Frieden, B.R. (1971) Evaluation, Design and Extrapolation Methods for Optical Signals Based on Use of the Prolate Functions. Progress in Optics, 9, 311-407.

has been cited by the following article:

• TITLE: Linear Prolate Functions for Signal Extrapolation with Time Shift

  AUTHORS: Daniela Valente, Michael Cada, Jacek Ilow

  KEYWORDS: Real-Valued Band Limited Eigenvectors, Signal Decomposition, Signal Extrapolation

  JOURNAL NAME: Applied Mathematics, Vol.8 No.4, April 13, 2017

  ABSTRACT: We propose a low complexity iterative algorithm for band limited signal extrapolation. The extrapolation method is based on the decomposition of finite segments of the signal via truncated series of real-valued linear prolate functions. Our theoretical derivation shows that given a truncated series (up to a selectable value) of prolate functions, it is possible to extrapolate the band limited function elsewhere if each extrapolated portion of the function is subject only to moderate truncation errors that we quantify in this paper. The effects of different sources of errors have been analyzed via extensive simulations. We have investigated a property of the signal decomposition formula based on linear prolate functions whereby the integration interval does not need to be symmetric with respect to the origin while time-shifted prolate functions are used in the series.