Fast implementation of time-frequency representations modified by the reassignment method

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 the signal components, Auger and Flandrin (see IEEE Trans. on Acoustics, Speech and Signal Processing, vol.43, p.1068-89, 1995) generalized the reassignment method (first applied to the spectrogram) to any bilinear representation. Unfortunately, this process is computationally expensive. In order to quicken the computation time and to improve the representations readability, we first introduce a new fast algorithm which allows the recursive evaluation of classical spectrograms and spectrograms modified by the reassignment method. We show that rectangular, half-sine, Hamming, Hanning and Blackman functions can be used as running 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