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

This paper proposes an improved and adaptive variant of the differential evolution algorithm for the design of two-channel quadrature mirror filters with linear phase characteristics. To match the ideal system response characteristics, the algorithm is employed to optimize the values of the filter bank coefficients. The filter response is optimized in both passband and stopband. The overall filter bank response aims at minimizing objectives like reconstruction error, mean square error in passband, and mean square error in stopband. Effective designing can be achieved by efficiently minimizing the objective function. The proposed algorithm is able to perform better than the other existing design methods. Five different design examples are presented to validate the effectiveness of the proposed approach over other conventional design techniques, as well as state-of-the-art evolutionary algorithms found in the literature.

[1]  Sotirios K Goudos,et al.  Pareto Optimal Microwave Filter Design Using Multiobjective Differential Evolution , 2010, IEEE Transactions on Antennas and Propagation.

[2]  Yong Ching Lim,et al.  The design of weighted minimax quadrature mirror filters , 1993, IEEE Trans. Signal Process..

[3]  Girish Kumar Singh,et al.  Design of Quadrature Mirror Filter Bank using Particle Swarm Optimization (PSO) , 2009 .

[4]  Andreas Antoniou,et al.  An improved method for the design of FIR quadrature mirror-image filter banks , 1998, IEEE Trans. Signal Process..

[5]  R. Crochiere,et al.  Quadrature mirror filter design in the time domain , 1984 .

[6]  Tülay Yildirim,et al.  Performance Evaluation of Evolutionary Algorithms for Optimal Filter Design , 2012, IEEE Transactions on Evolutionary Computation.

[7]  F. Wilcoxon.  Individual Comparisons by Ranking Methods , 1945 .

[8]  P. N. Suganthan,et al.  Differential Evolution: A Survey of the State-of-the-Art , 2011, IEEE Transactions on Evolutionary Computation.

[9]  Jie Chen,et al.  Optimal Contraction Theorem for Exploration–Exploitation Tradeoff in Search and Optimization , 2009, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[10]  V. Zingarelli,et al.  An analytical formula for the design of quadrature mirror filters , 1984 .

[11]  Kok Lay Teo,et al.  Two-Channel Linear Phase FIR QMF Bank Minimax Design via Global Nonconvex Optimization Programming , 2010, IEEE Transactions on Signal Processing.

[12]  R. Storn,et al.  Differential evolution a simple and efficient adaptive scheme for global optimization over continu , 1997 .

[13]  Amit Konar,et al.  Two-Dimensional IIR Filter Design with Modern Search Heuristics: a Comparative Study , 2006, Int. J. Comput. Intell. Appl..

[14]  Gurvinder S. Baicher.  Towards optimal implementation of a class of quadrature mirror filter using genetic algorithms , 2010, 2010 IEEE Fifth International Conference on Bio-Inspired Computing: Theories and Applications (BIC-TA).

[15]  Nurhan Karaboga,et al.  Digital IIR Filter Design Using Differential Evolution Algorithm , 2005, EURASIP J. Adv. Signal Process..

[16]  O. P. Sahu,et al.  Marquardt optimization method to design two-channel quadrature mirror filter banks , 2006, Digit. Signal Process..

[17]  Jun Zhang,et al.  Orthogonal Learning Particle Swarm Optimization , 2009, IEEE Transactions on Evolutionary Computation.

[18]  Sanjit K. Mitra,et al.  High-speed A/D conversion incorporating a QMF bank , 1992 .

[19]  P. Vaidyanathan,et al.  Theory and design of uniform DFT, parallel, quadrature mirror filter banks , 1986 .

[20]  Sotirios K. Goudos,et al.  Application of a Differential Evolution Algorithm with Strategy Adaptation to the Design of Multi-Band Microwave Filters for Wireless Communications , 2010 .

[21]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[22]  Francisco Herrera,et al.  A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms , 2011, Swarm Evol. Comput..

[23]  Arthur C. Sanderson,et al.  JADE: Adaptive Differential Evolution With Optional External Archive , 2009, IEEE Transactions on Evolutionary Computation.

[24]  Tapio Saramäki,et al.  A general-purpose optimization approach for designing two-channel FIR filterbanks , 2003, IEEE Trans. Signal Process..

[25]  Ju-Hong Lee,et al.  Two-Channel Parallelogram QMF Banks Using 2-D NSHP Digital All-Pass Filters , 2010, IEEE Transactions on Circuits and Systems I: Regular Papers.

[26]  V. K. Jain,et al.  Eigen design of quadrature mirror filters , 1997 .

[27]  Ville Tirronen,et al.  Super-fit control adaptation in memetic differential evolution frameworks , 2009, Soft Comput..

[28]  P. N. Suganthan,et al.  Differential Evolution Algorithm With Strategy Adaptation for Global Numerical Optimization , 2009, IEEE Transactions on Evolutionary Computation.

[29]  Carlos A. Coello Coello,et al.  A comparative study of differential evolution variants for global optimization , 2006, GECCO.

[30]  Anil Kumar,et al.  An Improved Method for Designing Quadrature Mirror Filter Banks via Unconstrained Optimization , 2010, J. Math. Model. Algorithms.

[31]  Rainer Storn,et al.  Differential Evolution Design of an IIR-Filter with Requirements for Magnitude and Group Delay , 1995 .

[32]  Rainer Storn,et al.  Differential evolution design of an IIR-filter , 1996, Proceedings of IEEE International Conference on Evolutionary Computation.

[33]  Ville Tirronen,et al.  An Enhanced Memetic Differential Evolution in Filter Design for Defect Detection in Paper Production , 2008, Evolutionary Computation.

[34]  Nikolaus Hansen,et al.  A restart CMA evolution strategy with increasing population size , 2005, 2005 IEEE Congress on Evolutionary Computation.

[35]  Giovanni Iacca,et al.  Ockham's Razor in memetic computing: Three stage optimal memetic exploration , 2012, Inf. Sci..

[36]  James D. Johnston,et al.  A filter family designed for use in quadrature mirror filter banks , 1980, ICASSP.

[37]  M. K. Ibrahim,et al.  Adaptive antenna techniques using QMF banks , 1995 .

[38]  Shing-Chow Chan,et al.  New design and realization techniques for a class of perfect reconstruction two-channel FIR filterbanks and wavelets bases , 2004, IEEE Transactions on Signal Processing.

[39]  Tapio Saramäki,et al.  Two-Channel FIR Filter Banks – A Tutorial Review and New Results , 2014 .

[40]  Yong Ching Lim,et al.  New natural selection process and chromosome encoding for the design of multiplierless lattice QMF using genetic algorithm , 2001, ICECS 2001. 8th IEEE International Conference on Electronics, Circuits and Systems (Cat. No.01EX483).

[41]  Carlos García-Martínez,et al.  Memetic Algorithms for Continuous Optimisation Based on Local Search Chains , 2010, Evolutionary Computation.

[42]  Ville Tirronen,et al.  Recent advances in differential evolution: a survey and experimental analysis , 2010, Artificial Intelligence Review.

[43]  Girish Kumar Singh,et al.  Design of two-channel quadrature mirror filter bank using particle swarm optimization , 2010, Digit. Signal Process..

[44]  Jing J. Liang,et al.  Comprehensive learning particle swarm optimizer for global optimization of multimodal functions , 2006, IEEE Transactions on Evolutionary Computation.

[45]  Charng-Kann Chen,et al.  Design of quadrature mirror filters with linear phase in the frequency domain , 1992 .

[46]  Amit Konar,et al.  Differential Evolution Using a Neighborhood-Based Mutation Operator , 2009, IEEE Transactions on Evolutionary Computation.