On the existence of a disk algebra basis

In this paper, approximation of discrete-time systems by fixed pole orthono rmal basis functions is investigated. It is shown that if accumulation poin ts of basis poles do not cover the entire unit circle, then the Fourier ser ies 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 extend ed to rational wavelets. (C) 2000 Published by Elsevier Science B.V. All ri ghts reserved.