Simultaneous minimization of various worst case measures of error in FIR filter bank

Abstract

We present the optimum running-type approximation of FIR filter bank that minimizes various worst-case measures of error, simultaneously, with respect to each of two different sets of signals. The first set is a set of piecewise analytic time-limited but approximately band-limited signals. When a supreme signal that realizes the prescribed worst-case measure of error exists, we prove, firstly, that there exists one-to-one correspondence between error in a wide time interval and error in a small interval. Based on this one-to-one correspondence, we prove that the approximation presented in this paper is the optimum in some sense. Secondly, we consider a set of band-limited signals with a main-lobe and a pair of small side-lobes and obtain similar conclusion.