Analysis and identification of discrete-time systems via discrete Legendre orthogonal polynomials

A new method of using discrete Legendre orthogonal polynomials (DLOPs) is proposed for the analysis and identification of linear time invariant discrete time systems. It is based on representing the DLOP expansion vector of the delayed function y(k — 1) in terms of that of the original discrete function y(k). Several examples are worked out to illustrate the utility of the method.