Numerical Algorithms for the Computation of Generalized Prolate Spheroidal Functions

Publication date: 8 October 2017

Abstract: Generalized Prolate Spheroidal Functions (GPSF) are the eigenfunctions of the truncated Fourier transform, restricted to D-dimensional balls in the spatial domain and frequency domain. Despite their useful properties in many applications, GPSFs are often replaced by crude approximations. The purpose of this paper is to review the elements of computing GPSFs and associated eigenvalues. This paper is accompanied by open-source code.

Has companion code repository: https://github.com/lederman/Prol

Mathematics Subject Classification ID

Computation of special functions and constants, construction of tables (65D20) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Numerical approximation and evaluation of special functions (33F05) Numerical methods in Fourier analysis (65T99)

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