The approximation of almost time and band limited functions by their expansion in some orthogonal polynomials bases
Provides theoretical approximation rates for a niche class of functions in signal processing, but the results are incremental and lack concrete numerical benchmarks.
The paper investigates the approximation quality of almost time and band-limited functions using Hermite, Legendre, and Chebyshev polynomial expansions, deriving rates for Sobolev space approximation and Legendre series of prolate spheroidal wave functions, with numerical examples.
The aim of this paper is to investigate the quality of approximation of almost time and almost band-limited functions by its expansion in three classical orthogonal polynomials bases: the Hermite, Legendre and Chebyshev bases. As a corollary, this allows us to obtain the quality of approximation in the L 2 --Sobolev space by these orthogonal polynomials bases. Also, we obtain the rate of the Legendre series expansion of the prolate spheroidal wave functions. Some numerical examples are given to illustrate the different results of this work.