https://hal-utt.archives-ouvertes.fr/hal-02359069Richard, CédricCédricRichardLM2S - Laboratoire Modélisation et Sûreté des Systèmes - ICD - Institut Charles Delaunay - UTT - Université de Technologie de Troyes - CNRS - Centre National de la Recherche ScientifiqueLengellé, RégisRégisLengelléLM2S - Laboratoire Modélisation et Sûreté des Systèmes - ICD - Institut Charles Delaunay - UTT - Université de Technologie de Troyes - CNRS - Centre National de la Recherche ScientifiqueRecursive implementation of some time-frequency representationsHAL CCSD1997[SPI.SIGNAL] Engineering Sciences [physics]/Signal and Image processingVU VAN, Jean-Baptiste2019-11-12 11:53:362022-08-31 18:56:352019-11-12 11:53:36enConference papers10.1109/TFSA.1996.5474761Cohen'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.