Two-Channel Quincunx QMF Banks Using Two-Dimensional Digital Allpass Filters

Abstract

This paper presents a novel structure for the analysis and synthesis filters of two-channel quincunx quadrature mirror filter (QQMF) banks. This structure uses an appropriate combination of 2-D recursive digital allpass filters (DAFs) with symmetric half-plane (SHP) support regions. The proposed analysis/synthesis filters possess a 2-D doubly complementary half-band (DC-HB) property that facilitates the design and implementation of the proposed two-channel QQMF banks. Moreover, the proposed structure provides approximately linear-phase response without magnitude distortion. The design problem of the proposed QQMF banks is appropriately formulated to result in a linear optimization problem that only minimizes the linear-phase error associated with the 2-D SHP DAFs in the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> th-norm ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Lp</i> ) sense. Efficient design techniques are developed to solve the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Lp</i> optimization problem for finding the coefficients of the 2-D recursive SHP DAFs. Finally, we provide simulation results for illustration and comparison.