椭圆球面波函数的快速重构算法

摘要

椭圆球面渡函数是一种极具应用前景的非正弦函数。针对现有求解算法效率低，不易硬件实现的问题，基于带通采样定理并结合椭圆球面波函数的时限带限特性，提出了一种快速重构算法并推导得出了重构函数，给出了近似解析解表达式，对比分析了算法的求解精度和计算复杂度。结果表明：该算法求解速度快、精度高、计算复杂度低，可用于任意频段上的椭圆球面波函数的数值求解。该算法更适于硬件实现。%Prolate spheroidal wave funetion（PSWF）is non-sinusoidal and it is diffi- cult for hardware implementation. The inefficiency and limitation of numerical algorithm restrict its theoretical development and application. For solving this problem, a new fast reconstructing algorithm for solving PSWF is proposed based on the sampling theorem. The reconstructing function and the approximate analytic solution are derived and the complexity of the algorithm is analyzed. The simulation result shows that the proposed method is more efficient than existing ones in the same precision. The proposed algorithm can be used for calculating numerical solutions of PSWF in any frequency bands and it is convenient for hardware implementation.