The design of two-channel linear-phase quadrature mirror filter (QMF) banks constructed by real infinite impulse response (IIR) digital all-pass filters is considered. The design problem is appropriately formulated to result in a simple optimisation problem. Using a variant of Karmarkar's algorithm, the optimisation problem can be efficiently solved through a frequency sampling and iterative approximation method to find the real coefficients for the IIR digital all-pass filters. The resulting two-channel QMF banks possess an approximately linear phase response without magnitude distortion. The effectiveness of the proposed technique is achieved by forming an appropriate Chebyshev approximation of the desired phase response and then finding its solution from a linear subspace in a few iterations. Finally, several simulation examples are presented for illustration and comparison.
The design of two-channel linear-phase nonuniform-division filter (NDF) banks constructed by infinite impulse response (IIR) digital allpass filters (DAFs) in the sense of error criteria is considered. First, the theory of two-channel NDF bank structures using two IIR DAFs is developed. Then, the design problem is appropriately formulated to result in a simple optimization problem. Utilizing a variant of Karmarkar's algorithm, we can efficiently solve the optimization problem through a frequency sampling and iterative approximation method to find the coefficients for the IIR DAFs. The resulting two-channel NDF banks can possess approximately linear-phase response without magnitude distortion. The effectiveness of the proposed technique is achieved by forming an appropriate Chebyshev approximation of a desired phase response and then to find its solution from a linear subspace in a few iterations. Several simulation examples are presented for illustration and comparison.
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 allpass 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 linearphase error associated with the 2-D NSHP DAFs in the th-norm sense. Efficient design techniques are developed to solve the optimization problems. Simulation results for illustration and comparison are also provided. Index Terms-Doubly complementary (DC) filter, nonsymmetric half-plane (NSHP) filter, parallelogram quadrature mirror filter (PQMF) bank.
SUMMARYThis paper presents a general structure using 1-D and two-dimensional (2-D) recursive digital all-pass filters (DAFs) for the design of 2-D recursive circularly symmetric digital low-pass filters (CS-DLFs). The general structure is a cascade of two stages composed of all-pass building blocks. The first stage is a parallel connection of a 2-D recursive DAF with a symmetric half-plane (SHP) support for its filter coefficients and a 2-D pure delay block. The second stage composed of a parallel connection of a 1-D recursive DAF and a 1-D pure delay block is used for eliminating the unwanted pass-band induced by the first stage. As a result, the design of a 2-D CS-DLF in either the least-squares or the minimax sense can be formulated in a simple linear optimization problem in terms of the weighted-phase response error for each DAF. Design results with nearly circularly symmetric magnitude response and approximately linear phase are also provided for illustration and comparison.
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