Extrapolation of band-limited signals and the finite Zak transform

Abstract

We propose a new formulation of the Gerchberg–Papoulis algorithm for extrapolation of band-limited signals. The new formulation is obtained by translating the fundamental operations of the Gerchberg–Papoulis procedure, the truncation and the Fourier transform, into the language of the finite Zak transform. The use of the Zak transform results in a significant reduction in the number of multiplications required by the Gerchberg–Papoulis algorithm in the case of narrow-band and certain wide-band signals, and in an increased flexibility of the algorithm. Tensor product formalism will be used throughout this work as this formalism provides powerful tools for analyzing and coding constructions and algorithms.