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Source code for librosa.core.harmonic

#!/usr/bin/env python
# -*- coding: utf-8 -*-
"""Harmonic calculations for frequency representations"""

import numpy as np
import scipy.interpolate
import scipy.signal
from ..util.exceptions import ParameterError

__all__ = ["salience", "interp_harmonics"]


[docs]def salience( S, freqs, h_range, weights=None, aggregate=None, filter_peaks=True, fill_value=np.nan, kind="linear", axis=0, ): """Harmonic salience function. Parameters ---------- S : np.ndarray [shape=(d, n)] input time frequency magnitude representation (e.g. STFT or CQT magnitudes). Must be real-valued and non-negative. freqs : np.ndarray, shape=(S.shape[axis]) The frequency values corresponding to S's elements along the chosen axis. h_range : list-like, non-negative Harmonics to include in salience computation. The first harmonic (1) corresponds to ``S`` itself. Values less than one (e.g., 1/2) correspond to sub-harmonics. weights : list-like The weight to apply to each harmonic in the summation. (default: uniform weights). Must be the same length as ``harmonics``. aggregate : function aggregation function (default: `np.average`) If ``aggregate=np.average``, then a weighted average is computed per-harmonic according to the specified weights. For all other aggregation functions, all harmonics are treated equally. filter_peaks : bool If true, returns harmonic summation only on frequencies of peak magnitude. Otherwise returns harmonic summation over the full spectrum. Defaults to True. fill_value : float The value to fill non-peaks in the output representation. (default: `np.nan`) Only used if ``filter_peaks == True``. kind : str Interpolation type for harmonic estimation. See `scipy.interpolate.interp1d`. axis : int The axis along which to compute harmonics Returns ------- S_sal : np.ndarray, shape=(len(h_range), [x.shape]) ``S_sal`` will have the same shape as ``S``, and measure the overal harmonic energy at each frequency. See Also -------- interp_harmonics Examples -------- >>> y, sr = librosa.load(librosa.ex('trumpet'), duration=3) >>> S = np.abs(librosa.stft(y)) >>> freqs = librosa.fft_frequencies(sr) >>> harms = [1, 2, 3, 4] >>> weights = [1.0, 0.5, 0.33, 0.25] >>> S_sal = librosa.salience(S, freqs, harms, weights, fill_value=0) >>> print(S_sal.shape) (1025, 115) >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(nrows=2, sharex=True, sharey=True) >>> librosa.display.specshow(librosa.amplitude_to_db(S, ref=np.max), ... sr=sr, y_axis='log', x_axis='time', ax=ax[0]) >>> ax[0].set(title='Magnitude spectrogram') >>> ax[0].label_outer() >>> img = librosa.display.specshow(librosa.amplitude_to_db(S_sal, ... ref=np.max), ... sr=sr, y_axis='log', x_axis='time', ax=ax[1]) >>> ax[1].set(title='Salience spectrogram') >>> fig.colorbar(img, ax=ax, format="%+2.0f dB") """ if aggregate is None: aggregate = np.average if weights is None: weights = np.ones((len(h_range),)) else: weights = np.array(weights, dtype=float) S_harm = interp_harmonics(S, freqs, h_range, kind=kind, axis=axis) if aggregate is np.average: S_sal = aggregate(S_harm, axis=0, weights=weights) else: S_sal = aggregate(S_harm, axis=0) if filter_peaks: S_peaks = scipy.signal.argrelmax(S, axis=0) S_out = np.empty(S.shape) S_out.fill(fill_value) S_out[S_peaks[0], S_peaks[1]] = S_sal[S_peaks[0], S_peaks[1]] S_sal = S_out return S_sal
[docs]def interp_harmonics(x, freqs, h_range, kind="linear", fill_value=0, axis=0): """Compute the energy at harmonics of time-frequency representation. Given a frequency-based energy representation such as a spectrogram or tempogram, this function computes the energy at the chosen harmonics of the frequency axis. (See examples below.) The resulting harmonic array can then be used as input to a salience computation. Parameters ---------- x : np.ndarray The input energy freqs : np.ndarray, shape=(X.shape[axis]) The frequency values corresponding to X's elements along the chosen axis. h_range : list-like, non-negative Harmonics to compute. The first harmonic (1) corresponds to ``x`` itself. Values less than one (e.g., 1/2) correspond to sub-harmonics. kind : str Interpolation type. See `scipy.interpolate.interp1d`. fill_value : float The value to fill when extrapolating beyond the observed frequency range. axis : int The axis along which to compute harmonics Returns ------- x_harm : np.ndarray, shape=(len(h_range), [x.shape]) ``x_harm[i]`` will have the same shape as ``x``, and measure the energy at the ``h_range[i]`` harmonic of each frequency. See Also -------- scipy.interpolate.interp1d Examples -------- Estimate the harmonics of a time-averaged tempogram >>> y, sr = librosa.load(librosa.ex('choice')) >>> # Compute the time-varying tempogram and average over time >>> tempi = np.mean(librosa.feature.tempogram(y=y, sr=sr), axis=1) >>> # We'll measure the first five harmonics >>> h_range = [1, 2, 3, 4, 5] >>> f_tempo = librosa.tempo_frequencies(len(tempi), sr=sr) >>> # Build the harmonic tensor >>> t_harmonics = librosa.interp_harmonics(tempi, f_tempo, h_range) >>> print(t_harmonics.shape) (5, 384) >>> # And plot the results >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots() >>> librosa.display.specshow(t_harmonics, x_axis='tempo', sr=sr, ax=ax) >>> ax.set(yticks=0.5 + np.arange(len(h_range)), ... yticklabels=['{:.3g}'.format(_) for _ in h_range], ... ylabel='Harmonic', xlabel='Tempo (BPM)') We can also compute frequency harmonics for spectrograms. To calculate sub-harmonic energy, use values < 1. >>> y, sr = librosa.load(librosa.ex('trumpet'), duration=3) >>> h_range = [1./3, 1./2, 1, 2, 3, 4] >>> S = np.abs(librosa.stft(y)) >>> fft_freqs = librosa.fft_frequencies(sr=sr) >>> S_harm = librosa.interp_harmonics(S, fft_freqs, h_range, axis=0) >>> print(S_harm.shape) (6, 1025, 646) >>> fig, ax = plt.subplots(nrows=3, ncols=2, sharex=True, sharey=True) >>> for i, _sh in enumerate(S_harm): ... img = librosa.display.specshow(librosa.amplitude_to_db(_sh, ... ref=S.max()), ... sr=sr, y_axis='log', x_axis='time', ... ax=ax.flat[i]) ... ax.flat[i].set(title='h={:.3g}'.format(h_range[i])) ... ax.flat[i].label_outer() >>> fig.colorbar(img, ax=ax, format="%+2.f dB") """ # X_out will be the same shape as X, plus a leading # axis that has length = len(h_range) out_shape = [len(h_range)] out_shape.extend(x.shape) x_out = np.zeros(out_shape, dtype=x.dtype) if freqs.ndim == 1 and len(freqs) == x.shape[axis]: harmonics_1d( x_out, x, freqs, h_range, kind=kind, fill_value=fill_value, axis=axis ) elif freqs.ndim == 2 and freqs.shape == x.shape: harmonics_2d( x_out, x, freqs, h_range, kind=kind, fill_value=fill_value, axis=axis ) else: raise ParameterError( "freqs.shape={} does not match " "input shape={}".format(freqs.shape, x.shape) ) return x_out
def harmonics_1d(harmonic_out, x, freqs, h_range, kind="linear", fill_value=0, axis=0): """Populate a harmonic tensor from a time-frequency representation. Parameters ---------- harmonic_out : np.ndarray, shape=(len(h_range), X.shape) The output array to store harmonics X : np.ndarray The input energy freqs : np.ndarray, shape=(x.shape[axis]) The frequency values corresponding to x's elements along the chosen axis. h_range : list-like, non-negative Harmonics to compute. The first harmonic (1) corresponds to ``x`` itself. Values less than one (e.g., 1/2) correspond to sub-harmonics. kind : str Interpolation type. See `scipy.interpolate.interp1d`. fill_value : float The value to fill when extrapolating beyond the observed frequency range. axis : int The axis along which to compute harmonics See Also -------- harmonics scipy.interpolate.interp1d Examples -------- Estimate the harmonics of a time-averaged tempogram >>> y, sr = librosa.load(librosa.ex('choice')) >>> # Compute the time-varying tempogram and average over time >>> tempi = np.mean(librosa.feature.tempogram(y=y, sr=sr), axis=1) >>> # We'll measure the first five harmonics >>> h_range = [1, 2, 3, 4, 5] >>> f_tempo = librosa.tempo_frequencies(len(tempi), sr=sr) >>> # Build the harmonic tensor >>> t_harmonics = librosa.interp_harmonics(tempi, f_tempo, h_range) >>> print(t_harmonics.shape) (5, 384) >>> # And plot the results >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots() >>> librosa.display.specshow(t_harmonics, x_axis='tempo', sr=sr, ax=ax) >>> ax.set(yticks=0.5 + np.arange(len(h_range)), ... yticklabels=['{:.3g}'.format(_) for _ in h_range], ... ylabel='Harmonic') ... xlabel='Tempo (BPM)') We can also compute frequency harmonics for spectrograms. To calculate subharmonic energy, use values < 1. >>> h_range = [1./3, 1./2, 1, 2, 3, 4] >>> S = np.abs(librosa.stft(y)) >>> fft_freqs = librosa.fft_frequencies(sr=sr) >>> S_harm = librosa.interp_harmonics(S, fft_freqs, h_range, axis=0) >>> print(S_harm.shape) (6, 1025, 646) >>> fig, ax = plt.subplots(nrows=3, ncols=2, sharex=True, sharey=True) >>> for i, _sh in enumerate(S_harm): ... librosa.display.specshow(librosa.amplitude_to_db(_sh, ... ref=S.max()), ... sr=sr, y_axis='log', x_axis='time', ax=ax.flat[i]) ... ax.flat[i].set(title='h={:.3g}'.format(h_range[i])) ... ax.flat[i].label_outer() """ # Note: this only works for fixed-grid, 1d interpolation f_interp = scipy.interpolate.interp1d( freqs, x, kind=kind, axis=axis, copy=False, bounds_error=False, fill_value=fill_value, ) idx_out = [slice(None)] * harmonic_out.ndim # Compute the output index of the interpolated values interp_axis = 1 + (axis % x.ndim) # Iterate over the harmonics range for h_index, harmonic in enumerate(h_range): idx_out[0] = h_index # Iterate over frequencies for f_index, frequency in enumerate(freqs): # Offset the output axis by 1 to account for the harmonic index idx_out[interp_axis] = f_index # Estimate the harmonic energy at this frequency across time harmonic_out[tuple(idx_out)] = f_interp(harmonic * frequency) def harmonics_2d(harmonic_out, x, freqs, h_range, kind="linear", fill_value=0, axis=0): """Populate a harmonic tensor from a time-frequency representation with time-varying frequencies. Parameters ---------- harmonic_out : np.ndarray The output array to store harmonics x : np.ndarray The input energy freqs : np.ndarray, shape=x.shape The frequency values corresponding to each element of ``x`` h_range : list-like, non-negative Harmonics to compute. The first harmonic (1) corresponds to ``x`` itself. Values less than one (e.g., 1/2) correspond to sub-harmonics. kind : str Interpolation type. See `scipy.interpolate.interp1d`. fill_value : float The value to fill when extrapolating beyond the observed frequency range. axis : int The axis along which to compute harmonics See Also -------- harmonics harmonics_1d """ idx_in = [slice(None)] * x.ndim idx_freq = [slice(None)] * x.ndim idx_out = [slice(None)] * harmonic_out.ndim # This is the non-interpolation axis ni_axis = (1 + axis) % x.ndim # For each value in the non-interpolated axis, compute its harmonics for i in range(x.shape[ni_axis]): idx_in[ni_axis] = slice(i, i + 1) idx_freq[ni_axis] = i idx_out[1 + ni_axis] = idx_in[ni_axis] harmonics_1d( harmonic_out[tuple(idx_out)], x[tuple(idx_in)], freqs[tuple(idx_freq)], h_range, kind=kind, fill_value=fill_value, axis=axis, )