Simultaneous Minimization of Upper-Limit of Various Measures of Error in FIR Filter Banks Based on Mapping of Errors

摘要

(1) When a supreme signal that realizes the prescribed worst-case measure of error exists, we prove that there exists one-to-one correspondence between error in a wide time interval and error in a small segment. Based on this one-to-one correspondence, we prove that the approximation presented in this paper is the optimum. (2) Then, we consider a set of signals having Fourier spectrums expressed by Fourier series with many but finite terms. Under modification of this set of signals and aid of a Mini-Max theorem, we construct a concrete model of the optimum continuous approximation that realizes the optimum discrete approximation by sampling.