Explicit and Progressive Solution Method for Wigner-Ville Distribution of Prolate Spheroidal Wave Functions Signal

Considering the problems of the existing time-frequency analysis of Prolate Spheroidal Wave Functions (PSWFs) signals without explicit expressions, uncontrollable numerical simulation errors, and lack of symmetry in the time-frequency distribution results, Legendre polynomials and Wigner- Ville Distribution (WVD) are introduced in this paper, and an explicit and progressive solution method for PSWFs signal WVD is proposed. According to the error requirements, this method generates the Legendre polynomial WVD selfterms and cross-terms of the required order, and then multiplies them with the corresponding WVD-Legendre coefficients and superimposes linearly them to obtain the explicit and progressive expression of the PSWFs signal WVD. Theoretical and numerical simulation results show that the proposed method can produce an explicit and progressive expression of the PSWFs signal WVD that meets the error requirements, and can effectively maintain the original time-domain and frequency-domain symmetry of the signal. In addition, in the case of the same number of sampling points, compared with the PSWFs signal WVD based on the numerical solution, the PSWFs signal WVD obtained by the proposed method has a higher frequency domain resolution.