快收敛带通椭圆球面波函数重构求解算法

以提高带通椭圆球面波函数(BPSWF)重构求解精度为出发点,提出一种快速收敛的BPSWF函数重构求解算法。根据采样定理,由采样信号重构恢复带通信号的带通滤波选择本质,给出基于采样定理的带通椭圆球面波函数重构求解通式;分析了重构求解算法的主要误差因素,提出通过改善重构基函数收敛性,提高BPSWF函数重构求解精度的基本思想;通过频域设计构造了一种时域快速收敛的带通PSWF重构基函数,进而提出一种快速收敛的BPSWF函数重构求解算法。理论和仿真分析结果表明:新重构的求解方法更适合于低频段BPSWF求解,与sinc基函数重构求解方法相比,求解精度高,求得的PSWF函数正交性好,能量聚集性佳。

Fast convergent algorithm of reconstructing bandpass prolate spheroidal wave function

In order to improve the accuracy of reconstructing Bandpass Prolate Spherical Wave Function(BPSWF),a fact convergent reconstruction algorithm is developed.According to the sampling theorem and the fact that bandpass signal can be recovered from its well sampling signal with a suitable bandpass filter,a general construction formula is given.Main factors inducing the errors of the reconstruction algorithm are analyzed,and the basic idea of using more convergent base functions to improve the reconstruction accuracy is proposed.A group of fast convergent base is given by design in frequency domain;then,the fast convergent algorithm of reconstructing BPSWF is proposed.Theoretical analysis and simulation results demonstrate that the new reconstruction algorithm is fit for recovering BPSWF of low frequency.Compared with the reconstruction method with sinc base function,the proposed algorithm can achieve higher reconstruction accuracy,which makes the recovered BPSWF get better orthogonality and energy concentration characteristics.