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Detecting the Number of Components in a Nonstationary Signal Using the Renyi Eentropy of Its Time-Frequency Ddistributions

A time-frequency distribution provides many advantages in the analysis of multicomponent non- stationary signals. The simultaneous signal representation with respect to the time and frequency axis defines at each time moment the signal amplitude, frequency, bandwidth, and the number of components. The Rényi entropy, applied to a time-frequency distribution, has been shown to be a valuable indicator of the signal complexity. The aim of this paper is to determine which of the treated time-frequency distributions (TFDs) (namely, the Wigner-Ville distribution, the Choi-Williams distribution, and the spectrogram) has best properties for estimation of the number of components when there is no prior knowledge of the signal. The optimal Rényi entropy parameter α is determined for each TFD. The effects on the Rényi entropy of different time durations, bandwidths and amplitudes of the signal components have been analysed. The concept of a class, when the Rényi entropy is applied to TFDs, is also introduced.

Nonstationary Signals ; Time-Frequency distributions ; Renyi Entropy

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