On prolate spheroidal wave functions for signal processing

A spectral window, ideal from the energy concentration viewpoint, is known to be a prolate spheroidal wave function S-0l(c,eta). These functions exhib it unique properties that are of special importance in signal processing. H owever, in the literature they are often being reported as functions too di fficult to handle numerically and they are therefore in practice used much less than they should be. On the other hand, powerful and efficient numeric al techniques have been devised to compute the full set of prolate spheroid al wave functions and they have successfully been applied to various scatte ring problems in acoustics and electrodynamics. These techniques should be useful to problems in signal processing both in multiple applications of co nventional spheroidal functions and, appropriately modified, to compute so- called generalized spheroidal wave functions, in treating signals depending on several variables. (C) 2001 John Wiley & Sons, Inc.