椭圆球面波信号Wigner-Ville分布显式渐近求解方法

针对现有的椭圆球面波函数(PSWFs)信号时频分析无显式表达式、数值仿真误差不可控、时频分布结果对称性缺失等问题，该文引入Legendre多项式以及Wigner-Ville分布(WVD)，提出一种PSWFs信号WVD显式渐近求解方法。该方法根据误差要求，生成所需阶数的Legendre多项式WVD自项、交叉项，进而与对应的WVD-Legendre系数相乘后线性叠加，获取PSWFs信号WVD显式渐近表达式。理论及数值仿真结果表明，所提方法能够产生满足误差要求的PSWFs信号WVD显式渐近表达式，且能够有效保持信号原有的时域、频域对称性。此外，在相同采样点数情况下，相对于基于数值解的PSWFs信号WVD，所提方法获得的PSWFs信号WVD频域分辨率更高。

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 self-terms 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.