Quadrature mirror filter

About: Quadrature mirror filter is a research topic. Over the lifetime, 955 publications have been published within this topic receiving 28900 citations.

Generalized coiflets with nonzero-centered vanishing moments

Abstract: We show that imposing a certain number of vanishing moments on a scaling function (e.g., coiflets) leads to fairly small phase distortion on its associated filter bank in the neighborhood of DC. However, the phase distortion at the other frequencies can be much larger. We design a new class of real-valued, compactly supported, orthonormal, and nearly symmetric wavelets (we call them generalized coiflets) with a number of nonzero-centered vanishing moments equally distributed on scaling function and wavelet. Such a generalization of the original coiflets offers one more free parameter, the mean of the scaling function, in designing filter banks. Since this parameter uniquely characterizes the first several moments of the scaling function, it is related to the phase response of the lowpass filter at low frequencies. We search for the optimal parameter to minimize the maximum phase distortion of the filter bank over the lowpass half-band. Also, we are able to construct nearly odd-symmetric generalized coiflets, whose associated lowpass filters are surprisingly similar to those of some biorthogonal spline wavelets. These new wavelets can be useful in a broad range of signal and image processing applications because they provide a better tradeoff between the two desirable but conflicting properties of the compactly supported and real-valued wavelets, i.e., orthonormality versus symmetry, than the original coiflets.

An octave-band family of non-redundant directional filter banks

Abstract: This paper introduces an octave-band family of directional filter banks for images, capable of dividing the spatial frequency spectrum both angularly and radially using an efficient structure. The new directional filter bank employs efficient separable analysis and synthesis filters with perfect reconstruction. Unique to the octave-band directional filter bank family are the properties of joint radial frequency selectivity and pyramid oriented frequency selectivity, all within a maximally decimated structure.

Factorization approach to unitary time-varying filter bank trees and wavelets

Abstract: A complete factorization of all optimal (in terms of quick transition) time-varying FIR unitary filter bank tree topologies is obtained. This has applications in adaptive subband coding, tiling of the time-frequency plane and the construction of orthonormal wavelet and wavelet packet bases for the half-line and interval. For an M-channel filter bank the factorization allows one to construct entry/exit filters that allow the filter bank to be used on finite signals without distortion at the boundaries. One of the advantages of the approach is that an efficient implementation algorithm comes with the factorization. The factorization can be used to generate filter bank tree-structures where the tree topology changes over time. Explicit formulas for the transition filters are obtained for arbitrary tree transitions. The results hold for tree structures where filter banks with any number of channels or filters of any length are used. Time-varying wavelet and wavelet packet bases are also constructed using these filter bank structures. the present construction of wavelets is unique in several ways: 1) the number of entry/exit functions is equal to the number of entry/exit filters of the corresponding filter bank; 2) these functions are defined as linear combinations of the scaling functions-other methods involve infinite product constructions; 3) the functions are trivially as regular as the wavelet bases from which they are constructed. >

An efficient gbest-guided Cuckoo Search algorithm for higher order two channel filter bank design

Abstract: This paper proposes a new algorithm based on Gbest-guided Cuckoo Search (GCS) algorithm for the design of higher order Quadrature Mirror Filter (QMF) bank. Although the optimization of lower order filters can be performed easily by applying existing meta-heuristic optimization techniques like Particle Swarm Optimization (PSO), Artificial Bee Colony (ABC) etc., these methods are unsuccessful in searching higher order filter coefficients due to multimodality and nonlinear problem space; leads to some undesirable behaviors in filter responses like ripples in transition band, lower stop-band attenuation etc.. Comparison with other available results in the literature indicate that the proposed method exhibits an 69.02% increase in stop-band attenuation and 99.71% reduction in Perfect Reconstruction Error (PRE) of higher order filter bank. Besides, the percentage improvements in Fitness Function Evaluations (FFEs) of GCS based 55th order QMF bank design with respect to PSO, ABC and CSA are 81%, 82% and 59% respectively, and execution time is improved by 73%, 72% and 42% respectively. The simulation results also reveal that the proposed approach exhibits lowest mean and variance in different assessment parameters of filter bank and it does not require tuning of algorithmic parameters whereas in standard CSA replacement factor need to be adjusted. Further, the proposed algorithm is tested on six standard benchmark problems and complex benchmark functions from the CEC 2013 where it demonstrated significant performance improvements than other existing methods.