On the existence of a disk algebra basis

Abstract

In this paper, approximation of discrete-time systems by fixed pole orthonormal basis functions is investigated. It is shown that if accumulation points of basis poles do not cover the entire unit circle, then the Fourier series of some function in the disk algebra A (the set of functions continuous in the closed unit disk and analytic inside the unit circle) with respect to the basis diverges in the supremum norm. The divergence result is extended to rational wavelets.