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Band energy

The band energy is defined as the energy in an arbitrary frequency band $[f_l,f_u)$, where $f_l$ and $f_u$ are the lower and upper frequency bounds of the band.

$\begin{array}{rl}BandEnergy& =\sum _{m=m_l}^{m_u-1}{X}_p[m]\\ X_p& =|X{|}^2\\ m_l& =\lfloor M\frac{f_l}{2f_s}\rfloor \\ m_u& =\lfloor M\frac{f_u}{2f_s}\rfloor \end{array}$

Where $m\in [0,M)$ is the bin index of the spectrum $X$ and the power spectrum $X_p$.

References

• Eyben, F. (2016). Real-time Speech and Music Classification by Large Audio Feature Space Extraction. https://doi.org/10.1007/978-3-319-27299-3

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 band_energy(
    spectrum: np.ndarray, samplerate: float, f_lower: float, f_upper: float
) -> float:
    powerspectrum = np.abs(spectrum) ** 2
    n = len(powerspectrum)
    n_lower = int(2 * n * f_lower / samplerate)
    n_upper = int(2 * n * f_upper / samplerate)
    return np.sum(powerspectrum[n_lower:n_upper])

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