基于傅里叶级数的椭圆球面波信号时频分析

Prolate spheroidal wave functions signal time-frequency analysis based on Fourier series

基于数值仿真的椭圆球面波(PSWFs)信号时频分析,无法获取PSWFs信号某一频率幅值随时间变化显式表达式。针对这一问题,引入傅里叶级数,将PSWFs信号按傅里叶级数展开,利用Wigner-Ville分布(WVD)分析每一频率随时间的变化情况,并重点研究了PSWFs信号WVD时频中心点、时频峰值点、时频零点等特殊点随自身参数(时间带宽积、阶数)之间的变化规律。理论和仿真结果表明:PSWFs信号WVD具有良好的对称性,其时频中心点幅值极性与阶数有关;PSWFs信号WVD由时频峰值圈(时频峰值点连线)组成,且时频峰值圈位置及个数与阶数、时间带宽积密切相关。时频中心点、时频峰值点、时频零点等特殊点,可作为PSWFs信号WVD重要特征参量,其特性规律能够为PSWFs信号时频检测奠定理论基础。

The prolate spheroidal wave functions(PSWFs)signal time-frequency analysis based on numerical simulation fails to obtain the explicit expression that a certain frequency amplitude of PSWFs signal changes with time.Therefore,the Fourier series is introduced,the PSWFs signal is expanded according to the Fourier series,the Wigner-Ville distribution(WVD)is used to analyze that each frequency changes with time,and the change rule that the special points(time-frequency center point,time-frequency peak point and time-frequency zero point)of PSWFs signal WVD change with their own parameters(time-bandwidth product and order)is emphatically studied.The theoretical and simulation results show that the PSWFs signal WVD has good symmetry,and the amplitude polarity of its time-frequency center point is related to the order,the PSWFs signal WVD is composed of time-frequency peak circles(connecting lines of time-frequency peak points),and both the position and number of the peak circles are closely related to the order and time bandwidth product.The special points(time-frequency center point,time-frequency peak point and time-frequency zero point)can be taken as the important characteristic parameters of PSWFs signal WVD,and their characteristic rules can lay a theoretical foundation for the time-frequency detection of PSWFs signal.