  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.
