SYSTOLIC ALGORITHMS FOR THE SOLUTION OF TOEPLITZ MATRICES

Abstract

In this paper a factorisation of certain symmetric circulant banded linear systems proposed by Evans [Evans 1981] is described. It can be shown that a banded Toeplitz matrix can be factorised into the product of easily inverted cyclic matrices. By using this factorisation, a solution can be derived for such matrices. Toeplitz matrices have become increasingly important with the rapid growth of signal and image processing. To achieve high performance, new systolic array designs for the algorithm shown above are implemented, A full description of the systolic array designs are given in a later section. The performance of the designs are discussed.