中文摘要：

针对椭圆球面波函数（PSWF）信号的实时产生问题，给出了PSWF的傅里叶级数展开式，研究了PSWF信号的有限傅里叶展开，并对其误差进行了分析，最后提出了基于离散傅里叶逆变换重构产生PSWF信号波形的方法．该方法建立了PSWF信号与正余弦级数之间的联系，并将高效、成熟的傅里叶变换技术运用到PSWF信号的产生上，提高了PSWF数字波形产生的硬件可实现性．同时，也为其他复杂波形信号的实时产生提供了一种切实可行的产生方法．

英文摘要：

Aimed at the issue of the generation of prolate spheroidal wave function（PSWF） in real time, based on the properties of PSWFs, and starting from the Fourier series expansion, the Fourier expansion formulas of PSWFs was proposed, the finite Fourier expansion was investigated, and the error of the finite Fourier expansion was analysed. A method to reconstruct PSWFs based on IDFT was presented, which established a link between the PSWF signal and the sine or cosine series, introduced the efficient and mature Fourier transform technology to the generation of PSWFs, and improved hardware realizability of PSWFs, providing a practical way to generate other complex signal waveforms in real time.