Classification and labeling of the optimum discrete interpolation approximation by equivalent extension

Abstract

In the previous works, it is not shown that if there exists the concrete algorithm for deriving the optimum interpolation functions minimizing the supreme measure of the approximation error in |ω|≤π. In this paper, we show that FIR filter banks are classified into separable classes each of which has a fundamental FIR filter bank as its representative(label)and all the filter banks in a class have the solution because the fundamental filter bank has a solution.