,
reference_channel: Union[int, Tensor],
diagonal_loading: bool = True,
diag_eps: float = 1e-7,
eps: float = 1e-8,
) -> Tensor:
r"""Compute the Minimum Variance Distortionless Response (*MVDR* :cite:`capon1969high`) beamforming weights
by the method proposed by *Souden et, al.* :cite:`souden2009optimal`.
.. devices:: CPU CUDA
.. properties:: Autograd TorchScript
Given the power spectral density (PSD) matrix of target speech :math:`\bf{\Phi}_{\textbf{SS}}`,
the PSD matrix of noise :math:`\bf{\Phi}_{\textbf{NN}}`, and a one-hot vector that represents the
reference channel :math:`\bf{u}`, the method computes the MVDR beamforming weight martrix
:math:`\textbf{w}_{\text{MVDR}}`. The formula is defined as:
.. math::
\textbf{w}_{\text{MVDR}}(f) =
\frac{{{\bf{\Phi}_{\textbf{NN}}^{-1}}(f){\bf{\Phi}_{\textbf{SS}}}}(f)}
{\text{Trace}({{{\bf{\Phi}_{\textbf{NN}}^{-1}}(f) \bf{\Phi}_{\textbf{SS}}}(f))}}\bm{u}
Args:
psd_s (torch.Tensor): The complex-valued power spectral density (PSD) matrix of target speech.
Tensor with dimensions `(..., freq, channel, channel)`.
psd_n (torch.Tensor): The complex-valued power spectral density (PSD) matrix of noise.
Tensor with dimensions `(..., freq, channel, channel)`.
reference_channel (int or torch.Tensor): Specifies the reference channel.
If the dtype is ``int``, it represents the reference channel index.
If the dtype is ``torch.Tensor``, its shape is `(..., channel)`, where the ``channel`` dimension
is one-hot.
diagonal_loading (bool, optional): If ``True``, enables applying diagonal loading to ``psd_n``.
(Default: ``True``)
diag_eps (float, optional): The coefficient multiplied to the identity matrix for diagonal loading.
It is only effective when ``diagonal_loading`` is set to ``True``. (Default: ``1e-7``)
eps (float, optional): Value to add to the denominator in the beamforming weight formula.
(Default: ``1e-8``)
Returns:
torch.Tensor: The complex-valued MVDR beamforming weight matrix with dimensions `(..., freq, channel)`.
"""
_assert_psd_matrices(psd_s, psd_n)
if diagonal_loading:
psd_n = _tik_reg(psd_n, reg=diag_eps)
numerator = torch.linalg.solve(psd_n, psd_s) # psd_n.inv() @ psd_s
# ws: (..., C, C) / (...,) -> (..., C, C)
ws = numerator / (_compute_mat_trace(numerator)[..., None, None] + eps)
if torch.jit.isinstance(reference_channel, int):
beamform_weights = ws[..., :, reference_channel]
elif torch.jit.isinstance(reference_channel, Tensor):
reference_channel = reference_channel.to(psd_n.dtype)
# h: (..., F, C_1, C_2) x (..., C_2) -> (..., F, C_1)
beamform_weights = torch.einsum("...c,...c->...", [ws, reference_channel[..., None, None, :]])
else:
raise TypeError(f'Expected "int" or "Tensor" for reference_channel. Found: {type(reference_channel)}.')
return beamform_weights
[docs]def mvdr_weights_rtf(
rtf: Tensor,
psd_n: Tensor,
reference_channel: Optional[Union[int, Tensor]] = None,
diagonal_loading: bool = True,
diag_eps: float = 1e-7,
eps: float = 1e-8,
) -> Tensor:
r"""Compute the Minimum Variance Distortionless Response (*MVDR* :cite:`capon1969high`) beamforming weights
based on the relative transfer function (RTF) and power spectral density (PSD) matrix of noise.
.. devices:: CPU CUDA
.. properties:: Autograd TorchScript
Given the relative transfer function (RTF) matrix or the steering vector of target speech :math:`\bm{v}`,
the PSD matrix of noise :math:`\bf{\Phi}_{\textbf{NN}}`, and a one-hot vector that represents the
reference channel :math:`\bf{u}`, the method computes the MVDR beamforming weight martrix
:math:`\textbf{w}_{\text{MVDR}}`. The formula is defined as:
.. math::
\textbf{w}_{\text{MVDR}}(f) =
\frac{{{\bf{\Phi}_{\textbf{NN}}^{-1}}(f){\bm{v}}(f)}}
{{\bm{v}^{\mathsf{H}}}(f){\bf{\Phi}_{\textbf{NN}}^{-1}}(f){\bm{v}}(f)}
where :math:`(.)^{\mathsf{H}}` denotes the Hermitian Conjugate operation.
Args:
rtf (torch.Tensor): The complex-valued RTF vector of target speech.
Tensor with dimensions `(..., freq, channel)`.
psd_n (torch.Tensor): The complex-valued power spectral density (PSD) matrix of noise.
Tensor with dimensions `(..., freq, channel, channel)`.
reference_channel (int or torch.Tensor): Specifies the reference channel.
If the dtype is ``int``, it represents the reference channel index.
If the dtype is ``torch.Tensor``, its shape is `(..., channel)`, where the ``channel`` dimension
is one-hot.
diagonal_loading (bool, optional): If ``True``, enables applying diagonal loading to ``psd_n``.
(Default: ``True``)
diag_eps (float, optional): The coefficient multiplied to the identity matrix for diagonal loading.
It is only effective when ``diagonal_loading`` is set to ``True``. (Default: ``1e-7``)
eps (float, optional): Value to add to the denominator in the beamforming weight formula.
(Default: ``1e-8``)
Returns:
torch.Tensor: The complex-valued MVDR beamforming weight matrix with dimensions `(..., freq, channel)`.
"""
if rtf.ndim < 2:
raise ValueError(f"Expected at least 2D Tensor (..., freq, channel) for rtf. Found {rtf.shape}.")
if psd_n.ndim < 3:
raise ValueError(f"Expected at least 3D Tensor (..., freq, channel, channel) for psd_n. Found {psd_n.shape}.")
if not (rtf.is_complex() and psd_n.is_complex()):
raise TypeError(
"The type of rtf and psd_n must be ``torch.cfloat`` or ``torch.cdouble``. "
f"Found {rtf.dtype} for rtf and {psd_n.dtype} for psd_n."
)
if rtf.shape != psd_n.shape[:-1]:
raise ValueError(
"The dimensions of rtf and the dimensions withou the last dimension of psd_n should be the same. "
f"Found {rtf.shape} for rtf and {psd_n.shape} for psd_n."
)
if psd_n.shape[-1] != psd_n.shape[-2]:
raise ValueError(f"The last two dimensions of psd_n should be the same. Found {psd_n.shape}.")
if diagonal_loading:
psd_n = _tik_reg(psd_n, reg=diag_eps)
# numerator = psd_n.inv() @ stv
numerator = torch.linalg.solve(psd_n, rtf.unsqueeze(-1)).squeeze(-1) # (..., freq, channel)
# denominator = stv^H @ psd_n.inv() @ stv
denominator = torch.einsum("...d,...d->...", [rtf.conj(), numerator])
beamform_weights = numerator / (denominator.real.unsqueeze(-1) + eps)
# normalize the numerator
if reference_channel is not None:
if torch.jit.isinstance(reference_channel, int):
scale = rtf[..., reference_channel].conj()
elif torch.jit.isinstance(reference_channel, Tensor):
reference_channel = reference_channel.to(psd_n.dtype)
scale = torch.einsum("...c,...c->...", [rtf.conj(), reference_channel[..., None, :]])
else:
raise TypeError(f'Expected "int" or "Tensor" for reference_channel. Found: {type(reference_channel)}.')
beamform_weights = beamform_weights * scale[..., None]
return beamform_weights
[docs]def rtf_evd(psd_s: Tensor) -> Tensor:
r"""Estimate the relative transfer function (RTF) or the steering vector by eigenvalue decomposition.
.. devices:: CPU CUDA
.. properties:: TorchScript
Args:
psd_s (Tensor): The complex-valued power spectral density (PSD) matrix of target speech.
Tensor of dimension `(..., freq, channel, channel)`
Returns:
Tensor: The estimated complex-valued RTF of target speech.
Tensor of dimension `(..., freq, channel)`
"""
if not psd_s.is_complex():
raise TypeError(f"The type of psd_s must be ``torch.cfloat`` or ``torch.cdouble``. Found {psd_s.dtype}.")
if psd_s.shape[-1] != psd_s.shape[-2]:
raise ValueError(f"The last two dimensions of psd_s should be the same. Found {psd_s.shape}.")
_, v = torch.linalg.eigh(psd_s) # v is sorted along with eigenvalues in ascending order
rtf = v[..., -1] # choose the eigenvector with max eigenvalue
return rtf
[docs]def rtf_power(
psd_s: Tensor,
psd_n: Tensor,
reference_channel: Union[int, Tensor],
n_iter: int = 3,
diagonal_loading: bool = True,
diag_eps: float = 1e-7,
) -> Tensor:
r"""Estimate the relative transfer function (RTF) or the steering vector by the power method.
.. devices:: CPU CUDA
.. properties:: Autograd TorchScript
Args:
psd_s (torch.Tensor): The complex-valued power spectral density (PSD) matrix of target speech.
Tensor with dimensions `(..., freq, channel, channel)`.
psd_n (torch.Tensor): The complex-valued power spectral density (PSD) matrix of noise.
Tensor with dimensions `(..., freq, channel, channel)`.
reference_channel (int or torch.Tensor): Specifies the reference channel.
If the dtype is ``int``, it represents the reference channel index.
If the dtype is ``torch.Tensor``, its shape is `(..., channel)`, where the ``channel`` dimension
is one-hot.
diagonal_loading (bool, optional): If ``True``, enables applying diagonal loading to ``psd_n``.
(Default: ``True``)
diag_eps (float, optional): The coefficient multiplied to the identity matrix for diagonal loading.
It is only effective when ``diagonal_loading`` is set to ``True``. (Default: ``1e-7``)
Returns:
torch.Tensor: The estimated complex-valued RTF of target speech.
Tensor of dimension `(..., freq, channel)`.
"""
_assert_psd_matrices(psd_s, psd_n)
if n_iter <= 0:
raise ValueError("The number of iteration must be greater than 0.")
# Apply diagonal loading to psd_n to improve robustness.
if diagonal_loading:
psd_n = _tik_reg(psd_n, reg=diag_eps)
# phi is regarded as the first iteration
phi = torch.linalg.solve(psd_n, psd_s) # psd_n.inv() @ psd_s
if torch.jit.isinstance(reference_channel, int):
rtf = phi[..., reference_channel]
elif torch.jit.isinstance(reference_channel, Tensor):
reference_channel = reference_channel.to(psd_n.dtype)
rtf = torch.einsum("...c,...c->...", [phi, reference_channel[..., None, None, :]])
else:
raise TypeError(f'Expected "int" or "Tensor" for reference_channel. Found: {type(reference_channel)}.')
rtf = rtf.unsqueeze(-1) # (..., freq, channel, 1)
if n_iter >= 2:
# The number of iterations in the for loop is `n_iter - 2`
# because the `phi` above and `torch.matmul(psd_s, rtf)` are regarded as
# two iterations.
for _ in range(n_iter - 2):
rtf = torch.matmul(phi, rtf)
rtf = torch.matmul(psd_s, rtf)
else:
# if there is only one iteration, the rtf is the psd_s[..., referenc_channel]
# which is psd_n @ phi @ ref_channel
rtf = torch.matmul(psd_n, rtf)
return rtf.squeeze(-1)
[docs]def apply_beamforming(beamform_weights: Tensor, specgram: Tensor) -> Tensor:
r"""Apply the beamforming weight to the multi-channel noisy spectrum to obtain the single-channel enhanced spectrum.
.. devices:: CPU CUDA
.. properties:: Autograd TorchScript
.. math::
\hat{\textbf{S}}(f) = \textbf{w}_{\text{bf}}(f)^{\mathsf{H}} \textbf{Y}(f)
where :math:`\textbf{w}_{\text{bf}}(f)` is the beamforming weight for the :math:`f`-th frequency bin,
:math:`\textbf{Y}` is the multi-channel spectrum for the :math:`f`-th frequency bin.
Args:
beamform_weights (Tensor): The complex-valued beamforming weight matrix.
Tensor of dimension `(..., freq, channel)`
specgram (Tensor): The multi-channel complex-valued noisy spectrum.
Tensor of dimension `(..., channel, freq, time)`
Returns:
Tensor: The single-channel complex-valued enhanced spectrum.
Tensor of dimension `(..., freq, time)`
"""
if beamform_weights.shape[:-2] != specgram.shape[:-3]:
raise ValueError(
"The dimensions except the last two dimensions of beamform_weights should be the same "
"as the dimensions except the last three dimensions of specgram. "
f"Found {beamform_weights.shape} for beamform_weights and {specgram.shape} for specgram."
)
if not (beamform_weights.is_complex() and specgram.is_complex()):
raise TypeError(
"The type of beamform_weights and specgram must be ``torch.cfloat`` or ``torch.cdouble``. "
f"Found {beamform_weights.dtype} for beamform_weights and {specgram.dtype} for specgram."
)
# (..., freq, channel) x (..., channel, freq, time) -> (..., freq, time)
specgram_enhanced = torch.einsum("...fc,...cft->...ft", [beamform_weights.conj(), specgram])
return specgram_enhanced
def _check_shape_compatible(x: torch.Tensor, y: torch.Tensor) -> None:
if x.ndim != y.ndim:
raise ValueError(f"The operands must be the same dimension (got {x.ndim} and {y.ndim}).")
for i in range(x.ndim - 1):
xi = x.size(i)
yi = y.size(i)
if xi == yi or xi == 1 or yi == 1:
continue
raise ValueError(f"Leading dimensions of x and y are not broadcastable (got {x.shape} and {y.shape}).")
def _check_convolve_mode(mode: str) -> None:
valid_convolve_modes = ["full", "valid", "same"]
if mode not in valid_convolve_modes:
raise ValueError(f"Unrecognized mode value '{mode}'. Please specify one of {valid_convolve_modes}.")
def _apply_convolve_mode(conv_result: torch.Tensor, x_length: int, y_length: int, mode: str) -> torch.Tensor:
valid_convolve_modes = ["full", "valid", "same"]
if mode == "full":
return conv_result
elif mode == "valid":
target_length = max(x_length, y_length) - min(x_length, y_length) + 1
start_idx = (conv_result.size(-1) - target_length) // 2
return conv_result[..., start_idx : start_idx + target_length]
elif mode == "same":
start_idx = (conv_result.size(-1) - x_length) // 2
return conv_result[..., start_idx : start_idx + x_length]
else:
raise ValueError(f"Unrecognized mode value '{mode}'. Please specify one of {valid_convolve_modes}.")
[docs]def fftconvolve(x: torch.Tensor, y: torch.Tensor, mode: str = "full") -> torch.Tensor:
r"""
Convolves inputs along their last dimension using FFT. For inputs with large last dimensions, this function
is generally much faster than :meth:`convolve`.
Note that, in contrast to :meth:`torch.nn.functional.conv1d`, which actually applies the valid cross-correlation
operator, this function applies the true `convolution`_ operator.
Also note that this function can only output float tensors (int tensor inputs will be cast to float).
.. devices:: CPU CUDA
.. properties:: Autograd TorchScript
Args:
x (torch.Tensor): First convolution operand, with shape `(..., N)`.
y (torch.Tensor): Second convolution operand, with shape `(..., M)`
(leading dimensions must be broadcast-able with those of ``x``).
mode (str, optional): Must be one of ("full", "valid", "same").
* "full": Returns the full convolution result, with shape `(..., N + M - 1)`. (Default)
* "valid": Returns the segment of the full convolution result corresponding to where
the two inputs overlap completely, with shape `(..., max(N, M) - min(N, M) + 1)`.
* "same": Returns the center segment of the full convolution result, with shape `(..., N)`.
Returns:
torch.Tensor: Result of convolving ``x`` and ``y``, with shape `(..., L)`, where
the leading dimensions match those of ``x`` and `L` is dictated by ``mode``.
.. _convolution:
https://en.wikipedia.org/wiki/Convolution
"""
_check_shape_compatible(x, y)
_check_convolve_mode(mode)
n = x.size(-1) + y.size(-1) - 1
fresult = torch.fft.rfft(x, n=n) * torch.fft.rfft(y, n=n)
result = torch.fft.irfft(fresult, n=n)
return _apply_convolve_mode(result, x.size(-1), y.size(-1), mode)
[docs]def convolve(x: torch.Tensor, y: torch.Tensor, mode: str = "full") -> torch.Tensor:
r"""
Convolves inputs along their last dimension using the direct method.
Note that, in contrast to :meth:`torch.nn.functional.conv1d`, which actually applies the valid cross-correlation
operator, this function applies the true `convolution`_ operator.
.. devices:: CPU CUDA
.. properties:: Autograd TorchScript
Args:
x (torch.Tensor): First convolution operand, with shape `(..., N)`.
y (torch.Tensor): Second convolution operand, with shape `(..., M)`
(leading dimensions must be broadcast-able with those of ``x``).
mode (str, optional): Must be one of ("full", "valid", "same").
* "full": Returns the full convolution result, with shape `(..., N + M - 1)`. (Default)
* "valid": Returns the segment of the full convolution result corresponding to where
the two inputs overlap completely, with shape `(..., max(N, M) - min(N, M) + 1)`.
* "same": Returns the center segment of the full convolution result, with shape `(..., N)`.
Returns:
torch.Tensor: Result of convolving ``x`` and ``y``, with shape `(..., L)`, where
the leading dimensions match those of ``x`` and `L` is dictated by ``mode``.
.. _convolution:
https://en.wikipedia.org/wiki/Convolution
"""
_check_shape_compatible(x, y)
_check_convolve_mode(mode)
x_size, y_size = x.size(-1), y.size(-1)
if x.size(-1) < y.size(-1):
x, y = y, x
if x.shape[:-1] != y.shape[:-1]:
new_shape = [max(i, j) for i, j in zip(x.shape[:-1], y.shape[:-1])]
x = x.broadcast_to(new_shape + [x.shape[-1]])
y = y.broadcast_to(new_shape + [y.shape[-1]])
num_signals = torch.tensor(x.shape[:-1]).prod()
reshaped_x = x.reshape((int(num_signals), x.size(-1)))
reshaped_y = y.reshape((int(num_signals), y.size(-1)))
output = torch.nn.functional.conv1d(
input=reshaped_x,
weight=reshaped_y.flip(-1).unsqueeze(1),
stride=1,
groups=reshaped_x.size(0),
padding=reshaped_y.size(-1) - 1,
)
output_shape = x.shape[:-1] + (-1,)
result = output.reshape(output_shape)
return _apply_convolve_mode(result, x_size, y_size, mode)
[docs]def add_noise(
waveform: torch.Tensor, noise: torch.Tensor, snr: torch.Tensor, lengths: Optional[torch.Tensor] = None
) -> torch.Tensor:
r"""Scales and adds noise to waveform per signal-to-noise ratio.
Specifically, for each pair of waveform vector :math:`x \in \mathbb{R}^L` and noise vector
:math:`n \in \mathbb{R}^L`, the function computes output :math:`y` as
.. math::
y = x + a n \, \text{,}
where
.. math::
a = \sqrt{ \frac{ ||x||_{2}^{2} }{ ||n||_{2}^{2} } \cdot 10^{-\frac{\text{SNR}}{10}} } \, \text{,}
with :math:`\text{SNR}` being the desired signal-to-noise ratio between :math:`x` and :math:`n`, in dB.
Note that this function broadcasts singleton leading dimensions in its inputs in a manner that is
consistent with the above formulae and PyTorch's broadcasting semantics.
.. devices:: CPU CUDA
.. properties:: Autograd TorchScript
Args:
waveform (torch.Tensor): Input waveform, with shape `(..., L)`.
noise (torch.Tensor): Noise, with shape `(..., L)` (same shape as ``waveform``).
snr (torch.Tensor): Signal-to-noise ratios in dB, with shape `(...,)`.
lengths (torch.Tensor or None, optional): Valid lengths of signals in ``waveform`` and ``noise``, with shape
`(...,)` (leading dimensions must match those of ``waveform``). If ``None``, all elements in ``waveform``
and ``noise`` are treated as valid. (Default: ``None``)
Returns:
torch.Tensor: Result of scaling and adding ``noise`` to ``waveform``, with shape `(..., L)`
(same shape as ``waveform``).
"""
if not (waveform.ndim - 1 == noise.ndim - 1 == snr.ndim and (lengths is None or lengths.ndim == snr.ndim)):
raise ValueError("Input leading dimensions don't match.")
L = waveform.size(-1)
if L != noise.size(-1):
raise ValueError(f"Length dimensions of waveform and noise don't match (got {L} and {noise.size(-1)}).")
# compute scale
if lengths is not None:
mask = torch.arange(0, L, device=lengths.device).expand(waveform.shape) < lengths.unsqueeze(
-1
) # (*, L) < (*, 1) = (*, L)
masked_waveform = waveform * mask
masked_noise = noise * mask
else:
masked_waveform = waveform
masked_noise = noise
energy_signal = torch.linalg.vector_norm(masked_waveform, ord=2, dim=-1) ** 2 # (*,)
energy_noise = torch.linalg.vector_norm(masked_noise, ord=2, dim=-1) ** 2 # (*,)
original_snr_db = 10 * (torch.log10(energy_signal) - torch.log10(energy_noise))
scale = 10 ** ((original_snr_db - snr) / 20.0) # (*,)
# scale noise
scaled_noise = scale.unsqueeze(-1) * noise # (*, 1) * (*, L) = (*, L)
return waveform + scaled_noise # (*, L)
[docs]def speed(
waveform: torch.Tensor, orig_freq: int, factor: float, lengths: Optional[torch.Tensor] = None
) -> Tuple[torch.Tensor, Optional[torch.Tensor]]:
r"""Adjusts waveform speed.
.. devices:: CPU CUDA
.. properties:: Autograd TorchScript
Args:
waveform (torch.Tensor): Input signals, with shape `(..., time)`.
orig_freq (int): Original frequency of the signals in ``waveform``.
factor (float): Factor by which to adjust speed of input. Values greater than 1.0
compress ``waveform`` in time, whereas values less than 1.0 stretch ``waveform`` in time.
lengths (torch.Tensor or None, optional): Valid lengths of signals in ``waveform``, with shape `(...)`.
If ``None``, all elements in ``waveform`` are treated as valid. (Default: ``None``)
Returns:
(torch.Tensor, torch.Tensor or None):
torch.Tensor
Speed-adjusted waveform, with shape `(..., new_time).`
torch.Tensor or None
If ``lengths`` is not ``None``, valid lengths of signals in speed-adjusted waveform,
with shape `(...)`; otherwise, ``None``.
"""
source_sample_rate = int(factor * orig_freq)
target_sample_rate = int(orig_freq)
gcd = math.gcd(source_sample_rate, target_sample_rate)
source_sample_rate = source_sample_rate // gcd
target_sample_rate = target_sample_rate // gcd
if lengths is None:
out_lengths = None
else:
out_lengths = torch.ceil(lengths * target_sample_rate / source_sample_rate).to(lengths.dtype)
return resample(waveform, source_sample_rate, target_sample_rate), out_lengths
[docs]def preemphasis(waveform, coeff: float = 0.97) -> torch.Tensor:
r"""Pre-emphasizes a waveform along its last dimension, i.e.
for each signal :math:`x` in ``waveform``, computes
output :math:`y` as
.. math::
y[i] = x[i] - \text{coeff} \cdot x[i - 1]
.. devices:: CPU CUDA
.. properties:: Autograd TorchScript
Args:
waveform (torch.Tensor): Waveform, with shape `(..., N)`.
coeff (float, optional): Pre-emphasis coefficient. Typically between 0.0 and 1.0.
(Default: 0.97)
Returns:
torch.Tensor: Pre-emphasized waveform, with shape `(..., N)`.
"""
waveform = waveform.clone()
waveform[..., 1:] -= coeff * waveform[..., :-1]
return waveform
[docs]def deemphasis(waveform, coeff: float = 0.97) -> torch.Tensor:
r"""De-emphasizes a waveform along its last dimension.
Inverse of :meth:`preemphasis`. Concretely, for each signal
:math:`x` in ``waveform``, computes output :math:`y` as
.. math::
y[i] = x[i] + \text{coeff} \cdot y[i - 1]
.. devices:: CPU CUDA
.. properties:: Autograd TorchScript
Args:
waveform (torch.Tensor): Waveform, with shape `(..., N)`.
coeff (float, optional): De-emphasis coefficient. Typically between 0.0 and 1.0.
(Default: 0.97)
Returns:
torch.Tensor: De-emphasized waveform, with shape `(..., N)`.
"""
a_coeffs = torch.tensor([1.0, -coeff], dtype=waveform.dtype, device=waveform.device)
b_coeffs = torch.tensor([1.0, 0.0], dtype=waveform.dtype, device=waveform.device)
return torchaudio.functional.lfilter(waveform, a_coeffs=a_coeffs, b_coeffs=b_coeffs)
