Recursive implementation of some time-frequency representations

Cohen´s class of time-frequency distributions (CTFDs), which includes the spectrogram and the Wigner-Ville distribution, has significant potential for the analysis of non-stationary signals. In order to efficiently compute long signal time-frequency representations, we propose fast algorithms using a recursive approach. First, we introduce a recursive algorithm dedicated to the spectrogram computation. 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 specific CTFDs. We show that the windows mentioned above can also be used to compute recursively 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