DISCRETE-TO-DISCRETE PROLATE SPHEROIDAL WAVE FUNCTIONSAND FINITE DURATION DISCRETE FRACTIONAL FOURIER TRANSFORM

摘要

In practical applications, the signal we deal with is usuallya finite duration one. Continuous prolate spheroidal wavefunctions (PSWFs) were proposed by Slepian and are usefulfor analyzing the characters of the finite duration continuousFourier transform. Based on the PSWF, the finitefractional Fourier transform was developed. In this paper,for digital signal processing application, we derive discreteto-discrete prolate spheroidal wave functions. Then, wedefine the finite duration discrete fractional Fourier transform(fi-DFRFT) based on it. We can use the fi-DFRFT forfilter design, multiplexing, modulation, encryption, andoptical system simulation. The fi-DFRFT has the advantageof less complexity and is useful for deal with the noise thatis chirp-like and finite duration.