Features | latest | spectral-variance

Spectral variance

Spectral variance, also known as spectral spread, quantifies the dispersion or spread of the spectral content around its center of mass, the spectral centroid $f_{centroid}$.

The spectral variance is computed from the power spectrum $X_p=|X{|}^2\in {\mathbb{R}}^M$ using the following formula:

$$\text{SpectralVariance}=\sum _{m=0}^{M-1}(f(m)-f_{centroid}{)}^2\cdot p(m),$$

where:

• $f(m)$ is the frequency corresponding to bin $m$:

  $$f(m)=\frac{m\cdot f_s}{2(M-1)},$$

• $p(m)$ is the normalized power at bin $m$:

  $$p(m)=\frac{X_p[m]}{\sum _{m=0}^{M-1}{X}_p[m]}.$$

References

• https://www.mathworks.com/help/audio/ref/spectralspread.html
• Peeters, G. (2004). A large set of audio features for sound description (similarity and classification) in the CUIDADO project. In CUIDADO IST Project Report (Vol. 54).

Code

INFO

The following snippet is written in a generic and unoptimized manner. The code aims to be comprehensible to programmers familiar with various programming languages and may not represent the most efficient or idiomatic Python practices. Please refer to implementations for optimized implementations in different programming languages.

code.py

import numpy as np


def _spectral_centroid(spectrum: np.ndarray, samplerate: float):
    ps = np.abs(spectrum) ** 2
    ps_sum = 0.0
    ps_sum_weighted = 0.0
    for i, magnitude in enumerate(ps):
        ps_sum += magnitude
        ps_sum_weighted += magnitude * i
    return 0.5 * samplerate / (len(ps) - 1) * (ps_sum_weighted / ps_sum)


def spectral_variance(spectrum: np.ndarray, samplerate: float):
    f_centroid = _spectral_centroid(spectrum, samplerate)
    ps = np.abs(spectrum) ** 2
    ps_sum = 0.0
    ps_sum_weighted = 0.0
    for i, magnitude in enumerate(ps):
        f = 0.5 * samplerate / (len(ps) - 1) * i
        ps_sum += magnitude
        ps_sum_weighted += magnitude * (f - f_centroid) ** 2
    return ps_sum_weighted / ps_sum

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