Source code for librosa.feature.rhythm

#!/usr/bin/env python
# -*- coding: utf-8 -*-
"""Rhythmic feature extraction"""

import numpy as np

from .. import util

from ..core.audio import autocorrelate
from ..core.spectrum import stft
from ..util.exceptions import ParameterError
from ..filters import get_window


__all__ = ["tempogram", "fourier_tempogram"]


# -- Rhythmic features -- #
[docs]def tempogram( *, y=None, sr=22050, onset_envelope=None, hop_length=512, win_length=384, center=True, window="hann", norm=np.inf, ): """Compute the tempogram: local autocorrelation of the onset strength envelope. [#]_ .. [#] Grosche, Peter, Meinard Müller, and Frank Kurth. "Cyclic tempogram - A mid-level tempo representation for music signals." ICASSP, 2010. Parameters ---------- y : np.ndarray [shape=(..., n)] or None Audio time series. Multi-channel is supported. sr : number > 0 [scalar] sampling rate of ``y`` onset_envelope : np.ndarray [shape=(..., n) or (..., m, n)] or None Optional pre-computed onset strength envelope as provided by `librosa.onset.onset_strength`. If multi-dimensional, tempograms are computed independently for each band (first dimension). hop_length : int > 0 number of audio samples between successive onset measurements win_length : int > 0 length of the onset autocorrelation window (in frames/onset measurements) The default settings (384) corresponds to ``384 * hop_length / sr ~= 8.9s``. center : bool If `True`, onset autocorrelation windows are centered. If `False`, windows are left-aligned. window : string, function, number, tuple, or np.ndarray [shape=(win_length,)] A window specification as in `stft`. norm : {np.inf, -np.inf, 0, float > 0, None} Normalization mode. Set to `None` to disable normalization. Returns ------- tempogram : np.ndarray [shape=(..., win_length, n)] Localized autocorrelation of the onset strength envelope. If given multi-band input (``onset_envelope.shape==(m,n)``) then ``tempogram[i]`` is the tempogram of ``onset_envelope[i]``. Raises ------ ParameterError if neither ``y`` nor ``onset_envelope`` are provided if ``win_length < 1`` See Also -------- fourier_tempogram librosa.onset.onset_strength librosa.util.normalize librosa.stft Examples -------- >>> # Compute local onset autocorrelation >>> y, sr = librosa.load(librosa.ex('nutcracker'), duration=30) >>> hop_length = 512 >>> oenv = librosa.onset.onset_strength(y=y, sr=sr, hop_length=hop_length) >>> tempogram = librosa.feature.tempogram(onset_envelope=oenv, sr=sr, ... hop_length=hop_length) >>> # Compute global onset autocorrelation >>> ac_global = librosa.autocorrelate(oenv, max_size=tempogram.shape[0]) >>> ac_global = librosa.util.normalize(ac_global) >>> # Estimate the global tempo for display purposes >>> tempo = librosa.beat.tempo(onset_envelope=oenv, sr=sr, ... hop_length=hop_length)[0] >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(nrows=4, figsize=(10, 10)) >>> times = librosa.times_like(oenv, sr=sr, hop_length=hop_length) >>> ax[0].plot(times, oenv, label='Onset strength') >>> ax[0].label_outer() >>> ax[0].legend(frameon=True) >>> librosa.display.specshow(tempogram, sr=sr, hop_length=hop_length, >>> x_axis='time', y_axis='tempo', cmap='magma', ... ax=ax[1]) >>> ax[1].axhline(tempo, color='w', linestyle='--', alpha=1, ... label='Estimated tempo={:g}'.format(tempo)) >>> ax[1].legend(loc='upper right') >>> ax[1].set(title='Tempogram') >>> x = np.linspace(0, tempogram.shape[0] * float(hop_length) / sr, ... num=tempogram.shape[0]) >>> ax[2].plot(x, np.mean(tempogram, axis=1), label='Mean local autocorrelation') >>> ax[2].plot(x, ac_global, '--', alpha=0.75, label='Global autocorrelation') >>> ax[2].set(xlabel='Lag (seconds)') >>> ax[2].legend(frameon=True) >>> freqs = librosa.tempo_frequencies(tempogram.shape[0], hop_length=hop_length, sr=sr) >>> ax[3].semilogx(freqs[1:], np.mean(tempogram[1:], axis=1), ... label='Mean local autocorrelation', base=2) >>> ax[3].semilogx(freqs[1:], ac_global[1:], '--', alpha=0.75, ... label='Global autocorrelation', base=2) >>> ax[3].axvline(tempo, color='black', linestyle='--', alpha=.8, ... label='Estimated tempo={:g}'.format(tempo)) >>> ax[3].legend(frameon=True) >>> ax[3].set(xlabel='BPM') >>> ax[3].grid(True) """ from ..onset import onset_strength if win_length < 1: raise ParameterError("win_length must be a positive integer") ac_window = get_window(window, win_length, fftbins=True) if onset_envelope is None: if y is None: raise ParameterError("Either y or onset_envelope must be provided") onset_envelope = onset_strength(y=y, sr=sr, hop_length=hop_length) # Center the autocorrelation windows n = onset_envelope.shape[-1] if center: padding = [(0, 0) for _ in onset_envelope.shape] padding[-1] = (int(win_length // 2),) * 2 onset_envelope = np.pad( onset_envelope, padding, mode="linear_ramp", end_values=[0, 0] ) # Carve onset envelope into frames odf_frame = util.frame(onset_envelope, frame_length=win_length, hop_length=1) # Truncate to the length of the original signal if center: odf_frame = odf_frame[..., :n] # explicit broadcast of ac_window ac_window = util.expand_to(ac_window, ndim=odf_frame.ndim, axes=-2) # Window, autocorrelate, and normalize return util.normalize( autocorrelate(odf_frame * ac_window, axis=-2), norm=norm, axis=-2 )
[docs]def fourier_tempogram( *, y=None, sr=22050, onset_envelope=None, hop_length=512, win_length=384, center=True, window="hann", ): """Compute the Fourier tempogram: the short-time Fourier transform of the onset strength envelope. [#]_ .. [#] Grosche, Peter, Meinard Müller, and Frank Kurth. "Cyclic tempogram - A mid-level tempo representation for music signals." ICASSP, 2010. Parameters ---------- y : np.ndarray [shape=(..., n)] or None Audio time series. Multi-channel is supported. sr : number > 0 [scalar] sampling rate of ``y`` onset_envelope : np.ndarray [shape=(..., n)] or None Optional pre-computed onset strength envelope as provided by ``librosa.onset.onset_strength``. Multi-channel is supported. hop_length : int > 0 number of audio samples between successive onset measurements win_length : int > 0 length of the onset window (in frames/onset measurements) The default settings (384) corresponds to ``384 * hop_length / sr ~= 8.9s``. center : bool If `True`, onset windows are centered. If `False`, windows are left-aligned. window : string, function, number, tuple, or np.ndarray [shape=(win_length,)] A window specification as in `stft`. Returns ------- tempogram : np.ndarray [shape=(..., win_length // 2 + 1, n)] Complex short-time Fourier transform of the onset envelope. Raises ------ ParameterError if neither ``y`` nor ``onset_envelope`` are provided if ``win_length < 1`` See Also -------- tempogram librosa.onset.onset_strength librosa.util.normalize librosa.stft Examples -------- >>> # Compute local onset autocorrelation >>> y, sr = librosa.load(librosa.ex('nutcracker')) >>> hop_length = 512 >>> oenv = librosa.onset.onset_strength(y=y, sr=sr, hop_length=hop_length) >>> tempogram = librosa.feature.fourier_tempogram(onset_envelope=oenv, sr=sr, ... hop_length=hop_length) >>> # Compute the auto-correlation tempogram, unnormalized to make comparison easier >>> ac_tempogram = librosa.feature.tempogram(onset_envelope=oenv, sr=sr, ... hop_length=hop_length, norm=None) >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(nrows=3, sharex=True) >>> ax[0].plot(librosa.times_like(oenv), oenv, label='Onset strength') >>> ax[0].legend(frameon=True) >>> ax[0].label_outer() >>> librosa.display.specshow(np.abs(tempogram), sr=sr, hop_length=hop_length, >>> x_axis='time', y_axis='fourier_tempo', cmap='magma', ... ax=ax[1]) >>> ax[1].set(title='Fourier tempogram') >>> ax[1].label_outer() >>> librosa.display.specshow(ac_tempogram, sr=sr, hop_length=hop_length, >>> x_axis='time', y_axis='tempo', cmap='magma', ... ax=ax[2]) >>> ax[2].set(title='Autocorrelation tempogram') """ from ..onset import onset_strength if win_length < 1: raise ParameterError("win_length must be a positive integer") if onset_envelope is None: if y is None: raise ParameterError("Either y or onset_envelope must be provided") onset_envelope = onset_strength(y=y, sr=sr, hop_length=hop_length) # Generate the short-time Fourier transform return stft( onset_envelope, n_fft=win_length, hop_length=1, center=center, window=window )