Recovering signals from inner products involving prolate spheroidals in the presence of jitter

Abstract

Abstract. The paper deals with recovering band-and energy-limited signals from a finite set of perturbed inner products involving the prolate spheroidal wavefunctions. The measurement noise (bounded by δ) and jitter meant as perturbation of the ends of the integration interval (bounded by γ) are considered. The upper and lower bounds on the radius of information are established. We show how the error of the best algorithms depends on γ and δ. We prove that jitter causes error of order Ω 3 2 γ, where [−Ω, Ω] is a bandwidth, which is similar to the error caused by jitter in the case of recovering signals from samples.

Analysis of spectral approximations using prolate spheroidal wave functions

“…The prolate spheroidal wave functions, originated from the context of separation of variables for the Helmholtz equation in spheroidal coordinates (see, e.g., [20,12]), have been extensively used for a variety of physical and engineering applications, such as wave scattering, signal processing, and antenna theory (see, for instance, [3,11,17]). Most notably, a series of papers by Slepian et al [25,19,26] and the recent works by Xiao and Rokhlin et al [33,32,24,22] have shown that the PSWFs are a natural and optimal apparatus for approximating bandlimited functions.…”

A Review of Prolate Spheroidal Wave Functions from the Perspective of Spectral Methods

“…(iii) Development of numerical methods using PSWFs as basis functions, e.g., spectral/ spectral-elements methods (see, e.g., [5,7,10,13,50,51,92,107]), and wavelets (see, e.g., [15,[88][89][90]).…”