基于低通等效的带通PSWF脉冲产生方法

椭圆球面波函数不存在闭式解,带通 PSWF脉冲信号的实时求解产生限制了 PSWF的应用。针对这一问题,从带通信号低通等效的基本原理出发,分析了带通 PSWF脉冲信号的低通等效形式；在此基础上,反向运用低通等效原理,给出了一种带通 PSWF脉冲重构产生方法,并用 FPGA对该方法进行了设计实现。这一方法将带通 PSWF脉冲信号的产生转化为其低通等效形式的产生,可有效降低信号产生的复杂度,该方法引入了正余弦变换,建立了非正弦 PSWF脉冲产生与正余弦变换技术之间的联系,为 PSWF脉冲的工程应用奠定了基础。

A Novel Method of Generating Prolate Spheroidal Wave Functions Based on Low-Pass Equivalent

As prolate spheroidal wave function (PSWF) has no close solutions, for the issue of generating PSWF pulse in re.al time. Based on the low-pass equivalent principle, the low-pass equivalent form of the band-pass PSWF pulse was ana.lyzed, then, a method of generating PSWF based on low-pass equivalent was proposed. The method converted the genera.tion of band-pass PSWF into the generation of low-pass equivalent signal, led to a reduction in complexity of generatingPSWF in real time. The method introduced the sine or cosine convert, established a link between the PSWF signal and thesine or cosine convert, laid the foundation of the application of PSWF.