The Optimum Running Approximation of A Class of Time-Limited Signals That is Realized by FIR Filter Bank

摘要

For a certain FIR filter bank, when a supreme signal that realizes given running worst-case measure of error exists, we prove that there exists a one-to-one correspondence between error in a wide time interval and error in a small segment. Based on this correspondence, we prove that the presented approximation minimizes various continuous running worst-case measures of error at the same time. Finally, an application to transmultiplexer is discussed.