Discrete-time system modelling in L-p with orthonormal basis functions

In this paper, model sets for linear time-invariant systems spanned by fixe d pole orthonormal bases are investigated. The obtained model sets are show n to be complete in L-p(T) (1 < p < infinity), the Lebesque spaces of funct ions on the unit circle T, and in C(T), the space of periodic continuous fu nctions on T. The L-p norm error bounds for estimating systems in L-p(T) by the partial sums of the Fourier series formed by the orthonormal functions are computed for the case 1 < p < infinity. Some inequalities on the mean growth of the Fourier series are also derived. These results have applicati on in estimation and model reduction. (C) 2000 Elsevier Science B.V. All ri ghts reserved.