Discrete-time system modelling in Lp with orthonormal basis functions

Abstract

In this paper, model sets for linear time-invariant systems spanned by fixed pole orthonormal bases are investigated. The obtained model sets are shown to be complete in Lp(T) (1 < p < ?), the Lebesque spaces of functions on the unit circle T, and in C(T), the space of periodic continuous functions on T. The Lp norm error bounds for estimating systems in Lp(T) by the partial sums of the Fourier series formed by the orthonormal functions are computed for the case 1 < p < ?. Some inequalities on the mean growth of the Fourier series are also derived. These results have application in estimation and model reduction