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.