An Entropy Based Method for Local Time-Adaptation of the Spectrogram

TL;DR

This paper introduces an entropy-based method for adaptively optimizing the local time resolution of spectrograms in audio signals, enhancing visualization and analysis by minimizing Re9nyi entropy in a multi-frame Gabor decomposition.

Contribution

It presents a novel adaptive spectrogram technique using Re9nyi entropy to determine optimal local resolution, enabling perfect reconstruction of the original signal.

Findings

Improved spectrogram display with adaptive resolution.

Successful application to instrumental and synthetic sounds.

Maintains invertibility for perfect signal reconstruction.

Abstract

We propose a method for automatic local time-adaptation of the spectrogram of audio signals: it is based on the decomposition of a signal within a Gabor multi-frame through the STFT operator. The sparsity of the analysis in every individual frame of the multi-frame is evaluated through the R\'enyi entropy measures: the best local resolution is determined minimizing the entropy values. The overall spectrogram of the signal we obtain thus provides local optimal resolution adaptively evolving over time. We give examples of the performance of our algorithm with an instrumental sound and a synthetic one, showing the improvement in spectrogram displaying obtained with an automatic adaptation of the resolution. The analysis operator is invertible, thus leading to a perfect reconstruction of the original signal through the analysis coefficients.