Joint recursive implementation of time—frequency representations and their modified version by the reassignment method

Abstract

Abstract Cohen's class time—frequency distributions (CTFDs) have significant potential for the analysis of non-stationary signals, even if the poor readability of their representations makes visual interpretations difficult. To concentrate signal components, Auger and Flandrin recently generalized the reassignment method (first applied to the spectrogram in the 1970s) to any bilinear representations. Unfortunately, this process is computationally expensive. In order to reduce computation time and to improve representations readability, we first introduce a new fast algorithm which allows the recursive evaluation of classical spectrograms and spectrograms modified by the reassignment method. In a second step, we show that rectangular, half-sine, Hamming, Hanning and Blackman functions can be used as running ‘short-time’ windows. Then the previous algorithm is extended to CTFDs. We show that the windows mentioned above can also be used to compute recursively reassigned smoothed pseudo-Wigner—Ville distributions. Finally, we show that the constraints on candidate windows are not very restrictive: any function (assumed periodic) can be used in practice as long as it admits a ‘short enough’ Fourier series decomposition.