Two-Channel Parallelogram QMF Banks Using 2-D NSHP Digital All-Pass Filters

Abstract

This paper presents a novel structure for the analysis and synthesis filters of two-channel parallelogram quadrature mirror filter (PQMF) banks. Two-dimensional recursive digital all-pass filters (DAFs) with nonsymmetric half-plane (NSHP) support regions are used as the basic sections for building this structure. With an appropriate combination of the 2-D NSHP DAFs, the resultant analysis/synthesis filters possess a 2-D doubly complementary symmetry that facilitates the design and implementation of two-channel PQMF banks. Moreover, the proposed PQMF bank provides approximately linear-phase response without magnitude distortion. The design problem of the proposed PQMF bank is appropriately formulated to result in a minimization of the linear-phase error associated with the 2-D NSHP DAFs in the <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$p$</tex></formula> th-norm <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$(L_{p})$</tex></formula> sense. Efficient design techniques are developed to solve the <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$L_{p}$</tex> </formula> optimization problems. Simulation results for illustration and comparison are also provided.