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Source code for librosa.feature.spectral
#!/usr/bin/env python
# -*- coding: utf-8 -*-
"""Spectral feature extraction"""
import numpy as np
import scipy
import scipy.signal
import scipy.fftpack
from .. import util
from .. import filters
from ..util.exceptions import ParameterError
from ..core.convert import fft_frequencies
from ..core.audio import zero_crossings, to_mono
from ..core.spectrum import power_to_db, _spectrogram
from ..core.constantq import cqt, hybrid_cqt
from ..core.pitch import estimate_tuning
__all__ = [
"spectral_centroid",
"spectral_bandwidth",
"spectral_contrast",
"spectral_rolloff",
"spectral_flatness",
"poly_features",
"rms",
"zero_crossing_rate",
"chroma_stft",
"chroma_cqt",
"chroma_cens",
"melspectrogram",
"mfcc",
"tonnetz",
]
# -- Spectral features -- #
[docs]def spectral_centroid(
y=None,
sr=22050,
S=None,
n_fft=2048,
hop_length=512,
freq=None,
win_length=None,
window="hann",
center=True,
pad_mode="reflect",
):
"""Compute the spectral centroid.
Each frame of a magnitude spectrogram is normalized and treated as a
distribution over frequency bins, from which the mean (centroid) is
extracted per frame.
More precisely, the centroid at frame ``t`` is defined as [#]_::
centroid[t] = sum_k S[k, t] * freq[k] / (sum_j S[j, t])
where ``S`` is a magnitude spectrogram, and ``freq`` is the array of
frequencies (e.g., FFT frequencies in Hz) of the rows of ``S``.
.. [#] Klapuri, A., & Davy, M. (Eds.). (2007). Signal processing
methods for music transcription, chapter 5.
Springer Science & Business Media.
Parameters
----------
y : np.ndarray [shape=(n,)] or None
audio time series
sr : number > 0 [scalar]
audio sampling rate of ``y``
S : np.ndarray [shape=(d, t)] or None
(optional) spectrogram magnitude
n_fft : int > 0 [scalar]
FFT window size
hop_length : int > 0 [scalar]
hop length for STFT. See `librosa.stft` for details.
freq : None or np.ndarray [shape=(d,) or shape=(d, t)]
Center frequencies for spectrogram bins.
If `None`, then FFT bin center frequencies are used.
Otherwise, it can be a single array of ``d`` center frequencies,
or a matrix of center frequencies as constructed by
`librosa.reassigned_spectrogram`
win_length : int <= n_fft [scalar]
Each frame of audio is windowed by `window()`.
The window will be of length ``win_length`` and then padded
with zeros to match ``n_fft``.
If unspecified, defaults to ``win_length = n_fft``.
window : string, tuple, number, function, or np.ndarray [shape=(n_fft,)]
- a window specification (string, tuple, or number);
see `scipy.signal.get_window`
- a window function, such as `scipy.signal.windows.hann`
- a vector or array of length ``n_fft``
.. see also:: `librosa.filters.get_window`
center : boolean
- If `True`, the signal ``y`` is padded so that frame
`t` is centered at ``y[t * hop_length]``.
- If `False`, then frame ``t`` begins at ``y[t * hop_length]``
pad_mode : string
If ``center=True``, the padding mode to use at the edges of the signal.
By default, STFT uses reflection padding.
Returns
-------
centroid : np.ndarray [shape=(1, t)]
centroid frequencies
See Also
--------
librosa.stft
Short-time Fourier Transform
librosa.reassigned_spectrogram
Time-frequency reassigned spectrogram
Examples
--------
From time-series input:
>>> y, sr = librosa.load(librosa.ex('trumpet'))
>>> cent = librosa.feature.spectral_centroid(y=y, sr=sr)
>>> cent
array([[1768.888, 1921.774, ..., 5663.477, 5813.683]])
From spectrogram input:
>>> S, phase = librosa.magphase(librosa.stft(y=y))
>>> librosa.feature.spectral_centroid(S=S)
array([[1768.888, 1921.774, ..., 5663.477, 5813.683]])
Using variable bin center frequencies:
>>> freqs, times, D = librosa.reassigned_spectrogram(y, fill_nan=True)
>>> librosa.feature.spectral_centroid(S=np.abs(D), freq=freqs)
array([[1768.838, 1921.801, ..., 5663.513, 5813.747]])
Plot the result
>>> import matplotlib.pyplot as plt
>>> times = librosa.times_like(cent)
>>> fig, ax = plt.subplots()
>>> librosa.display.specshow(librosa.amplitude_to_db(S, ref=np.max),
... y_axis='log', x_axis='time', ax=ax)
>>> ax.plot(times, cent.T, label='Spectral centroid', color='w')
>>> ax.legend(loc='upper right')
>>> ax.set(title='log Power spectrogram')
"""
S, n_fft = _spectrogram(
y=y,
S=S,
n_fft=n_fft,
hop_length=hop_length,
win_length=win_length,
window=window,
center=center,
pad_mode=pad_mode,
)
if not np.isrealobj(S):
raise ParameterError(
"Spectral centroid is only defined " "with real-valued input"
)
elif np.any(S < 0):
raise ParameterError(
"Spectral centroid is only defined " "with non-negative energies"
)
# Compute the center frequencies of each bin
if freq is None:
freq = fft_frequencies(sr=sr, n_fft=n_fft)
if freq.ndim == 1:
freq = freq.reshape((-1, 1))
# Column-normalize S
return np.sum(freq * util.normalize(S, norm=1, axis=0), axis=0, keepdims=True)
[docs]def spectral_bandwidth(
y=None,
sr=22050,
S=None,
n_fft=2048,
hop_length=512,
win_length=None,
window="hann",
center=True,
pad_mode="reflect",
freq=None,
centroid=None,
norm=True,
p=2,
):
"""Compute p'th-order spectral bandwidth.
The spectral bandwidth [#]_ at frame ``t`` is computed by::
(sum_k S[k, t] * (freq[k, t] - centroid[t])**p)**(1/p)
.. [#] Klapuri, A., & Davy, M. (Eds.). (2007). Signal processing
methods for music transcription, chapter 5.
Springer Science & Business Media.
Parameters
----------
y : np.ndarray [shape=(n,)] or None
audio time series
sr : number > 0 [scalar]
audio sampling rate of ``y``
S : np.ndarray [shape=(d, t)] or None
(optional) spectrogram magnitude
n_fft : int > 0 [scalar]
FFT window size
hop_length : int > 0 [scalar]
hop length for STFT. See `librosa.stft` for details.
win_length : int <= n_fft [scalar]
Each frame of audio is windowed by `window()`.
The window will be of length ``win_length`` and then padded
with zeros to match ``n_fft``.
If unspecified, defaults to ``win_length = n_fft``.
window : string, tuple, number, function, or np.ndarray [shape=(n_fft,)]
- a window specification (string, tuple, or number);
see `scipy.signal.get_window`
- a window function, such as `scipy.signal.windows.hann`
- a vector or array of length ``n_fft``
.. see also:: `librosa.filters.get_window`
center : boolean
- If `True`, the signal ``y`` is padded so that frame
``t`` is centered at ``y[t * hop_length]``.
- If ``False``, then frame ``t`` begins at ``y[t * hop_length]``
pad_mode : string
If ``center=True``, the padding mode to use at the edges of the signal.
By default, STFT uses reflection padding.
freq : None or np.ndarray [shape=(d,) or shape=(d, t)]
Center frequencies for spectrogram bins.
If `None`, then FFT bin center frequencies are used.
Otherwise, it can be a single array of ``d`` center frequencies,
or a matrix of center frequencies as constructed by
`librosa.reassigned_spectrogram`
centroid : None or np.ndarray [shape=(1, t)]
pre-computed centroid frequencies
norm : bool
Normalize per-frame spectral energy (sum to one)
p : float > 0
Power to raise deviation from spectral centroid.
Returns
-------
bandwidth : np.ndarray [shape=(1, t)]
frequency bandwidth for each frame
Examples
--------
From time-series input
>>> y, sr = librosa.load(librosa.ex('trumpet'))
>>> spec_bw = librosa.feature.spectral_bandwidth(y=y, sr=sr)
>>> spec_bw
array([[1273.836, 1228.873, ..., 2952.357, 3013.68 ]])
From spectrogram input
>>> S, phase = librosa.magphase(librosa.stft(y=y))
>>> librosa.feature.spectral_bandwidth(S=S)
array([[1273.836, 1228.873, ..., 2952.357, 3013.68 ]])
Using variable bin center frequencies
>>> freqs, times, D = librosa.reassigned_spectrogram(y, fill_nan=True)
>>> librosa.feature.spectral_bandwidth(S=np.abs(D), freq=freqs)
array([[1274.637, 1228.786, ..., 2952.4 , 3013.735]])
Plot the result
>>> import matplotlib.pyplot as plt
>>> fig, ax = plt.subplots(nrows=2, sharex=True)
>>> times = librosa.times_like(spec_bw)
>>> centroid = librosa.feature.spectral_centroid(S=S)
>>> ax[0].semilogy(times, spec_bw[0], label='Spectral bandwidth')
>>> ax[0].set(ylabel='Hz', xticks=[], xlim=[times.min(), times.max()])
>>> ax[0].legend()
>>> ax[0].label_outer()
>>> librosa.display.specshow(librosa.amplitude_to_db(S, ref=np.max),
... y_axis='log', x_axis='time', ax=ax[1])
>>> ax[1].set(title='log Power spectrogram')
>>> ax[1].fill_between(times, centroid[0] - spec_bw[0], centroid[0] + spec_bw[0],
... alpha=0.5, label='Centroid +- bandwidth')
>>> ax[1].plot(times, centroid[0], label='Spectral centroid', color='w')
>>> ax[1].legend(loc='lower right')
"""
S, n_fft = _spectrogram(
y=y,
S=S,
n_fft=n_fft,
hop_length=hop_length,
win_length=win_length,
window=window,
center=center,
pad_mode=pad_mode,
)
if not np.isrealobj(S):
raise ParameterError(
"Spectral bandwidth is only defined " "with real-valued input"
)
elif np.any(S < 0):
raise ParameterError(
"Spectral bandwidth is only defined " "with non-negative energies"
)
if centroid is None:
centroid = spectral_centroid(
y=y, sr=sr, S=S, n_fft=n_fft, hop_length=hop_length, freq=freq
)
# Compute the center frequencies of each bin
if freq is None:
freq = fft_frequencies(sr=sr, n_fft=n_fft)
if freq.ndim == 1:
deviation = np.abs(np.subtract.outer(freq, centroid[0]))
else:
deviation = np.abs(freq - centroid[0])
# Column-normalize S
if norm:
S = util.normalize(S, norm=1, axis=0)
return np.sum(S * deviation ** p, axis=0, keepdims=True) ** (1.0 / p)
[docs]def spectral_contrast(
y=None,
sr=22050,
S=None,
n_fft=2048,
hop_length=512,
win_length=None,
window="hann",
center=True,
pad_mode="reflect",
freq=None,
fmin=200.0,
n_bands=6,
quantile=0.02,
linear=False,
):
"""Compute spectral contrast
Each frame of a spectrogram ``S`` is divided into sub-bands.
For each sub-band, the energy contrast is estimated by comparing
the mean energy in the top quantile (peak energy) to that of the
bottom quantile (valley energy). High contrast values generally
correspond to clear, narrow-band signals, while low contrast values
correspond to broad-band noise. [#]_
.. [#] Jiang, Dan-Ning, Lie Lu, Hong-Jiang Zhang, Jian-Hua Tao,
and Lian-Hong Cai.
"Music type classification by spectral contrast feature."
In Multimedia and Expo, 2002. ICME'02. Proceedings.
2002 IEEE International Conference on, vol. 1, pp. 113-116.
IEEE, 2002.
Parameters
----------
y : np.ndarray [shape=(n,)] or None
audio time series
sr : number > 0 [scalar]
audio sampling rate of ``y``
S : np.ndarray [shape=(d, t)] or None
(optional) spectrogram magnitude
n_fft : int > 0 [scalar]
FFT window size
hop_length : int > 0 [scalar]
hop length for STFT. See `librosa.stft` for details.
win_length : int <= n_fft [scalar]
Each frame of audio is windowed by `window()`.
The window will be of length `win_length` and then padded
with zeros to match ``n_fft``.
If unspecified, defaults to ``win_length = n_fft``.
window : string, tuple, number, function, or np.ndarray [shape=(n_fft,)]
- a window specification (string, tuple, or number);
see `scipy.signal.get_window`
- a window function, such as `scipy.signal.windows.hann`
- a vector or array of length ``n_fft``
.. see also:: `librosa.filters.get_window`
center : boolean
- If `True`, the signal ``y`` is padded so that frame
``t`` is centered at ``y[t * hop_length]``.
- If `False`, then frame ``t`` begins at ``y[t * hop_length]``
pad_mode : string
If ``center=True``, the padding mode to use at the edges of the signal.
By default, STFT uses reflection padding.
freq : None or np.ndarray [shape=(d,)]
Center frequencies for spectrogram bins.
If `None`, then FFT bin center frequencies are used.
Otherwise, it can be a single array of ``d`` center frequencies.
fmin : float > 0
Frequency cutoff for the first bin ``[0, fmin]``
Subsequent bins will cover ``[fmin, 2*fmin]`, `[2*fmin, 4*fmin]``, etc.
n_bands : int > 1
number of frequency bands
quantile : float in (0, 1)
quantile for determining peaks and valleys
linear : bool
If `True`, return the linear difference of magnitudes:
``peaks - valleys``.
If `False`, return the logarithmic difference:
``log(peaks) - log(valleys)``.
Returns
-------
contrast : np.ndarray [shape=(n_bands + 1, t)]
each row of spectral contrast values corresponds to a given
octave-based frequency
Examples
--------
>>> y, sr = librosa.load(librosa.ex('trumpet'))
>>> S = np.abs(librosa.stft(y))
>>> contrast = librosa.feature.spectral_contrast(S=S, sr=sr)
>>> import matplotlib.pyplot as plt
>>> fig, ax = plt.subplots(nrows=2, sharex=True)
>>> img1 = librosa.display.specshow(librosa.amplitude_to_db(S,
... ref=np.max),
... y_axis='log', x_axis='time', ax=ax[0])
>>> fig.colorbar(img1, ax=[ax[0]], format='%+2.0f dB')
>>> ax[0].set(title='Power spectrogram')
>>> ax[0].label_outer()
>>> img2 = librosa.display.specshow(contrast, x_axis='time', ax=ax[1])
>>> fig.colorbar(img2, ax=[ax[1]])
>>> ax[1].set(ylabel='Frequency bands', title='Spectral contrast')
"""
S, n_fft = _spectrogram(
y=y,
S=S,
n_fft=n_fft,
hop_length=hop_length,
win_length=win_length,
window=window,
center=center,
pad_mode=pad_mode,
)
# Compute the center frequencies of each bin
if freq is None:
freq = fft_frequencies(sr=sr, n_fft=n_fft)
freq = np.atleast_1d(freq)
if freq.ndim != 1 or len(freq) != S.shape[0]:
raise ParameterError(
"freq.shape mismatch: expected " "({:d},)".format(S.shape[0])
)
if n_bands < 1 or not isinstance(n_bands, (int, np.integer)):
raise ParameterError("n_bands must be a positive integer")
if not 0.0 < quantile < 1.0:
raise ParameterError("quantile must lie in the range (0, 1)")
if fmin <= 0:
raise ParameterError("fmin must be a positive number")
octa = np.zeros(n_bands + 2)
octa[1:] = fmin * (2.0 ** np.arange(0, n_bands + 1))
if np.any(octa[:-1] >= 0.5 * sr):
raise ParameterError(
"Frequency band exceeds Nyquist. " "Reduce either fmin or n_bands."
)
valley = np.zeros((n_bands + 1, S.shape[1]))
peak = np.zeros_like(valley)
for k, (f_low, f_high) in enumerate(zip(octa[:-1], octa[1:])):
current_band = np.logical_and(freq >= f_low, freq <= f_high)
idx = np.flatnonzero(current_band)
if k > 0:
current_band[idx[0] - 1] = True
if k == n_bands:
current_band[idx[-1] + 1 :] = True
sub_band = S[current_band]
if k < n_bands:
sub_band = sub_band[:-1]
# Always take at least one bin from each side
idx = np.rint(quantile * np.sum(current_band))
idx = int(np.maximum(idx, 1))
sortedr = np.sort(sub_band, axis=0)
valley[k] = np.mean(sortedr[:idx], axis=0)
peak[k] = np.mean(sortedr[-idx:], axis=0)
if linear:
return peak - valley
else:
return power_to_db(peak) - power_to_db(valley)
[docs]def spectral_rolloff(
y=None,
sr=22050,
S=None,
n_fft=2048,
hop_length=512,
win_length=None,
window="hann",
center=True,
pad_mode="reflect",
freq=None,
roll_percent=0.85,
):
"""Compute roll-off frequency.
The roll-off frequency is defined for each frame as the center frequency
for a spectrogram bin such that at least roll_percent (0.85 by default)
of the energy of the spectrum in this frame is contained in this bin and
the bins below. This can be used to, e.g., approximate the maximum (or
minimum) frequency by setting roll_percent to a value close to 1 (or 0).
Parameters
----------
y : np.ndarray [shape=(n,)] or None
audio time series
sr : number > 0 [scalar]
audio sampling rate of ``y``
S : np.ndarray [shape=(d, t)] or None
(optional) spectrogram magnitude
n_fft : int > 0 [scalar]
FFT window size
hop_length : int > 0 [scalar]
hop length for STFT. See `librosa.stft` for details.
win_length : int <= n_fft [scalar]
Each frame of audio is windowed by `window()`.
The window will be of length `win_length` and then padded
with zeros to match ``n_fft``.
If unspecified, defaults to ``win_length = n_fft``.
window : string, tuple, number, function, or np.ndarray [shape=(n_fft,)]
- a window specification (string, tuple, or number);
see `scipy.signal.get_window`
- a window function, such as `scipy.signal.windows.hann`
- a vector or array of length ``n_fft``
.. see also:: `librosa.filters.get_window`
center : boolean
- If `True`, the signal ``y`` is padded so that frame
``t`` is centered at ``y[t * hop_length]``.
- If `False`, then frame ``t`` begins at ``y[t * hop_length]``
pad_mode : string
If ``center=True``, the padding mode to use at the edges of the signal.
By default, STFT uses reflection padding.
freq : None or np.ndarray [shape=(d,) or shape=(d, t)]
Center frequencies for spectrogram bins.
If `None`, then FFT bin center frequencies are used.
Otherwise, it can be a single array of ``d`` center frequencies,
.. note:: ``freq`` is assumed to be sorted in increasing order
roll_percent : float [0 < roll_percent < 1]
Roll-off percentage.
Returns
-------
rolloff : np.ndarray [shape=(1, t)]
roll-off frequency for each frame
Examples
--------
From time-series input
>>> y, sr = librosa.load(librosa.ex('trumpet'))
>>> # Approximate maximum frequencies with roll_percent=0.85 (default)
>>> librosa.feature.spectral_rolloff(y=y, sr=sr)
array([[2583.984, 3036.182, ..., 9173.145, 9248.511]])
>>> # Approximate maximum frequencies with roll_percent=0.99
>>> rolloff = librosa.feature.spectral_rolloff(y=y, sr=sr, roll_percent=0.99)
>>> rolloff
array([[ 7192.09 , 6739.893, ..., 10960.4 , 10992.7 ]])
>>> # Approximate minimum frequencies with roll_percent=0.01
>>> rolloff_min = librosa.feature.spectral_rolloff(y=y, sr=sr, roll_percent=0.01)
>>> rolloff_min
array([[516.797, 538.33 , ..., 764.429, 764.429]])
From spectrogram input
>>> S, phase = librosa.magphase(librosa.stft(y))
>>> librosa.feature.spectral_rolloff(S=S, sr=sr)
array([[2583.984, 3036.182, ..., 9173.145, 9248.511]])
>>> # With a higher roll percentage:
>>> librosa.feature.spectral_rolloff(y=y, sr=sr, roll_percent=0.95)
array([[ 3919.043, 3994.409, ..., 10443.604, 10594.336]])
>>> import matplotlib.pyplot as plt
>>> fig, ax = plt.subplots()
>>> librosa.display.specshow(librosa.amplitude_to_db(S, ref=np.max),
... y_axis='log', x_axis='time', ax=ax)
>>> ax.plot(librosa.times_like(rolloff), rolloff[0], label='Roll-off frequency (0.99)')
>>> ax.plot(librosa.times_like(rolloff), rolloff_min[0], color='w',
... label='Roll-off frequency (0.01)')
>>> ax.legend(loc='lower right')
>>> ax.set(title='log Power spectrogram')
"""
if not 0.0 < roll_percent < 1.0:
raise ParameterError("roll_percent must lie in the range (0, 1)")
S, n_fft = _spectrogram(
y=y,
S=S,
n_fft=n_fft,
hop_length=hop_length,
win_length=win_length,
window=window,
center=center,
pad_mode=pad_mode,
)
if not np.isrealobj(S):
raise ParameterError(
"Spectral rolloff is only defined " "with real-valued input"
)
elif np.any(S < 0):
raise ParameterError(
"Spectral rolloff is only defined " "with non-negative energies"
)
# Compute the center frequencies of each bin
if freq is None:
freq = fft_frequencies(sr=sr, n_fft=n_fft)
# Make sure that frequency can be broadcast
if freq.ndim == 1:
freq = freq.reshape((-1, 1))
total_energy = np.cumsum(S, axis=0)
threshold = roll_percent * total_energy[-1]
ind = np.where(total_energy < threshold, np.nan, 1)
return np.nanmin(ind * freq, axis=0, keepdims=True)
[docs]def spectral_flatness(
y=None,
S=None,
n_fft=2048,
hop_length=512,
win_length=None,
window="hann",
center=True,
pad_mode="reflect",
amin=1e-10,
power=2.0,
):
"""Compute spectral flatness
Spectral flatness (or tonality coefficient) is a measure to
quantify how much noise-like a sound is, as opposed to being
tone-like [#]_. A high spectral flatness (closer to 1.0)
indicates the spectrum is similar to white noise.
It is often converted to decibel.
.. [#] Dubnov, Shlomo "Generalization of spectral flatness
measure for non-gaussian linear processes"
IEEE Signal Processing Letters, 2004, Vol. 11.
Parameters
----------
y : np.ndarray [shape=(n,)] or None
audio time series
S : np.ndarray [shape=(d, t)] or None
(optional) pre-computed spectrogram magnitude
n_fft : int > 0 [scalar]
FFT window size
hop_length : int > 0 [scalar]
hop length for STFT. See `librosa.stft` for details.
win_length : int <= n_fft [scalar]
Each frame of audio is windowed by `window()`.
The window will be of length `win_length` and then padded
with zeros to match ``n_fft``.
If unspecified, defaults to ``win_length = n_fft``.
window : string, tuple, number, function, or np.ndarray [shape=(n_fft,)]
- a window specification (string, tuple, or number);
see `scipy.signal.get_window`
- a window function, such as `scipy.signal.windows.hann`
- a vector or array of length ``n_fft``
.. see also:: `librosa.filters.get_window`
center : boolean
- If `True`, the signal ``y`` is padded so that frame
``t`` is centered at ``y[t * hop_length]``.
- If `False`, then frame `t` begins at ``y[t * hop_length]``
pad_mode : string
If ``center=True``, the padding mode to use at the edges of the signal.
By default, STFT uses reflection padding.
amin : float > 0 [scalar]
minimum threshold for ``S`` (=added noise floor for numerical stability)
power : float > 0 [scalar]
Exponent for the magnitude spectrogram.
e.g., 1 for energy, 2 for power, etc.
Power spectrogram is usually used for computing spectral flatness.
Returns
-------
flatness : np.ndarray [shape=(1, t)]
spectral flatness for each frame.
The returned value is in [0, 1] and often converted to dB scale.
Examples
--------
From time-series input
>>> y, sr = librosa.load(librosa.ex('trumpet'))
>>> flatness = librosa.feature.spectral_flatness(y=y)
>>> flatness
array([[0.001, 0. , ..., 0.218, 0.184]], dtype=float32)
From spectrogram input
>>> S, phase = librosa.magphase(librosa.stft(y))
>>> librosa.feature.spectral_flatness(S=S)
array([[0.001, 0. , ..., 0.218, 0.184]], dtype=float32)
From power spectrogram input
>>> S, phase = librosa.magphase(librosa.stft(y))
>>> S_power = S ** 2
>>> librosa.feature.spectral_flatness(S=S_power, power=1.0)
array([[0.001, 0. , ..., 0.218, 0.184]], dtype=float32)
"""
if amin <= 0:
raise ParameterError("amin must be strictly positive")
S, n_fft = _spectrogram(
y=y,
S=S,
n_fft=n_fft,
hop_length=hop_length,
power=1.0,
win_length=win_length,
window=window,
center=center,
pad_mode=pad_mode,
)
if not np.isrealobj(S):
raise ParameterError(
"Spectral flatness is only defined " "with real-valued input"
)
elif np.any(S < 0):
raise ParameterError(
"Spectral flatness is only defined " "with non-negative energies"
)
S_thresh = np.maximum(amin, S ** power)
gmean = np.exp(np.mean(np.log(S_thresh), axis=0, keepdims=True))
amean = np.mean(S_thresh, axis=0, keepdims=True)
return gmean / amean
[docs]def rms(
y=None, S=None, frame_length=2048, hop_length=512, center=True, pad_mode="reflect"
):
"""Compute root-mean-square (RMS) value for each frame, either from the
audio samples ``y`` or from a spectrogram ``S``.
Computing the RMS value from audio samples is faster as it doesn't require
a STFT calculation. However, using a spectrogram will give a more accurate
representation of energy over time because its frames can be windowed,
thus prefer using ``S`` if it's already available.
Parameters
----------
y : np.ndarray [shape=(n,)] or None
(optional) audio time series. Required if ``S`` is not input.
S : np.ndarray [shape=(d, t)] or None
(optional) spectrogram magnitude. Required if ``y`` is not input.
frame_length : int > 0 [scalar]
length of analysis frame (in samples) for energy calculation
hop_length : int > 0 [scalar]
hop length for STFT. See `librosa.stft` for details.
center : bool
If `True` and operating on time-domain input (``y``), pad the signal
by ``frame_length//2`` on either side.
If operating on spectrogram input, this has no effect.
pad_mode : str
Padding mode for centered analysis. See `numpy.pad` for valid
values.
Returns
-------
rms : np.ndarray [shape=(1, t)]
RMS value for each frame
Examples
--------
>>> y, sr = librosa.load(librosa.ex('trumpet'))
>>> librosa.feature.rms(y=y)
array([[1.248e-01, 1.259e-01, ..., 1.845e-05, 1.796e-05]],
dtype=float32)
Or from spectrogram input
>>> S, phase = librosa.magphase(librosa.stft(y))
>>> rms = librosa.feature.rms(S=S)
>>> import matplotlib.pyplot as plt
>>> fig, ax = plt.subplots(nrows=2, sharex=True)
>>> times = librosa.times_like(rms)
>>> ax[0].semilogy(times, rms[0], label='RMS Energy')
>>> ax[0].set(xticks=[])
>>> ax[0].legend()
>>> ax[0].label_outer()
>>> librosa.display.specshow(librosa.amplitude_to_db(S, ref=np.max),
... y_axis='log', x_axis='time', ax=ax[1])
>>> ax[1].set(title='log Power spectrogram')
Use a STFT window of constant ones and no frame centering to get consistent
results with the RMS computed from the audio samples ``y``
>>> S = librosa.magphase(librosa.stft(y, window=np.ones, center=False))[0]
>>> librosa.feature.rms(S=S)
>>> plt.show()
"""
if y is not None:
y = to_mono(y)
if center:
y = np.pad(y, int(frame_length // 2), mode=pad_mode)
x = util.frame(y, frame_length=frame_length, hop_length=hop_length)
# Calculate power
power = np.mean(np.abs(x) ** 2, axis=0, keepdims=True)
elif S is not None:
# Check the frame length
if S.shape[0] != frame_length // 2 + 1:
raise ParameterError(
"Since S.shape[0] is {}, "
"frame_length is expected to be {} or {}; "
"found {}".format(
S.shape[0], S.shape[0] * 2 - 2, S.shape[0] * 2 - 1, frame_length
)
)
# power spectrogram
x = np.abs(S) ** 2
# Adjust the DC and sr/2 component
x[0] *= 0.5
if frame_length % 2 == 0:
x[-1] *= 0.5
# Calculate power
power = 2 * np.sum(x, axis=0, keepdims=True) / frame_length ** 2
else:
raise ParameterError("Either `y` or `S` must be input.")
return np.sqrt(power)
[docs]def poly_features(
y=None,
sr=22050,
S=None,
n_fft=2048,
hop_length=512,
win_length=None,
window="hann",
center=True,
pad_mode="reflect",
order=1,
freq=None,
):
"""Get coefficients of fitting an nth-order polynomial to the columns
of a spectrogram.
Parameters
----------
y : np.ndarray [shape=(n,)] or None
audio time series
sr : number > 0 [scalar]
audio sampling rate of ``y``
S : np.ndarray [shape=(d, t)] or None
(optional) spectrogram magnitude
n_fft : int > 0 [scalar]
FFT window size
hop_length : int > 0 [scalar]
hop length for STFT. See `librosa.stft` for details.
win_length : int <= n_fft [scalar]
Each frame of audio is windowed by `window()`.
The window will be of length `win_length` and then padded
with zeros to match ``n_fft``.
If unspecified, defaults to ``win_length = n_fft``.
window : string, tuple, number, function, or np.ndarray [shape=(n_fft,)]
- a window specification (string, tuple, or number);
see `scipy.signal.get_window`
- a window function, such as `scipy.signal.windows.hann`
- a vector or array of length ``n_fft``
.. see also:: `librosa.filters.get_window`
center : boolean
- If `True`, the signal ``y`` is padded so that frame
`t` is centered at ``y[t * hop_length]``.
- If `False`, then frame ``t`` begins at ``y[t * hop_length]``
pad_mode : string
If ``center=True``, the padding mode to use at the edges of the signal.
By default, STFT uses reflection padding.
order : int > 0
order of the polynomial to fit
freq : None or np.ndarray [shape=(d,) or shape=(d, t)]
Center frequencies for spectrogram bins.
If `None`, then FFT bin center frequencies are used.
Otherwise, it can be a single array of ``d`` center frequencies,
or a matrix of center frequencies as constructed by
`librosa.reassigned_spectrogram`
Returns
-------
coefficients : np.ndarray [shape=(order+1, t)]
polynomial coefficients for each frame.
``coeffecients[0]`` corresponds to the highest degree (``order``),
``coefficients[1]`` corresponds to the next highest degree (``order-1``),
down to the constant term ``coefficients[order]``.
Examples
--------
>>> y, sr = librosa.load(librosa.ex('trumpet'))
>>> S = np.abs(librosa.stft(y))
Fit a degree-0 polynomial (constant) to each frame
>>> p0 = librosa.feature.poly_features(S=S, order=0)
Fit a linear polynomial to each frame
>>> p1 = librosa.feature.poly_features(S=S, order=1)
Fit a quadratic to each frame
>>> p2 = librosa.feature.poly_features(S=S, order=2)
Plot the results for comparison
>>> import matplotlib.pyplot as plt
>>> fig, ax = plt.subplots(nrows=4, sharex=True, figsize=(8, 8))
>>> times = librosa.times_like(p0)
>>> ax[0].plot(times, p0[0], label='order=0', alpha=0.8)
>>> ax[0].plot(times, p1[1], label='order=1', alpha=0.8)
>>> ax[0].plot(times, p2[2], label='order=2', alpha=0.8)
>>> ax[0].legend()
>>> ax[0].label_outer()
>>> ax[0].set(ylabel='Constant term ')
>>> ax[1].plot(times, p1[0], label='order=1', alpha=0.8)
>>> ax[1].plot(times, p2[1], label='order=2', alpha=0.8)
>>> ax[1].set(ylabel='Linear term')
>>> ax[1].label_outer()
>>> ax[1].legend()
>>> ax[2].plot(times, p2[0], label='order=2', alpha=0.8)
>>> ax[2].set(ylabel='Quadratic term')
>>> ax[2].legend()
>>> librosa.display.specshow(librosa.amplitude_to_db(S, ref=np.max),
... y_axis='log', x_axis='time', ax=ax[3])
"""
S, n_fft = _spectrogram(
y=y,
S=S,
n_fft=n_fft,
hop_length=hop_length,
win_length=win_length,
window=window,
center=center,
pad_mode=pad_mode,
)
# Compute the center frequencies of each bin
if freq is None:
freq = fft_frequencies(sr=sr, n_fft=n_fft)
# If frequencies are constant over frames, then we only need to fit once
if freq.ndim == 1:
coefficients = np.polyfit(freq, S, order)
else:
# Else, fit each frame independently and stack the results
coefficients = np.concatenate(
[[np.polyfit(freq[:, i], S[:, i], order)] for i in range(S.shape[1])],
axis=0,
).T
return coefficients
[docs]def zero_crossing_rate(y, frame_length=2048, hop_length=512, center=True, **kwargs):
"""Compute the zero-crossing rate of an audio time series.
Parameters
----------
y : np.ndarray [shape=(n,)]
Audio time series
frame_length : int > 0
Length of the frame over which to compute zero crossing rates
hop_length : int > 0
Number of samples to advance for each frame
center : bool
If `True`, frames are centered by padding the edges of ``y``.
This is similar to the padding in `librosa.stft`,
but uses edge-value copies instead of reflection.
kwargs : additional keyword arguments
See `librosa.zero_crossings`
.. note:: By default, the ``pad`` parameter is set to `False`, which
differs from the default specified by
`librosa.zero_crossings`.
Returns
-------
zcr : np.ndarray [shape=(1, t)]
``zcr[0, i]`` is the fraction of zero crossings in frame ``i``
See Also
--------
librosa.zero_crossings
Compute zero-crossings in a time-series
Examples
--------
>>> y, sr = librosa.load(librosa.ex('trumpet'))
>>> librosa.feature.zero_crossing_rate(y)
array([[0.044, 0.074, ..., 0.488, 0.355]])
"""
util.valid_audio(y)
if center:
y = np.pad(y, int(frame_length // 2), mode="edge")
y_framed = util.frame(y, frame_length, hop_length)
kwargs["axis"] = 0
kwargs.setdefault("pad", False)
crossings = zero_crossings(y_framed, **kwargs)
return np.mean(crossings, axis=0, keepdims=True)
# -- Chroma --#
[docs]def chroma_stft(
y=None,
sr=22050,
S=None,
norm=np.inf,
n_fft=2048,
hop_length=512,
win_length=None,
window="hann",
center=True,
pad_mode="reflect",
tuning=None,
n_chroma=12,
**kwargs,
):
"""Compute a chromagram from a waveform or power spectrogram.
This implementation is derived from ``chromagram_E`` [#]_
.. [#] Ellis, Daniel P.W. "Chroma feature analysis and synthesis"
2007/04/21
http://labrosa.ee.columbia.edu/matlab/chroma-ansyn/
Parameters
----------
y : np.ndarray [shape=(n,)] or None
audio time series
sr : number > 0 [scalar]
sampling rate of ``y``
S : np.ndarray [shape=(d, t)] or None
power spectrogram
norm : float or None
Column-wise normalization.
See `librosa.util.normalize` for details.
If `None`, no normalization is performed.
n_fft : int > 0 [scalar]
FFT window size if provided ``y, sr`` instead of ``S``
hop_length : int > 0 [scalar]
hop length if provided ``y, sr`` instead of ``S``
win_length : int <= n_fft [scalar]
Each frame of audio is windowed by `window()`.
The window will be of length `win_length` and then padded
with zeros to match ``n_fft``.
If unspecified, defaults to ``win_length = n_fft``.
window : string, tuple, number, function, or np.ndarray [shape=(n_fft,)]
- a window specification (string, tuple, or number);
see `scipy.signal.get_window`
- a window function, such as `scipy.signal.windows.hann`
- a vector or array of length ``n_fft``
.. see also:: `librosa.filters.get_window`
center : boolean
- If `True`, the signal ``y`` is padded so that frame
``t`` is centered at ``y[t * hop_length]``.
- If `False`, then frame ``t`` begins at ``y[t * hop_length]``
pad_mode : string
If ``center=True``, the padding mode to use at the edges of the signal.
By default, STFT uses reflection padding.
tuning : float [scalar] or None.
Deviation from A440 tuning in fractional chroma bins.
If `None`, it is automatically estimated.
n_chroma : int > 0 [scalar]
Number of chroma bins to produce (12 by default).
kwargs : additional keyword arguments
Arguments to parameterize chroma filters.
See `librosa.filters.chroma` for details.
Returns
-------
chromagram : np.ndarray [shape=(n_chroma, t)]
Normalized energy for each chroma bin at each frame.
See Also
--------
librosa.filters.chroma
Chroma filter bank construction
librosa.util.normalize
Vector normalization
Examples
--------
>>> y, sr = librosa.load(librosa.ex('nutcracker'), duration=15)
>>> librosa.feature.chroma_stft(y=y, sr=sr)
array([[1. , 0.962, ..., 0.143, 0.278],
[0.688, 0.745, ..., 0.103, 0.162],
...,
[0.468, 0.598, ..., 0.18 , 0.342],
[0.681, 0.702, ..., 0.553, 1. ]], dtype=float32)
Use an energy (magnitude) spectrum instead of power spectrogram
>>> S = np.abs(librosa.stft(y))
>>> chroma = librosa.feature.chroma_stft(S=S, sr=sr)
>>> chroma
array([[1. , 0.973, ..., 0.527, 0.569],
[0.774, 0.81 , ..., 0.518, 0.506],
...,
[0.624, 0.73 , ..., 0.611, 0.644],
[0.766, 0.822, ..., 0.92 , 1. ]], dtype=float32)
Use a pre-computed power spectrogram with a larger frame
>>> S = np.abs(librosa.stft(y, n_fft=4096))**2
>>> chroma = librosa.feature.chroma_stft(S=S, sr=sr)
>>> chroma
array([[0.994, 0.873, ..., 0.169, 0.227],
[0.735, 0.64 , ..., 0.141, 0.135],
...,
[0.6 , 0.937, ..., 0.214, 0.257],
[0.743, 0.937, ..., 0.684, 0.815]], dtype=float32)
>>> import matplotlib.pyplot as plt
>>> fig, ax = plt.subplots()
>>> img = librosa.display.specshow(chroma, y_axis='chroma', x_axis='time', ax=ax)
>>> fig.colorbar(img, ax=ax)
>>> ax.set(title='Chromagram')
"""
S, n_fft = _spectrogram(
y=y,
S=S,
n_fft=n_fft,
hop_length=hop_length,
power=2,
win_length=win_length,
window=window,
center=center,
pad_mode=pad_mode,
)
if tuning is None:
tuning = estimate_tuning(S=S, sr=sr, bins_per_octave=n_chroma)
# Get the filter bank
chromafb = filters.chroma(sr, n_fft, tuning=tuning, n_chroma=n_chroma, **kwargs)
# Compute raw chroma
raw_chroma = np.dot(chromafb, S)
# Compute normalization factor for each frame
return util.normalize(raw_chroma, norm=norm, axis=0)
[docs]def chroma_cqt(
y=None,
sr=22050,
C=None,
hop_length=512,
fmin=None,
norm=np.inf,
threshold=0.0,
tuning=None,
n_chroma=12,
n_octaves=7,
window=None,
bins_per_octave=36,
cqt_mode="full",
):
r"""Constant-Q chromagram
Parameters
----------
y : np.ndarray [shape=(n,)]
audio time series
sr : number > 0
sampling rate of ``y``
C : np.ndarray [shape=(d, t)] [Optional]
a pre-computed constant-Q spectrogram
hop_length : int > 0
number of samples between successive chroma frames
fmin : float > 0
minimum frequency to analyze in the CQT.
Default: `C1 ~= 32.7 Hz`
norm : int > 0, +-np.inf, or None
Column-wise normalization of the chromagram.
threshold : float
Pre-normalization energy threshold. Values below the
threshold are discarded, resulting in a sparse chromagram.
tuning : float
Deviation (in fractions of a CQT bin) from A440 tuning
n_chroma : int > 0
Number of chroma bins to produce
n_octaves : int > 0
Number of octaves to analyze above ``fmin``
window : None or np.ndarray
Optional window parameter to `filters.cq_to_chroma`
bins_per_octave : int > 0, optional
Number of bins per octave in the CQT.
Must be an integer multiple of ``n_chroma``.
Default: 36 (3 bins per semitone)
If `None`, it will match ``n_chroma``.
cqt_mode : ['full', 'hybrid']
Constant-Q transform mode
Returns
-------
chromagram : np.ndarray [shape=(n_chroma, t)]
The output chromagram
See Also
--------
librosa.util.normalize
librosa.cqt
librosa.hybrid_cqt
chroma_stft
Examples
--------
Compare a long-window STFT chromagram to the CQT chromagram
>>> y, sr = librosa.load(librosa.ex('nutcracker'), duration=15)
>>> chroma_stft = librosa.feature.chroma_stft(y=y, sr=sr,
... n_chroma=12, n_fft=4096)
>>> chroma_cq = librosa.feature.chroma_cqt(y=y, sr=sr)
>>> import matplotlib.pyplot as plt
>>> fig, ax = plt.subplots(nrows=2, sharex=True, sharey=True)
>>> librosa.display.specshow(chroma_stft, y_axis='chroma', x_axis='time', ax=ax[0])
>>> ax[0].set(title='chroma_stft')
>>> ax[0].label_outer()
>>> img = librosa.display.specshow(chroma_cq, y_axis='chroma', x_axis='time', ax=ax[1])
>>> ax[1].set(title='chroma_cqt')
>>> fig.colorbar(img, ax=ax)
"""
cqt_func = {"full": cqt, "hybrid": hybrid_cqt}
if bins_per_octave is None:
bins_per_octave = n_chroma
elif np.remainder(bins_per_octave, n_chroma) != 0:
raise ParameterError(
"bins_per_octave={} must be an integer "
"multiple of n_chroma={}".format(bins_per_octave, n_chroma)
)
# Build the CQT if we don't have one already
if C is None:
C = np.abs(
cqt_func[cqt_mode](
y,
sr=sr,
hop_length=hop_length,
fmin=fmin,
n_bins=n_octaves * bins_per_octave,
bins_per_octave=bins_per_octave,
tuning=tuning,
)
)
# Map to chroma
cq_to_chr = filters.cq_to_chroma(
C.shape[0],
bins_per_octave=bins_per_octave,
n_chroma=n_chroma,
fmin=fmin,
window=window,
)
chroma = cq_to_chr.dot(C)
if threshold is not None:
chroma[chroma < threshold] = 0.0
# Normalize
if norm is not None:
chroma = util.normalize(chroma, norm=norm, axis=0)
return chroma
[docs]def chroma_cens(
y=None,
sr=22050,
C=None,
hop_length=512,
fmin=None,
tuning=None,
n_chroma=12,
n_octaves=7,
bins_per_octave=36,
cqt_mode="full",
window=None,
norm=2,
win_len_smooth=41,
smoothing_window="hann",
):
r"""Computes the chroma variant "Chroma Energy Normalized" (CENS)
To compute CENS features, following steps are taken after obtaining chroma vectors
using `chroma_cqt`: [#]_.
1. L-1 normalization of each chroma vector
2. Quantization of amplitude based on "log-like" amplitude thresholds
3. (optional) Smoothing with sliding window. Default window length = 41 frames
4. (not implemented) Downsampling
CENS features are robust to dynamics, timbre and articulation, thus these are commonly used in audio
matching and retrieval applications.
.. [#] Meinard Müller and Sebastian Ewert
"Chroma Toolbox: MATLAB implementations for extracting variants of chroma-based audio features"
In Proceedings of the International Conference on Music Information Retrieval (ISMIR), 2011.
Parameters
----------
y : np.ndarray [shape=(n,)]
audio time series
sr : number > 0
sampling rate of ``y``
C : np.ndarray [shape=(d, t)] [Optional]
a pre-computed constant-Q spectrogram
hop_length : int > 0
number of samples between successive chroma frames
fmin : float > 0
minimum frequency to analyze in the CQT.
Default: `C1 ~= 32.7 Hz`
norm : int > 0, +-np.inf, or None
Column-wise normalization of the chromagram.
tuning : float
Deviation (in fractions of a CQT bin) from A440 tuning
n_chroma : int > 0
Number of chroma bins to produce
n_octaves : int > 0
Number of octaves to analyze above ``fmin``
window : None or np.ndarray
Optional window parameter to `filters.cq_to_chroma`
bins_per_octave : int > 0
Number of bins per octave in the CQT.
Default: 36
cqt_mode : ['full', 'hybrid']
Constant-Q transform mode
win_len_smooth : int > 0 or None
Length of temporal smoothing window. `None` disables temporal smoothing.
Default: 41
smoothing_window : str, float or tuple
Type of window function for temporal smoothing. See `librosa.filters.get_window` for possible inputs.
Default: 'hann'
Returns
-------
cens : np.ndarray [shape=(n_chroma, t)]
The output cens-chromagram
See Also
--------
chroma_cqt
Compute a chromagram from a constant-Q transform.
chroma_stft
Compute a chromagram from an STFT spectrogram or waveform.
librosa.filters.get_window
Compute a window function.
Examples
--------
Compare standard cqt chroma to CENS.
>>> y, sr = librosa.load(librosa.ex('nutcracker'), duration=15)
>>> chroma_cens = librosa.feature.chroma_cens(y=y, sr=sr)
>>> chroma_cq = librosa.feature.chroma_cqt(y=y, sr=sr)
>>> import matplotlib.pyplot as plt
>>> fig, ax = plt.subplots(nrows=2, sharex=True, sharey=True)
>>> img = librosa.display.specshow(chroma_cq, y_axis='chroma', x_axis='time', ax=ax[0])
>>> ax[0].set(title='chroma_cq')
>>> ax[0].label_outer()
>>> librosa.display.specshow(chroma_cens, y_axis='chroma', x_axis='time', ax=ax[1])
>>> ax[1].set(title='chroma_cens')
>>> fig.colorbar(img, ax=ax)
"""
if not (
(win_len_smooth is None)
or (isinstance(win_len_smooth, (int, np.integer)) and win_len_smooth > 0)
):
raise ParameterError(
"win_len_smooth={} must be a positive integer or None".format(
win_len_smooth
)
)
chroma = chroma_cqt(
y=y,
C=C,
sr=sr,
hop_length=hop_length,
fmin=fmin,
bins_per_octave=bins_per_octave,
tuning=tuning,
norm=None,
n_chroma=n_chroma,
n_octaves=n_octaves,
cqt_mode=cqt_mode,
window=window,
)
# L1-Normalization
chroma = util.normalize(chroma, norm=1, axis=0)
# Quantize amplitudes
QUANT_STEPS = [0.4, 0.2, 0.1, 0.05]
QUANT_WEIGHTS = [0.25, 0.25, 0.25, 0.25]
chroma_quant = np.zeros_like(chroma)
for cur_quant_step_idx, cur_quant_step in enumerate(QUANT_STEPS):
chroma_quant += (chroma > cur_quant_step) * QUANT_WEIGHTS[cur_quant_step_idx]
if win_len_smooth:
# Apply temporal smoothing
win = filters.get_window(smoothing_window, win_len_smooth + 2, fftbins=False)
win /= np.sum(win)
win = np.atleast_2d(win)
cens = scipy.signal.convolve2d(chroma_quant, win, mode="same", boundary="fill")
else:
cens = chroma_quant
# L2-Normalization
return util.normalize(cens, norm=norm, axis=0)
[docs]def tonnetz(y=None, sr=22050, chroma=None, **kwargs):
"""Computes the tonal centroid features (tonnetz)
This representation uses the method of [#]_ to project chroma features
onto a 6-dimensional basis representing the perfect fifth, minor third,
and major third each as two-dimensional coordinates.
.. [#] Harte, C., Sandler, M., & Gasser, M. (2006). "Detecting Harmonic
Change in Musical Audio." In Proceedings of the 1st ACM Workshop
on Audio and Music Computing Multimedia (pp. 21-26).
Santa Barbara, CA, USA: ACM Press. doi:10.1145/1178723.1178727.
Parameters
----------
y : np.ndarray [shape=(n,)] or None
Audio time series.
sr : number > 0 [scalar]
sampling rate of ``y``
chroma : np.ndarray [shape=(n_chroma, t)] or None
Normalized energy for each chroma bin at each frame.
If `None`, a cqt chromagram is performed.
kwargs
Additional keyword arguments to `chroma_cqt`, if ``chroma`` is not
pre-computed.
Returns
-------
tonnetz : np.ndarray [shape(6, t)]
Tonal centroid features for each frame.
Tonnetz dimensions:
- 0: Fifth x-axis
- 1: Fifth y-axis
- 2: Minor x-axis
- 3: Minor y-axis
- 4: Major x-axis
- 5: Major y-axis
See Also
--------
chroma_cqt
Compute a chromagram from a constant-Q transform.
chroma_stft
Compute a chromagram from an STFT spectrogram or waveform.
Examples
--------
Compute tonnetz features from the harmonic component of a song
>>> y, sr = librosa.load(librosa.ex('nutcracker'), duration=10, offset=10)
>>> y = librosa.effects.harmonic(y)
>>> tonnetz = librosa.feature.tonnetz(y=y, sr=sr)
>>> tonnetz
array([[ 0.007, -0.026, ..., 0.055, 0.056],
[-0.01 , -0.009, ..., -0.012, -0.017],
...,
[ 0.006, -0.021, ..., -0.012, -0.01 ],
[-0.009, 0.031, ..., -0.05 , -0.037]])
Compare the tonnetz features to `chroma_cqt`
>>> import matplotlib.pyplot as plt
>>> fig, ax = plt.subplots(nrows=2, sharex=True)
>>> img1 = librosa.display.specshow(tonnetz,
... y_axis='tonnetz', x_axis='time', ax=ax[0])
>>> ax[0].set(title='Tonal Centroids (Tonnetz)')
>>> ax[0].label_outer()
>>> img2 = librosa.display.specshow(librosa.feature.chroma_cqt(y, sr=sr),
... y_axis='chroma', x_axis='time', ax=ax[1])
>>> ax[1].set(title='Chroma')
>>> fig.colorbar(img1, ax=[ax[0]])
>>> fig.colorbar(img2, ax=[ax[1]])
"""
if y is None and chroma is None:
raise ParameterError(
"Either the audio samples or the chromagram must be "
"passed as an argument."
)
if chroma is None:
chroma = chroma_cqt(y=y, sr=sr, **kwargs)
# Generate Transformation matrix
dim_map = np.linspace(0, 12, num=chroma.shape[0], endpoint=False)
scale = np.asarray([7.0 / 6, 7.0 / 6, 3.0 / 2, 3.0 / 2, 2.0 / 3, 2.0 / 3])
V = np.multiply.outer(scale, dim_map)
# Even rows compute sin()
V[::2] -= 0.5
R = np.array([1, 1, 1, 1, 0.5, 0.5]) # Fifths # Minor # Major
phi = R[:, np.newaxis] * np.cos(np.pi * V)
# Do the transform to tonnetz
return phi.dot(util.normalize(chroma, norm=1, axis=0))
# -- Mel spectrogram and MFCCs -- #
[docs]def mfcc(
y=None, sr=22050, S=None, n_mfcc=20, dct_type=2, norm="ortho", lifter=0, **kwargs
):
"""Mel-frequency cepstral coefficients (MFCCs)
Parameters
----------
y : np.ndarray [shape=(n,)] or None
audio time series
sr : number > 0 [scalar]
sampling rate of ``y``
S : np.ndarray [shape=(d, t)] or None
log-power Mel spectrogram
n_mfcc: int > 0 [scalar]
number of MFCCs to return
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 ortho-normal
DCT basis.
Normalization is not supported for ``dct_type=1``.
lifter : number >= 0
If ``lifter>0``, apply *liftering* (cepstral filtering) to the MFCCs::
M[n, :] <- M[n, :] * (1 + sin(pi * (n + 1) / lifter) * lifter / 2)
Setting ``lifter >= 2 * n_mfcc`` emphasizes the higher-order coefficients.
As ``lifter`` increases, the coefficient weighting becomes approximately linear.
kwargs : additional keyword arguments
Arguments to `melspectrogram`, if operating
on time series input
Returns
-------
M : np.ndarray [shape=(n_mfcc, t)]
MFCC sequence
See Also
--------
melspectrogram
scipy.fftpack.dct
Examples
--------
Generate mfccs from a time series
>>> y, sr = librosa.load(librosa.ex('trumpet'))
>>> librosa.feature.mfcc(y=y, sr=sr)
array([[-249.124, -236.652, ..., -619.714, -619.714],
[ 73.787, 51.215, ..., 0. , 0. ],
...,
[ -10.144, -9.091, ..., 0. , 0. ],
[ -13.994, -21.184, ..., 0. , 0. ]],
dtype=float32)
Using a different hop length and HTK-style Mel frequencies
>>> librosa.feature.mfcc(y=y, sr=sr, hop_length=1024, htk=True)
array([[-274.064, -296.403, ..., -643.958, -643.958],
[ 63.888, 0.907, ..., 0. , 0. ],
...,
[ 13.069, 36.896, ..., 0. , 0. ],
[ -2.986, -13.714, ..., 0. , 0. ]],
dtype=float32)
Use a pre-computed log-power Mel spectrogram
>>> S = librosa.feature.melspectrogram(y=y, sr=sr, n_mels=128,
... fmax=8000)
>>> librosa.feature.mfcc(S=librosa.power_to_db(S))
array([[-222.66 , -209.08 , ..., -627.181, -627.181],
[ 32.214, 2.315, ..., 0. , 0. ],
...,
[ 0.872, -4.195, ..., 0. , 0. ],
[ 29.123, 33.193, ..., 0. , 0. ]],
dtype=float32)
Get more components
>>> mfccs = librosa.feature.mfcc(y=y, sr=sr, n_mfcc=40)
Visualize the MFCC series
>>> import matplotlib.pyplot as plt
>>> fig, ax = plt.subplots()
>>> img = librosa.display.specshow(mfccs, x_axis='time', ax=ax)
>>> fig.colorbar(img, ax=ax)
>>> ax.set(title='MFCC')
Compare different DCT bases
>>> m_slaney = librosa.feature.mfcc(y=y, sr=sr, dct_type=2)
>>> m_htk = librosa.feature.mfcc(y=y, sr=sr, dct_type=3)
>>> fig, ax = plt.subplots(nrows=2, sharex=True, sharey=True)
>>> img1 = librosa.display.specshow(m_slaney, x_axis='time', ax=ax[0])
>>> ax[0].set(title='RASTAMAT / Auditory toolbox (dct_type=2)')
>>> fig.colorbar(img, ax=[ax[0]])
>>> img2 = librosa.display.specshow(m_htk, x_axis='time', ax=ax[1])
>>> ax[1].set(title='HTK-style (dct_type=3)')
>>> fig.colorbar(img2, ax=[ax[1]])
"""
if S is None:
S = power_to_db(melspectrogram(y=y, sr=sr, **kwargs))
M = scipy.fftpack.dct(S, axis=0, type=dct_type, norm=norm)[:n_mfcc]
if lifter > 0:
M *= (
1
+ (lifter / 2)
* np.sin(np.pi * np.arange(1, 1 + n_mfcc, dtype=M.dtype) / lifter)[
:, np.newaxis
]
)
return M
elif lifter == 0:
return M
else:
raise ParameterError(
"MFCC lifter={} must be a non-negative number".format(lifter)
)
[docs]def melspectrogram(
y=None,
sr=22050,
S=None,
n_fft=2048,
hop_length=512,
win_length=None,
window="hann",
center=True,
pad_mode="reflect",
power=2.0,
**kwargs,
):
"""Compute a mel-scaled spectrogram.
If a spectrogram input ``S`` is provided, then it is mapped directly onto
the mel basis by ``mel_f.dot(S)``.
If a time-series input ``y, sr`` is provided, then its magnitude spectrogram
``S`` is first computed, and then mapped onto the mel scale by
``mel_f.dot(S**power)``.
By default, ``power=2`` operates on a power spectrum.
Parameters
----------
y : np.ndarray [shape=(n,)] or None
audio time-series
sr : number > 0 [scalar]
sampling rate of ``y``
S : np.ndarray [shape=(d, t)]
spectrogram
n_fft : int > 0 [scalar]
length of the FFT window
hop_length : int > 0 [scalar]
number of samples between successive frames.
See `librosa.stft`
win_length : int <= n_fft [scalar]
Each frame of audio is windowed by `window()`.
The window will be of length `win_length` and then padded
with zeros to match ``n_fft``.
If unspecified, defaults to ``win_length = n_fft``.
window : string, tuple, number, function, or np.ndarray [shape=(n_fft,)]
- a window specification (string, tuple, or number);
see `scipy.signal.get_window`
- a window function, such as `scipy.signal.windows.hann`
- a vector or array of length ``n_fft``
.. see also:: `librosa.filters.get_window`
center : boolean
- If `True`, the signal ``y`` is padded so that frame
``t`` is centered at ``y[t * hop_length]``.
- If `False`, then frame ``t`` begins at ``y[t * hop_length]``
pad_mode : string
If ``center=True``, the padding mode to use at the edges of the signal.
By default, STFT uses reflection padding.
power : float > 0 [scalar]
Exponent for the magnitude melspectrogram.
e.g., 1 for energy, 2 for power, etc.
kwargs : additional keyword arguments
Mel filter bank parameters.
See `librosa.filters.mel` for details.
Returns
-------
S : np.ndarray [shape=(n_mels, t)]
Mel spectrogram
See Also
--------
librosa.filters.mel
Mel filter bank construction
librosa.stft
Short-time Fourier Transform
Examples
--------
>>> y, sr = librosa.load(librosa.ex('trumpet'))
>>> librosa.feature.melspectrogram(y=y, sr=sr)
array([[3.837e-06, 1.451e-06, ..., 8.352e-14, 1.296e-11],
[2.213e-05, 7.866e-06, ..., 8.532e-14, 1.329e-11],
...,
[1.115e-05, 5.192e-06, ..., 3.675e-08, 2.470e-08],
[6.473e-07, 4.402e-07, ..., 1.794e-08, 2.908e-08]],
dtype=float32)
Using a pre-computed power spectrogram would give the same result:
>>> D = np.abs(librosa.stft(y))**2
>>> S = librosa.feature.melspectrogram(S=D, sr=sr)
Display of mel-frequency spectrogram coefficients, with custom
arguments for mel filterbank construction (default is fmax=sr/2):
>>> # Passing through arguments to the Mel filters
>>> S = librosa.feature.melspectrogram(y=y, sr=sr, n_mels=128,
... fmax=8000)
>>> import matplotlib.pyplot as plt
>>> fig, ax = plt.subplots()
>>> S_dB = librosa.power_to_db(S, ref=np.max)
>>> img = librosa.display.specshow(S_dB, x_axis='time',
... y_axis='mel', sr=sr,
... fmax=8000, ax=ax)
>>> fig.colorbar(img, ax=ax, format='%+2.0f dB')
>>> ax.set(title='Mel-frequency spectrogram')
"""
S, n_fft = _spectrogram(
y=y,
S=S,
n_fft=n_fft,
hop_length=hop_length,
power=power,
win_length=win_length,
window=window,
center=center,
pad_mode=pad_mode,
)
# Build a Mel filter
mel_basis = filters.mel(sr, n_fft, **kwargs)
return np.dot(mel_basis, S)