Analytical Minimization of L₂-Sensitivity for All-Pass Fractional Delay Digital Filters with Normalized Lattice Structure

Abstract

This letter theoretically analyzes and minimizes the L₂-sensitivity for all-pass fractional delay digital filters of which structure is given by the normalized lattice structure. The L₂-sensitivity is well known as one of the useful evaluation functions for measuring the performance degradation caused by quantizing filter coefficients into finite number of bits. This letter deals with two cases: L₂-sensitivity minimization problem with scaling constraint, and the one without scaling constraint. It is proved that, in both of these two cases, any all-pass fractional delay digital filter with the normalized lattice structure becomes an optimal structure that analytically minimizes the L₂-sensitivity.