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