Análise tempo-frequência de sinais via frame de Gabor e estatística de alta ordem: um enfoque computacional

Abstract

This work presents the computational modeling of synthetic and experimental signals, focusing on time-frequency analysis. To that end, an implementation of the Fourier transform (TF) was used to produce the frequency content, also known as Power Spectral Density (PSD) power spectral density. In order to produce more focused resolution spectrograms in the time-frequency plane, a Gaussian window adjusted by local kurtosis estimates was introduced in TF. Interpreting the resulting scheme as an internal product between the signal and the action of modulation and translation combinations c.f (shifts time-frequency) on the window, we obtain the Gabor frames adjusted by high-order statistics. This adaptation of the short-time Fourier transform (STFT) is more suitable for non-stationary signal analysis because of its ability to adjust to local characteristics. However, despite the uncertainty principle, in its weak version for the STFT, impose restrictions on the concentration of the spectrogram in the time-frequency plane. The implementation of the adapted STFT was able to generate spectrograms that were clear enough to locate the contribution moments of the frequencies, as well as their evolution.