372 lines
13 KiB
Python
372 lines
13 KiB
Python
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#!/usr/bin/env python
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# -*- coding: utf-8 -*-
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"""Feature inversion"""
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import warnings
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import numpy as np
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import scipy.fftpack
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from ..util.exceptions import ParameterError
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from ..core.spectrum import griffinlim
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from ..core.spectrum import db_to_power
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from ..util.utils import tiny
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from .. import filters
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from ..util import nnls, expand_to
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from numpy.typing import DTypeLike
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from typing import Any, Callable, Optional, Union
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from .._typing import _WindowSpec, _PadModeSTFT
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__all__ = ["mel_to_stft", "mel_to_audio", "mfcc_to_mel", "mfcc_to_audio"]
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def mel_to_stft(
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M: np.ndarray,
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*,
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sr: float = 22050,
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n_fft: int = 2048,
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power: float = 2.0,
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**kwargs: Any,
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) -> np.ndarray:
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"""Approximate STFT magnitude from a Mel power spectrogram.
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Parameters
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----------
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M : np.ndarray [shape=(..., n_mels, n), non-negative]
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The spectrogram as produced by `feature.melspectrogram`
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sr : number > 0 [scalar]
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sampling rate of the underlying signal
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n_fft : int > 0 [scalar]
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number of FFT components in the resulting STFT
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power : float > 0 [scalar]
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Exponent for the magnitude melspectrogram
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**kwargs : additional keyword arguments for Mel filter bank parameters
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fmin : float >= 0 [scalar]
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lowest frequency (in Hz)
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fmax : float >= 0 [scalar]
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highest frequency (in Hz).
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If `None`, use ``fmax = sr / 2.0``
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htk : bool [scalar]
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use HTK formula instead of Slaney
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norm : {None, 'slaney', or number} [scalar]
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If 'slaney', divide the triangular mel weights by the width of
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the mel band (area normalization).
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If numeric, use `librosa.util.normalize` to normalize each filter
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by to unit l_p norm. See `librosa.util.normalize` for a full
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description of supported norm values (including `+-np.inf`).
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Otherwise, leave all the triangles aiming for a peak value of 1.0
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dtype : np.dtype
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The data type of the output basis.
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By default, uses 32-bit (single-precision) floating point.
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Returns
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-------
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S : np.ndarray [shape=(..., n_fft, t), non-negative]
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An approximate linear magnitude spectrogram
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See Also
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--------
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librosa.feature.melspectrogram
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librosa.stft
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librosa.filters.mel
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librosa.util.nnls
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Examples
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--------
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>>> y, sr = librosa.load(librosa.ex('trumpet'))
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>>> S = librosa.util.abs2(librosa.stft(y))
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>>> mel_spec = librosa.feature.melspectrogram(S=S, sr=sr)
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>>> S_inv = librosa.feature.inverse.mel_to_stft(mel_spec, sr=sr)
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Compare the results visually
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>>> import matplotlib.pyplot as plt
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>>> fig, ax = plt.subplots(nrows=3, sharex=True, sharey=True)
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>>> img = librosa.display.specshow(librosa.amplitude_to_db(S, ref=np.max, top_db=None),
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... y_axis='log', x_axis='time', ax=ax[0])
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>>> ax[0].set(title='Original STFT')
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>>> ax[0].label_outer()
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>>> librosa.display.specshow(librosa.amplitude_to_db(S_inv, ref=np.max, top_db=None),
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... y_axis='log', x_axis='time', ax=ax[1])
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>>> ax[1].set(title='Reconstructed STFT')
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>>> ax[1].label_outer()
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>>> librosa.display.specshow(librosa.amplitude_to_db(np.abs(S_inv - S),
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... ref=S.max(), top_db=None),
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... vmax=0, y_axis='log', x_axis='time', cmap='magma', ax=ax[2])
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>>> ax[2].set(title='Residual error (dB)')
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>>> fig.colorbar(img, ax=ax, format="%+2.f dB")
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"""
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# Construct a mel basis with dtype matching the input data
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mel_basis = filters.mel(
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sr=sr, n_fft=n_fft, n_mels=M.shape[-2], dtype=M.dtype, **kwargs
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)
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# Find the non-negative least squares solution, and apply
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# the inverse exponent.
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# We'll do the exponentiation in-place.
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inverse = nnls(mel_basis, M)
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return np.power(inverse, 1.0 / power, out=inverse)
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def mel_to_audio(
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M: np.ndarray,
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*,
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sr: float = 22050,
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n_fft: int = 2048,
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hop_length: Optional[int] = None,
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win_length: Optional[int] = None,
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window: _WindowSpec = "hann",
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center: bool = True,
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pad_mode: _PadModeSTFT = "constant",
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power: float = 2.0,
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n_iter: int = 32,
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length: Optional[int] = None,
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dtype: DTypeLike = np.float32,
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**kwargs: Any,
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) -> np.ndarray:
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"""Invert a mel power spectrogram to audio using Griffin-Lim.
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This is primarily a convenience wrapper for:
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>>> S = librosa.feature.inverse.mel_to_stft(M)
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>>> y = librosa.griffinlim(S)
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Parameters
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----------
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M : np.ndarray [shape=(..., n_mels, n), non-negative]
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The spectrogram as produced by `feature.melspectrogram`
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sr : number > 0 [scalar]
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sampling rate of the underlying signal
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n_fft : int > 0 [scalar]
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number of FFT components in the resulting STFT
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hop_length : None or int > 0
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The hop length of the STFT. If not provided, it will default to ``n_fft // 4``
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win_length : None or int > 0
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The window length of the STFT. By default, it will equal ``n_fft``
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window : string, tuple, number, function, or np.ndarray [shape=(n_fft,)]
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A window specification as supported by `stft` or `istft`
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center : boolean
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If `True`, the STFT is assumed to use centered frames.
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If `False`, the STFT is assumed to use left-aligned frames.
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pad_mode : string
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If ``center=True``, the padding mode to use at the edges of the signal.
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By default, STFT uses zero padding.
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power : float > 0 [scalar]
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Exponent for the magnitude melspectrogram
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n_iter : int > 0
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The number of iterations for Griffin-Lim
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length : None or int > 0
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If provided, the output ``y`` is zero-padded or clipped to exactly ``length``
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samples.
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dtype : np.dtype
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Real numeric type for the time-domain signal. Default is 32-bit float.
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**kwargs : additional keyword arguments for Mel filter bank parameters
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fmin : float >= 0 [scalar]
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lowest frequency (in Hz)
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fmax : float >= 0 [scalar]
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highest frequency (in Hz).
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If `None`, use ``fmax = sr / 2.0``
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htk : bool [scalar]
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use HTK formula instead of Slaney
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norm : {None, 'slaney', or number} [scalar]
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If 'slaney', divide the triangular mel weights by the width of
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the mel band (area normalization).
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If numeric, use `librosa.util.normalize` to normalize each filter
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by to unit l_p norm. See `librosa.util.normalize` for a full
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description of supported norm values (including `+-np.inf`).
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Otherwise, leave all the triangles aiming for a peak value of 1.0
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Returns
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-------
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y : np.ndarray [shape(..., n,)]
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time-domain signal reconstructed from ``M``
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See Also
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--------
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librosa.griffinlim
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librosa.feature.melspectrogram
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librosa.filters.mel
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librosa.feature.inverse.mel_to_stft
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"""
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stft = mel_to_stft(M, sr=sr, n_fft=n_fft, power=power, **kwargs)
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return griffinlim(
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stft,
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n_iter=n_iter,
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hop_length=hop_length,
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win_length=win_length,
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n_fft=n_fft,
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window=window,
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center=center,
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dtype=dtype,
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length=length,
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pad_mode=pad_mode,
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)
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def mfcc_to_mel(
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mfcc: np.ndarray,
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*,
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n_mels: int = 128,
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dct_type: int = 2,
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norm: Optional[str] = "ortho",
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ref: float = 1.0,
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lifter: float = 0,
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) -> np.ndarray:
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"""Invert Mel-frequency cepstral coefficients to approximate a Mel power
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spectrogram.
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This inversion proceeds in two steps:
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1. The inverse DCT is applied to the MFCCs
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2. `librosa.db_to_power` is applied to map the dB-scaled result to a power spectrogram
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Parameters
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----------
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mfcc : np.ndarray [shape=(..., n_mfcc, n)]
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The Mel-frequency cepstral coefficients
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n_mels : int > 0
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The number of Mel frequencies
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dct_type : {1, 2, 3}
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Discrete cosine transform (DCT) type
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By default, DCT type-2 is used.
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norm : None or 'ortho'
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If ``dct_type`` is `2 or 3`, setting ``norm='ortho'`` uses an orthonormal
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DCT basis.
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Normalization is not supported for `dct_type=1`.
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ref : float
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Reference power for (inverse) decibel calculation
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lifter : number >= 0
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If ``lifter>0``, apply inverse liftering (inverse cepstral filtering)::
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M[n, :] <- M[n, :] / (1 + sin(pi * (n + 1) / lifter) * lifter / 2)
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Returns
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-------
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M : np.ndarray [shape=(..., n_mels, n)]
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An approximate Mel power spectrum recovered from ``mfcc``
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Warns
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-----
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UserWarning
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due to critical values in lifter array that invokes underflow.
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See Also
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--------
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librosa.feature.mfcc
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librosa.feature.melspectrogram
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scipy.fftpack.dct
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"""
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if lifter > 0:
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n_mfcc = mfcc.shape[-2]
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idx = np.arange(1, 1 + n_mfcc, dtype=mfcc.dtype)
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idx = expand_to(idx, ndim=mfcc.ndim, axes=-2)
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lifter_sine = 1 + lifter * 0.5 * np.sin(np.pi * idx / lifter)
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# raise a UserWarning if lifter array includes critical values
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if np.any(np.abs(lifter_sine) < np.finfo(lifter_sine.dtype).eps):
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warnings.warn(
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message="lifter array includes critical values that may invoke underflow.",
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category=UserWarning,
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stacklevel=2,
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)
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# lifter mfcc values
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mfcc = mfcc / (lifter_sine + tiny(mfcc))
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elif lifter != 0:
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raise ParameterError("MFCC to mel lifter must be a non-negative number.")
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logmel = scipy.fftpack.idct(mfcc, axis=-2, type=dct_type, norm=norm, n=n_mels)
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return db_to_power(logmel, ref=ref)
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def mfcc_to_audio(
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mfcc: np.ndarray,
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*,
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n_mels: int = 128,
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dct_type: int = 2,
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norm: Optional[str] = "ortho",
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ref: float = 1.0,
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lifter: float = 0,
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**kwargs: Any,
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) -> np.ndarray:
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"""Convert Mel-frequency cepstral coefficients to a time-domain audio signal
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This function is primarily a convenience wrapper for the following steps:
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1. Convert mfcc to Mel power spectrum (`mfcc_to_mel`)
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2. Convert Mel power spectrum to time-domain audio (`mel_to_audio`)
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Parameters
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----------
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mfcc : np.ndarray [shape=(..., n_mfcc, n)]
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The Mel-frequency cepstral coefficients
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n_mels : int > 0
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The number of Mel frequencies
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dct_type : {1, 2, 3}
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Discrete cosine transform (DCT) type
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By default, DCT type-2 is used.
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norm : None or 'ortho'
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If ``dct_type`` is `2 or 3`, setting ``norm='ortho'`` uses an orthonormal
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DCT basis.
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Normalization is not supported for ``dct_type=1``.
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ref : float
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Reference power for (inverse) decibel calculation
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lifter : number >= 0
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If ``lifter>0``, apply inverse liftering (inverse cepstral filtering)::
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M[n, :] <- M[n, :] / (1 + sin(pi * (n + 1) / lifter)) * lifter / 2
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**kwargs : additional keyword arguments to pass through to `mel_to_audio`
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M : np.ndarray [shape=(..., n_mels, n), non-negative]
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The spectrogram as produced by `feature.melspectrogram`
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sr : number > 0 [scalar]
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sampling rate of the underlying signal
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n_fft : int > 0 [scalar]
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number of FFT components in the resulting STFT
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hop_length : None or int > 0
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The hop length of the STFT. If not provided, it will default to ``n_fft // 4``
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win_length : None or int > 0
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The window length of the STFT. By default, it will equal ``n_fft``
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window : string, tuple, number, function, or np.ndarray [shape=(n_fft,)]
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A window specification as supported by `stft` or `istft`
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center : boolean
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If `True`, the STFT is assumed to use centered frames.
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If `False`, the STFT is assumed to use left-aligned frames.
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pad_mode : string
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If ``center=True``, the padding mode to use at the edges of the signal.
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By default, STFT uses zero padding.
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power : float > 0 [scalar]
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Exponent for the magnitude melspectrogram
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n_iter : int > 0
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The number of iterations for Griffin-Lim
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length : None or int > 0
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If provided, the output ``y`` is zero-padded or clipped to exactly ``length``
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samples.
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dtype : np.dtype
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Real numeric type for the time-domain signal. Default is 32-bit float.
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**kwargs : additional keyword arguments for Mel filter bank parameters
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fmin : float >= 0 [scalar]
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lowest frequency (in Hz)
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fmax : float >= 0 [scalar]
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|
highest frequency (in Hz).
|
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|
|
If `None`, use ``fmax = sr / 2.0``
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|
|
htk : bool [scalar]
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||
|
|
use HTK formula instead of Slaney
|
||
|
|
|
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|
|
Returns
|
||
|
|
-------
|
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|
|
y : np.ndarray [shape=(..., n)]
|
||
|
|
A time-domain signal reconstructed from `mfcc`
|
||
|
|
|
||
|
|
See Also
|
||
|
|
--------
|
||
|
|
mfcc_to_mel
|
||
|
|
mel_to_audio
|
||
|
|
librosa.feature.mfcc
|
||
|
|
librosa.griffinlim
|
||
|
|
scipy.fftpack.dct
|
||
|
|
"""
|
||
|
|
mel_spec = mfcc_to_mel(
|
||
|
|
mfcc, n_mels=n_mels, dct_type=dct_type, norm=norm, ref=ref, lifter=lifter
|
||
|
|
)
|
||
|
|
|
||
|
|
return mel_to_audio(mel_spec, **kwargs)
|