Finite Prolate Spheroidal Sequences and Their Applications I: Generation and Properties

The finite prolate spheroidal sequences are those finite sequences which have extremal energy concentrations both in space and spatial frequency. The first part of the paper is devoted to a study of the eigenvalue problem defining the sequences. This reveals those fundamental properties of the sequences which are relevant in image processing applications and shows how they can be generated efficiently. A new version of the sampling theorem is also demonstrated.