A Multidimensional Extension of Papoulis’ Generalized Sampling Expansion with the Application in Minimum Density Sampling

Abstract

This chapter is divided into two parts. In Part I, PapouHs’ one-dimensional generalized sampling expansion (GSE) is extended to multidimensional (M—D) band-limited functions. In Part II, using sample decimation, we will utilize the M—D GSE formulation to reduce the sampling density of M—D band-limited functions. The ultimate reduction leads to the minimum sampling density, which is equal to the area of the support of the function’s Fourier spectrum. This rate is analogous to the definition of the Nyquist rate for one-dimensional (1—D) band-limited functions.