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 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.

Neural network‐based design of 2‐channel quadrature mirror filter banks

“…If the third term on the right-hand part does not affect the optimization performance, the corresponding term −u m /τ m in (22) can be ignored to enhance convergence speed. 44,46,52 …”

Adaptive-Differential-Evolution-Based Design of Two-Channel Quadrature Mirror Filter Banks for Sub-Band Coding and Data Transmission

“…2) P-Best Crossover: The crossover operation used in MJADE_pBX is named as p-best crossover where for each donor vector, a vector is randomly selected from the p topranking vectors (according to their objective function values) in the current population and then normal binomial crossover is performed as in (19) between the donor vector and the randomly selected p-best vector to generate the trial vector at the same index. The parameter p is linearly reduced with generations in the following way:…”

2D orthogonal symmetricwavelet filters using allpass filters

“…Two dimensional (2D) wavelet filters are often needed to decompose 2D signals into directional components in image and video processing applications, and have been discussed in [4], [6], [11], [12]. In [6], a class of two channel quincunx wavelet filters had been presented by mapping 1D biorthogonal wavelet filters to the 2D case, but the resulting 2D quincunx wavelet filters are biorthogonal, not orthogonal.…”

“…In [6], a class of two channel quincunx wavelet filters had been presented by mapping 1D biorthogonal wavelet filters to the 2D case, but the resulting 2D quincunx wavelet filters are biorthogonal, not orthogonal. In [11] and [12], a class of two channel quincunx and parallelogram QMF banks had been proposed by using 2D nonseparable allpass filters. However, the proposed QMF banks did not satisfy the perfect reconstruction (PR) condition, and an additional 2D allpass filter was needed to compensate the phase distortion as a phase equalizer.…”