On prolate spheroidal wave functions for signal processing

Abstract

AbstractA spectral window, ideal from the energy concentration viewpoint, is known to be a prolate spheroidal wave function S0l(c,η). These functions exhibit unique properties that are of special importance in signal processing. However, in the literature they are often being reported as functions too difficult to handle numerically and they are therefore in practice used much less than they should be. On the other hand, powerful and efficient numerical techniques have been devised to compute the full set of prolate spheroidal wave functions and they have successfully been applied to various scattering problems in acoustics and electrodynamics. These techniques should be useful to problems in signal processing both in multiple applications of conventional spheroidal functions and, appropriately modified, to compute so‐called generalized spheroidal wave functions, in treating signals depending on several variables. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001