基于带通采样的椭圆球面波函数数值解法

摘要

针对椭圆球面波函数原数值解法存在计算量大、计算时间长的问题,提出了基于带通采样的新数值解法.新数值解法根据带通采样定理确定采样频率,利用原数值解法求得椭圆球面波函数带通采样值,对带通采样值进行上抽样、数字滤波和格拉姆-施密特正交化,求得椭圆球面波函数的近似数值解.理论分析和仿真结果表明,新数值解法能有效降低计算量、计算时间,而且采样点数量越大,效果越好.%Original numerical solution has the following disadvantages: heavy calculation burden and long computing time, a new numerical solution based on bandpass sampling is proposed. The new solution specifies sampling frequency according to bandpass sampling theorem, achieves bandpass sampling value of prolate spheroidal wave functions with original numerical solution, and achieves approximate value by conducting upsampling, digits filtering and Gram-Schmidt's orthogonalization for bandpass sampling value. Theoretical analysis and simulation results show that the new numerical solution can effectively reduced calculation burden and computing time. In addition, the larger the number of sampling points is, the better the effect will be.