Source code for librosa.core.harmonic

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

import warnings

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

__all__ = ["salience", "interp_harmonics"]

[docs]def salience( S, *, freqs, harmonics, weights=None, aggregate=None, filter_peaks=True, fill_value=np.nan, kind="linear", axis=-2, ): """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. harmonics : 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 ``S_sal`` will have the same shape as ``S``, and measure the overall 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=sr) >>> harms = [1, 2, 3, 4] >>> weights = [1.0, 0.5, 0.33, 0.25] >>> S_sal = librosa.salience(S, freqs=freqs, harmonics=harms, weights=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(harmonics),)) else: weights = np.array(weights, dtype=float) S_harm = interp_harmonics(S, freqs=freqs, harmonics=harmonics, kind=kind, axis=axis) if aggregate is np.average: S_sal = aggregate(S_harm, axis=axis - 1, weights=weights) else: S_sal = aggregate(S_harm, axis=axis - 1) if filter_peaks: S_peaks = scipy.signal.argrelmax(S, axis=axis) S_out = np.empty(S.shape) S_out.fill(fill_value) S_out[S_peaks] = S_sal[S_peaks] S_sal = S_out return S_sal
[docs]def interp_harmonics(x, *, freqs, harmonics, kind="linear", fill_value=0, axis=-2): """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. harmonics : list-like, non-negative Harmonics to compute as ``harmonics[i] * freqs``. The first harmonic (1) corresponds to ``freqs``. 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 ``x_harm[i]`` will have the same shape as ``x``, and measure the energy at the ``harmonics[i]`` harmonic of each frequency. A new dimension indexing harmonics will be inserted immediately before ``axis``. See Also -------- scipy.interpolate.interp1d Examples -------- Estimate the harmonics of a time-averaged tempogram >>> y, sr = librosa.load(librosa.ex('sweetwaltz')) >>> # 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 >>> harmonics = [1, 2, 3, 4, 5] >>> f_tempo = librosa.tempo_frequencies(len(tempi), sr=sr) >>> # Build the harmonic tensor; we only have one axis here (tempo) >>> t_harmonics = librosa.interp_harmonics(tempi, freqs=f_tempo, harmonics=harmonics, axis=0) >>> 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=np.arange(len(harmonics)), ... yticklabels=['{:.3g}'.format(_) for _ in harmonics], ... 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) >>> harmonics = [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, freqs=fft_freqs, harmonics=harmonics, 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(harmonics[i])) ... ax.flat[i].label_outer() >>> fig.colorbar(img, ax=ax, format="%+2.f dB") """ if freqs.ndim == 1 and len(freqs) == x.shape[axis]: # Build the 1-D interpolator. # All frames have a common domain, so we only need one interpolator here. # First, verify that the input frequencies are unique if not is_unique(freqs, axis=0): warnings.warn( "Frequencies are not unique. This may produce incorrect harmonic interpolations.", stacklevel=2, ) f_interp = scipy.interpolate.interp1d( freqs, x, axis=axis, bounds_error=False, copy=False, kind=kind, fill_value=fill_value, ) # Set the interpolation points f_out = np.multiply.outer(harmonics, freqs) # Interpolate return f_interp(f_out) elif freqs.shape == x.shape: if not np.all(is_unique(freqs, axis=axis)): warnings.warn( "Frequencies are not unique. This may produce incorrect harmonic interpolations.", stacklevel=2, ) # If we have time-varying frequencies, then it must match exactly the shape of the input # We'll define a frame-wise interpolator helper function that we will vectorize over # the entire input array def _f_interp(_a, _b): interp = scipy.interpolate.interp1d( _a, _b, bounds_error=False, copy=False, kind=kind, fill_value=fill_value ) return interp(np.multiply.outer(_a, harmonics)) # Signature is expanding frequency into a new dimension xfunc = np.vectorize(_f_interp, signature="(f),(f)->(f,h)") # Rotate the vectorizing axis to the tail so that we get parallelism over frames # Afterward, we're swapping (-1, axis-1) instead of (-1,axis) # because a new dimension has been inserted return ( xfunc(freqs.swapaxes(axis, -1), x.swapaxes(axis, -1)) .swapaxes( # Return the original target axis to its place -2, axis, ) .swapaxes( # Put the new harmonic axis directly in front of the target axis -1, axis - 1, ) ) else: raise ParameterError( "freqs.shape={} does not match " "input shape={}".format(freqs.shape, x.shape) )