Source code for torchaudio.functional.functional
# -*- coding: utf-8 -*-
import io
import math
import warnings
from typing import Optional, Tuple
import torch
from torch import Tensor
from torchaudio._internal import module_utils as _mod_utils
import torchaudio
__all__ = [
"spectrogram",
"griffinlim",
"amplitude_to_DB",
"DB_to_amplitude",
"compute_deltas",
"compute_kaldi_pitch",
"create_fb_matrix",
"create_dct",
"compute_deltas",
"detect_pitch_frequency",
"DB_to_amplitude",
"mu_law_encoding",
"mu_law_decoding",
"complex_norm",
"angle",
"magphase",
"phase_vocoder",
'mask_along_axis',
'mask_along_axis_iid',
'sliding_window_cmn',
"spectral_centroid",
"apply_codec",
"resample",
]
[docs]def spectrogram(
waveform: Tensor,
pad: int,
window: Tensor,
n_fft: int,
hop_length: int,
win_length: int,
power: Optional[float],
normalized: bool,
center: bool = True,
pad_mode: str = "reflect",
onesided: bool = True,
return_complex: bool = False,
) -> Tensor:
r"""Create a spectrogram or a batch of spectrograms from a raw audio signal.
The spectrogram can be either magnitude-only or complex.
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): Whether to normalize by magnitude after stft
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):
Indicates whether the resulting complex-valued Tensor should be represented with
native complex dtype, such as `torch.cfloat` and `torch.cdouble`, or real dtype
mimicking complex value with an extra dimension for real and imaginary parts.
This argument is only effective when ``power=None``.
See also ``torch.view_as_real``.
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 power is None and not return_complex:
warnings.warn(
"The use of pseudo complex type in spectrogram is now deprecated."
"Please migrate to native complex type by providing `return_complex=True`. "
"Please refer to https://github.com/pytorch/audio/issues/1337 "
"for more details about torchaudio's plan to migrate to native complex type."
)
if pad > 0:
# TODO add "with torch.no_grad():" back when JIT supports it
waveform = torch.nn.functional.pad(waveform, (pad, pad), "constant")
# 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=False,
onesided=onesided,
return_complex=True,
)
# unpack batch
spec_f = spec_f.reshape(shape[:-1] + spec_f.shape[-2:])
if normalized:
spec_f /= window.pow(2.).sum().sqrt()
if power is not None:
if power == 1.0:
return spec_f.abs()
return spec_f.abs().pow(power)
if not return_complex:
return torch.view_as_real(spec_f)
return spec_f
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.
Implementation ported from
:footcite:`brian_mcfee-proc-scipy-2015`, :footcite:`6701851` and :footcite:`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:
torch.Tensor: waveform of (..., time), where time equals the ``length`` parameter if given.
"""
assert momentum < 1, 'momentum={} > 1 can be unstable'.format(momentum)
assert momentum >= 0, 'momentum={} < 0'.format(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., 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 / (1 + 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.
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.
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
[docs]def create_fb_matrix(
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.
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 (Optional[str]): 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 * create_fb_matrix(A.size(-1), ...)``.
"""
if norm is not None and norm != "slaney":
raise ValueError("norm must be one of None or 'slaney'")
# freq bins
# Equivalent filterbank construction by Librosa
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)
# calculate the difference between each mel point and each stft freq point in hertz
f_diff = f_pts[1:] - f_pts[:-1] # (n_mels + 1)
slopes = f_pts.unsqueeze(0) - all_freqs.unsqueeze(1) # (n_freqs, n_mels + 2)
# create overlapping triangles
zero = torch.zeros(1)
down_slopes = (-1.0 * slopes[:, :-2]) / f_diff[:-1] # (n_freqs, n_mels)
up_slopes = slopes[:, 2:] / f_diff[1:] # (n_freqs, n_mels)
fb = torch.max(zero, torch.min(down_slopes, up_slopes))
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.).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 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.
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``).
"""
# 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:
assert norm == "ortho"
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. For more info see the
`Wikipedia Entry <https://en.wikipedia.org/wiki/%CE%9C-law_algorithm>`_
This algorithm assumes 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():
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. 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]@_mod_utils.deprecated(
"Please convert the input Tensor to complex type with `torch.view_as_complex` then "
"use `torch.abs`. "
"Please refer to https://github.com/pytorch/audio/issues/1337 "
"for more details about torchaudio's plan to migrate to native complex type."
)
def complex_norm(
complex_tensor: Tensor,
power: float = 1.0
) -> Tensor:
r"""Compute the norm of complex tensor input.
Args:
complex_tensor (Tensor): Tensor shape of `(..., complex=2)`
power (float): Power of the norm. (Default: `1.0`).
Returns:
Tensor: Power of the normed input tensor. Shape of `(..., )`
"""
# Replace by torch.norm once issue is fixed
# https://github.com/pytorch/pytorch/issues/34279
return complex_tensor.pow(2.).sum(-1).pow(0.5 * power)
[docs]@_mod_utils.deprecated(
"Please convert the input Tensor to complex type with `torch.view_as_complex` then "
"use `torch.angle`. "
"Please refer to https://github.com/pytorch/audio/issues/1337 "
"for more details about torchaudio's plan to migrate to native complex type."
)
def angle(
complex_tensor: Tensor
) -> Tensor:
r"""Compute the angle of complex tensor input.
Args:
complex_tensor (Tensor): Tensor shape of `(..., complex=2)`
Return:
Tensor: Angle of a complex tensor. Shape of `(..., )`
"""
return torch.atan2(complex_tensor[..., 1], complex_tensor[..., 0])
[docs]@_mod_utils.deprecated(
"Please convert the input Tensor to complex type with `torch.view_as_complex` then "
"use `torch.abs` and `torch.angle`. "
"Please refer to https://github.com/pytorch/audio/issues/1337 "
"for more details about torchaudio's plan to migrate to native complex type."
)
def magphase(
complex_tensor: Tensor,
power: float = 1.0
) -> Tuple[Tensor, Tensor]:
r"""Separate a complex-valued spectrogram with shape `(..., 2)` into its magnitude and phase.
Args:
complex_tensor (Tensor): Tensor shape of `(..., complex=2)`
power (float): Power of the norm. (Default: `1.0`)
Returns:
(Tensor, Tensor): The magnitude and phase of the complex tensor
"""
mag = complex_norm(complex_tensor, power)
phase = angle(complex_tensor)
return mag, phase
[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``.
Args:
complex_specgrams (Tensor):
Either a real tensor of dimension of ``(..., freq, num_frame, complex=2)``
or 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 - With Tensor of complex dtype
>>> 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])
Example - With Tensor of real dtype and extra dimension for complex field
>>> freq, hop_length = 1025, 512
>>> # (channel, freq, time, complex=2)
>>> complex_specgrams = torch.randn(2, freq, 300, 2)
>>> 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, 2])
"""
if rate == 1.0:
return complex_specgrams
if not complex_specgrams.is_complex():
warnings.warn(
"The use of pseudo complex type in `torchaudio.functional.phase_vocoder` and "
"`torchaudio.transforms.TimeStretch` is now deprecated."
"Please migrate to native complex type by converting the input tensor with "
"`torch.view_as_complex`. "
"Please refer to https://github.com/pytorch/audio/issues/1337 "
"for more details about torchaudio's plan to migrate to native complex type."
)
if complex_specgrams.size(-1) != 2:
raise ValueError(
"complex_specgrams must be either native complex tensors or "
"real valued tensors with shape (..., 2)")
is_complex = complex_specgrams.is_complex()
if not is_complex:
complex_specgrams = torch.view_as_complex(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:])
if not is_complex:
return torch.view_as_real(complex_specgrams_stretch)
return complex_specgrams_stretch
[docs]def mask_along_axis_iid(
specgrams: Tensor,
mask_param: int,
mask_value: float,
axis: int
) -> Tensor:
r"""
Apply a mask along ``axis``. Mask will be applied from indices ``[v_0, v_0 + v)``, where
``v`` is sampled from ``uniform(0, mask_param)``, and ``v_0`` from ``uniform(0, max_v - v)``.
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)
Returns:
Tensor: Masked spectrograms of dimensions (batch, channel, freq, time)
"""
if axis != 2 and axis != 3:
raise ValueError('Only Frequency and Time masking are supported')
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[..., None, None]
mask_end = (min_value + value)[..., 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
) -> Tensor:
r"""
Apply a mask along ``axis``. Mask will be applied from indices ``[v_0, v_0 + v)``, where
``v`` is sampled from ``uniform(0, mask_param)``, and ``v_0`` from ``uniform(0, max_v - v)``.
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)
Returns:
Tensor: Masked spectrogram of dimensions (channel, freq, time)
"""
if axis != 1 and axis != 2:
raise ValueError('Only Frequency and Time masking are supported')
# 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)
assert mask_end - mask_start < 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:
.. 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])
assert win_length >= 3
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.
)
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.
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.
Args:
specgram (Tensor): Tensor of audio 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.
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., 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]@_mod_utils.requires_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.
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):
When True, both the input and output Tensor have dimension ``[channel, time]``.
Otherwise, they have dimension ``[time, channel]``.
compression (float): Used for formats other than WAV.
For more details see :py:func:`torchaudio.backend.sox_io_backend.save`.
encoding (str, optional): Changes the encoding for the supported formats.
For more details see :py:func:`torchaudio.backend.sox_io_backend.save`.
bits_per_sample (int, optional): Changes the bit depth for the supported formats.
For more details see :py:func:`torchaudio.backend.sox_io_backend.save`.
Returns:
torch.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, _ = torchaudio.sox_effects.sox_effects.apply_effects_file(
bytes, effects=[["rate", f"{sample_rate}"]], channels_first=channels_first, format=format)
return augmented
[docs]@_mod_utils.requires_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 :footcite:`6854049`.
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: float,
new_freq: float,
gcd: int,
lowpass_filter_width: int,
rolloff: float,
resampling_method: str,
beta: Optional[float],
device: torch.device = torch.device("cpu"),
dtype: Optional[torch.dtype] = None):
if not (int(orig_freq) == orig_freq and int(new_freq) == new_freq):
warnings.warn(
"Non-integer frequencies are being cast to ints and may result in poor resampling quality "
"because the underlying algorithm requires an integer ratio between `orig_freq` and `new_freq`. "
"Using non-integer valued frequencies will throw an error in release 0.10. "
"To work around this issue, 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 or to leave feedback about this change, please refer to "
"https://github.com/pytorch/audio/issues/1487."
)
if resampling_method not in ['sinc_interpolation', 'kaiser_window']:
raise ValueError('Invalid resampling method: {}'.format(resampling_method))
orig_freq = int(orig_freq) // gcd
new_freq = int(new_freq) // gcd
assert lowpass_filter_width > 0
kernels = []
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, device=device, dtype=idx_dtype)
for i in range(new_freq):
t = (-i / new_freq + idx / orig_freq) * 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_interpolation":
window = torch.cos(t * math.pi / lowpass_filter_width / 2)**2
else:
# kaiser_window
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
kernel = torch.where(t == 0, torch.tensor(1.).to(t), torch.sin(t) / t)
kernel.mul_(window)
kernels.append(kernel)
scale = base_freq / orig_freq
kernels = torch.stack(kernels).view(new_freq, 1, -1).mul_(scale)
if dtype is None:
kernels = kernels.to(dtype=torch.float32)
return kernels, width
def _apply_sinc_resample_kernel(
waveform: Tensor,
orig_freq: float,
new_freq: float,
gcd: int,
kernel: Tensor,
width: int,
):
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: float,
new_freq: float,
lowpass_filter_width: int = 6,
rolloff: float = 0.99,
resampling_method: str = "sinc_interpolation",
beta: Optional[float] = None,
) -> Tensor:
r"""Resamples the waveform at the new frequency using bandlimited interpolation.
https://ccrma.stanford.edu/~jos/resample/Theory_Ideal_Bandlimited_Interpolation.html
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 (float): The original frequency of the signal
new_freq (float): 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_interpolation``, ``kaiser_window``] (Default: ``'sinc_interpolation'``)
beta (float or None): The shape parameter used for kaiser window.
Returns:
Tensor: The waveform at the new frequency of dimension (..., time).
"""
assert orig_freq > 0.0 and new_freq > 0.0
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
