Linear-phase quadrature mirror filters with coefficients −1, 0 and + 1

Abstract

This paper considers the linear-phase quadrature mirror filters (LP-QMFs) with coefficients constrained to the values of −1, 0 and + 1. A new filter structure and a design technique based on a recently developed weighted least-squares (WLS) algorithm are presented. First, we design an LP-QMF with continuous coefficients using the WLS algorithm. This design process provides two favourable design results that the prototype LP analysis filter has least-squares stopband response and the resulting QMF bank shows quasi-equiripple reconstruction error behavior. In conjunction with the new proposed filter structure, we then present an efficient method to obtain a design solution with coefficients restricted to −1, 0 and + 1 in the minimax sense. Several design examples demonstrating the effectiveness of the proposed technique are provided.