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Recursive implementation of some time-frequency representations

Abstract : 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.
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Submitted on : Tuesday, November 12, 2019 - 11:53:36 AM
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Cédric Richard, Régis Lengellé. Recursive implementation of some time-frequency representations. Third International Symposium on Time-Frequency and Time-Scale Analysis (TFTS-96), Jun 1997, Paris, France. pp.313-316, ⟨10.1109/TFSA.1996.547476⟩. ⟨hal-02359069⟩



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