The representation of two-dimensional sequences as one-dimensional sequences

Abstract

A number of signal processing techniques which have been developed for processing one-dimensional sequences do not generalize to the processing of two-dimensional signals, largely due to the absence of a two-dimensional factorization theorem. In an attempt to circumvent this problem, a specific representation of two-dimensional sequences as one-dimensional sequences is presented in this paper. Using this mapping several two-dimensional problems can be viewed as one-dimensional problems and approached using one-dimensional techniques. This representation is valid both for signals of finite extent and for the more general class of signals with rational Z-transforms. In this paper we consider applications of these techniques for high speed convolution, processing of drum scans, and two-dimensional finite impulse response (FIR) filter design.