In the following example, any version of example.com/othermodule is replaced with the specified fork of its code.

require example.com/othermodule v1.2.3

replace example.com/othermodule => example.com/myfork/othermodule v1.2.3-fixed
The following example replaces module version v1.2.5 with version v1.2.3 of the same module.

replace example.com/othermodule v1.2.5 => example.com/othermodule v1.2.3
The following example specifies that a local directory should be used as a replacement for all versions of the module.

require example.com/othermodule v1.2.3

replace example.com/othermodule => ../othermodule
The following example specifies that a local directory should be used as a replacement for v1.2.5 only.

require example.com/othermodule v1.2.5

replace example.com/othermodule v1.2.5 => ../othermodule
The following example specifies that version v1.2.3 should be used instead of any other version of the module.

require example.com/othermodule v1.2.2

replace example.com/othermodule => example.com/othermodule v1.2.3
Note that a replace directive alone does not add a module to the module graph. A require directive that refers to a replaced module version is also needed, either in the main module’s go.mod file or a dependency’s go.mod file. If you don’t have a specific version to replace, you can use a fake version, as in the example below. Note that this will break modules that depend on your module, since replace directives are only applied in the main module.

require example.com/mod v0.0.0-replace

replace example.com/mod v0.0.0-replace => ./mod
A go.mod file includes directives as shown in the following example. These are described elsewhere in this topic.

module example.com/mymodule

go 1.14

require (
    example.com/othermodule v1.2.3
    example.com/thismodule v1.2.3
    example.com/thatmodule v1.2.3
)

replace example.com/thatmodule => ../thatmodule
exclude example.com/thismodule v1.3.0
To reference a published module, a go.mod file would typically omit the replace directive and use a require directive with a tagged version number at the end.

require example.com/greetings v1.1.0

1) If you want to restrict requests for /login.php, you need to use a RewriteCond to check the actual request. Otherwise you're going to go into a loop.

You could also redirect them to /login if you want and let the first rule take care of it:

2) You can check if an actual file exists before you rewrite the php, again by using RewriteCond and checking using "-f"

So first we check to make sure the request starts with "/ajax/" and we select the next part "(.+)". In the next RewriteCond, we use the %1 backreference to access the previous match. So if the request was for "/ajax/blahblah/", the next RewriteCond would check for "/doc_root/ajax/blahblah.php". The !-f means "if the file doesn't exist". Thus, in this example, if "/doc_root/ajax/blahblah.php" doesn't exist, then we rewrite the request to "/ajax/no_action.php". You'd have to replace that with something that you want to handle all of the "bad" requests. Maybe point it to a blank script that simple does nothing so nobody would know the wiser. You can then make a rewrite to change /ajax/(.+)/ to /ajax/$1.php:


RewriteCond %{THE_REQUEST} ^[A-Z]{3,9}\ /login.php
RewriteRule ^ /file_not_exist.html [L]


RewriteRule ^ /login/ [L,R=301]


RewriteCond %{REQUEST_URI} ^/ajax/(.+)/?
RewriteCond %{DOCUMENT_ROOT}/ajax/%1.php !-f
RewriteRule ^ /ajax/no_action.php [L]


RewriteRule ^ajax/([A-Za-z]+)/?$ /ajax/$1.php [L]
Shortcuts

# -*- coding: utf-8 -*-

from collections.abc import Sequence
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",
    "inverse_spectrogram",
    "griffinlim",
    "amplitude_to_DB",
    "DB_to_amplitude",
    "compute_deltas",
    "compute_kaldi_pitch",
    "create_fb_matrix",
    "melscale_fbanks",
    "linear_fbanks",
    "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",
    "edit_distance",
    "pitch_shift",
    "rnnt_loss",
]


[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 = True,
) -> 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.
            (See also ``torch.view_as_real``.)
            This argument is only effective when ``power=None``. It is ignored for
            cases where ``power`` is a number as in those cases, the returned tensor is
            power spectrogram, which is a real-valued tensor.

    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


[docs]def inverse_spectrogram(
        spectrogram: Tensor,
        length: Optional[int],
        pad: int,
        window: Tensor,
        n_fft: int,
        hop_length: int,
        win_length: int,
        normalized: bool,
        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.

    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): Whether the stft output was normalized by magnitude
        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.
    """

    if spectrogram.dtype == torch.float32 or spectrogram.dtype == torch.float64:
        warnings.warn(
            "The use of pseudo complex type in inverse_spectrogram is now deprecated. "
            "Please migrate to native complex type by using a complex tensor as input. "
            "If the input is generated via spectrogram() function or transform, please use "
            "return_complex=True as an argument to that function. "
            "Please refer to https://github.com/pytorch/audio/issues/1337 "
            "for more details about torchaudio's plan to migrate to native complex type."
        )
        spectrogram = torch.view_as_complex(spectrogram)

    if normalized:
        spectrogram = spectrogram * window.pow(2.).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=False,
        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_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
    *librosa* [:footcite:`brian_mcfee-proc-scipy-2015`], *A fast Griffin-Lim algorithm* [:footcite:`6701851`]
    and *Signal estimation from modified short-time Fourier transform* [: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:
        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


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 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 (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 * create_fb_matrix(A.size(-1), ...)``.
    """
    warnings.warn(
        "The use of `create_fb_matrix` is now deprecated and will be removed in "
        "the 0.11 release. "
        "Please migrate your code to use `melscale_fbanks` instead. "
        "For more information, please refer to https://github.com/pytorch/audio/issues/1574."
    )

    return melscale_fbanks(
        n_freqs=n_freqs,
        f_min=f_min,
        f_max=f_max,
        n_mels=n_mels,
        sample_rate=sample_rate,
        norm=norm,
        mel_scale=mel_scale
    )


[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.

    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.).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.

    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.

    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.",
    version="0.11",
)
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, optional): 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.",
    version="0.11",
)
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.",
    version="0.11",
)
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, optional): 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 support for pseudo complex type in `torchaudio.functional.phase_vocoder` and "
            "`torchaudio.transforms.TimeStretch` is now deprecated and will be removed "
            "from 0.11 release."
            "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 not in [2, 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 not in [1, 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 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.

    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, 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, _ = 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 *A pitch extraction algorithm tuned
    for automatic speech recognition* [: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: int,
        new_freq: int,
        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):
        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 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: int,
        new_freq: int,
        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: int,
        new_freq: int,
        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 (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_interpolation``, ``kaiser_window``] (Default: ``'sinc_interpolation'``)
        beta (float or None, optional): 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


[docs]@torch.jit.unused
def edit_distance(seq1: Sequence, seq2: Sequence) -> int:
    """
    Calculate the word level edit (Levenshtein) distance between two sequences.

    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.

    torchscipt is not supported for this function.

    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 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.

    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)`.
    """
    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)
    waveform_shift = resample(waveform_stretch, int(sample_rate / rate), sample_rate)
    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
    wavefor

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