A compact algorithm for evaluating linear prolate functions

Linear prolate functions (LPFs) are a set of bandlimited functions constructed to be invariant to the Fourier transform and orthonormal on the real line for the given bandwidth. Their unique properties make LPFs useful in signal processing. A method is described to evaluate the LPs by solving the eigensystem of the corresponding differential equation. The eigenvectors of this system provide the coefficients of the representation of the required functions into a series of spherical Bessel functions. The method omits several cumbersome steps inherent to previous algorithms without loss of accuracy.