Design of Two-Channel Quadrature Mirror Filter Banks Using Differential Evolution with Global and Local Neighborhoods

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7076)


This paper introduces a novel method named DEGL (Differential Evolution with global and local neighborhoods) regarding the design of two channel quadrature mirror filter with linear phase characteristics. To match the ideal system response characteristics, this improved variant of Differential Evolution technique is employed to optimize the values of the filter bank coefficients. The filter response is optimized in both pass band and stop band. The overall filter bank response consists of objective functions termed as reconstruction error, mean square error in pass band and mean square error in stop band. Effective designing can be performed if the objective function is properly minimized. The proposed algorithm can perform much better than the other existing design methods. Three different design examples are presented here for the illustrations of the benefits provided by the proposed algorithm.


Filter banks Quadrature Mirror Filter Sub-band coding perfect reconstruction DEGL 


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  1. 1.
    Vaidyanathan, P.P.: Multirate Systems and Filter Banks. Prentice Hall Inc. (1993)Google Scholar
  2. 2.
    Chandran, S., Ibrahim, M.K.: Adaptive antenna techniques using QMF bank. In: IEEE International Conference on Antennas and Propagation, pp. 257–260 (April 1995)Google Scholar
  3. 3.
    Petraglia, A., Mitra, S.K.: High speed A /D conversion incorporating a QMF. IEEE Trans. on Instrumentation and Measurement 41(3), 427–431 (1992)CrossRefGoogle Scholar
  4. 4.
    Chan, S.C., Pun, C.K.S., Ho, K.L.: New design and realization techniques for a class of perfect reconstruction two-channel FIR filter banks and wavelet bases. IEEE Transactions Signal Processing 52(7), 2135–2141 (2004)CrossRefGoogle Scholar
  5. 5.
    Johnston, J.D.: A filter family designed for use in quadrature mirror filter banks. In: Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing, pp. 291–294 (April 1980)Google Scholar
  6. 6.
    Pirani, G., Zingarelli, V.: An analytical formula for the design of quadrature mirror filters. IEEE Transactions Acoustic, Speech, Signal Processing ASSP-32, 645–648 (1984)CrossRefGoogle Scholar
  7. 7.
    Jain, V.K., Crochiere, R.E.: Quadrature mirror filter design in time domain. IEEE Transactions on Acoustics Speech and Signal Processing ASSP-32, 353–361 (1984)CrossRefGoogle Scholar
  8. 8.
    Chen, C.K., Leem, J.H.: Design of quadrature mirror filters with linear phase in the frequency domain. IEEE Transactions on Circuits and Systems II 39(9), 593–605 (1992)CrossRefGoogle Scholar
  9. 9.
    Lim, Y.C., Yang, R.H., Koh, S.N.: The design of weighted minimax quadrature mirror filters. IEEE Transactions Signal Processing 41(5), 1780–1789 (1993)CrossRefzbMATHGoogle Scholar
  10. 10.
    Andrew, L., Franques, V.T., Jain, V.K.: Eigen design of quadrature mirror fil-ters. IEEE Trans. Circuits Syst. II Analog Digit.Signal Process. 44(9), 754–757 (1997)CrossRefGoogle Scholar
  11. 11.
    Yu, Y.J., Lim, Y.C.: New natural selection process and chromosome encoding for the design of multiplier less lattice QMF using genetic algorithm. In: 8th IEEE International Conf. Electronics, Circuits and Systems, vol. 3, pp. 1273–1276 (2001)Google Scholar
  12. 12.
    Bregovic, R., Saramaki, T.: Two-channel FIR filter banks - A tutorial review and new results. In: Proceeding Second International Workshop on Transforms and Filter Banks, Brandenburg, Germany (March 1999)Google Scholar
  13. 13.
    Bregovic, R., Saramaki, T.: A general-purpose optimization approach for design-ing two-channel FIR filter banks. IEEE Transactions on Signal Processing 51(7) (July 2003)Google Scholar
  14. 14.
    Kumar, A., Singh, G.K., Anand, R.S.: Design of Quadrature Mirror Filter Bank us-ing Particle Swarm Optimization (PSO). International Journal of Recent Trends in Engineering 1(3) (May 2009)Google Scholar
  15. 15.
    Upendar, J., Gupta, C.P., Singh, G.K.: Design of two-channel quadrature mirror filter bank using particle swarm optimization. Elsevier Science Direct Digital Signal Processing 20, 304–313 (2010)CrossRefGoogle Scholar
  16. 16.
    Storn, R., Price, K.: Differential evolution a simple and efficient heuristic for global optimization over continuous spaces. J. Global Optimization 11(4), 341–359 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Mendes, R., Kennedy, J.: The fully informed particle swarm: Simpler may be better. IEEE Trans. Evol. Comput. 8(3), 204–210 (2004)CrossRefGoogle Scholar
  18. 18.
    Storn, R., Price, K.V.: Differential Evolution - a simple and efficient adaptive scheme for global optimization over continuous spaces, Technical Report TR-95-012, ICSI (1995),
  19. 19.
    Liang, J.J., Qin, A.K., Suganthan, P.N., Baskar, S.: Comprehensive learning particle swarm optimizer for global optimization of multimodal functions. IEEE Trans. Evol. Comput. 10(3), 281–295 (2006)CrossRefGoogle Scholar
  20. 20.
    Das, S., Abraham, A., Chakraborty, U.K., Konar, A.: Differential Evolution Using a Neighborhood-Based Mutation Operator. IEEE Transactions on Evolutionary Computation 13(3), 526–553 (2009)CrossRefGoogle Scholar
  21. 21.
    Qu, B.Y., Suganthan, P.N., Liang, J.J.: Differential Evolution with Neighborhood Mutation for Multimodal Optimization. IEEE Trans. on Evolutionary Computation, doi:10.1109/TEVC.2011.2161873Google Scholar

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© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Electronics & Tele-Comm. EngineeringJadavpur UniversityKolkataIndia

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