Evolutionary time-frequency analysis

Adapted waveform analysis uses libraries of bases and an efficient functional to match a basis to a given signal or family of signals. In particular, wavelet packets and localized trigonometric functions support the expansion of waveforms in bases whose elements have good time-frequency localization properties. In this paper, we use an evolutionary computation approach to conduct time-frequency analysis for signal processing applications. We propose a methodology for evolving parsimonious signal representations, based on the identification of the most well-adapted basis from several dictionaries. Two error criteria are introduced to assess misidentification error rates. One criterion works in transformed space and has a visual interpretation in terms of time-frequency diagrams. The other criterion measures the deviation of the original signal from the reconstructed signal through evolutionary decomposition. Statistical measures of the identification errors involved in the waveform decomposition process are presented