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Design of an Optimal Piece-Wise Spline Wigner-Ville Distribution for TFD Performance Evaluation and Comparison

This paper proposes a new performance evaluation process for time-frequency distributions (TFD) by designing a reference optimal TFD and novel accuracy and resolution measures. The motivation comes from the need for a TFD performance evaluation method that is objective, capable of quantifying the TFD accuracy and resolution, can determine the performance difference among different TFDs, and suitable for signals with an arbitrary number of components, instantaneous frequency and amplitude. We formulate the proposed optimal TFD, namely the piece-wise spline Wigner-Ville distribution (PW-WVD), by decomposing a standard non-stationary signal model using piece-wise linear frequency modulated (LFM) basis and by exploiting the Wigner-Ville distribution optimality for LFM signals. We compare the designed PW-WVD to conventional optimal TFDs and show that the former is more suitable to serve as a reference for TFD performance evaluation. Using the PW-WVD we derive TFD accuracy and resolution measures, compare them to conventional approaches, and analyze their sensitivity to form a TFD selection criteria. We evaluate the accuracy and resolution of twelve different TFDs and develop precise TFD selection strategies with or without prior information on the signal parameters. Results indicate that the compact kernel distribution is the best performing TFD given no prior information on the signal parameters and different TFDs must be selected upon the availability of prior information.