Design of Two Channel Quadrature Mirror Filter Bank: A Multi-Objective Approach

  • Subhrajit Roy
  • Sk. Minhazul Islam
  • Saurav Ghosh
  • Shizheng Zhao
  • Ponnuthurai Nagaratnam Suganthan
  • Swagatam Das
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7077)

Abstract

In Digital Signal processing domain the Quadrature Mirror Filter (QMF) design problem is one of the most important problems of current interest. While designing a Quadrature Mirror Filter the goal of the designer is to achieve minimum values of Mean Square Error in Pass Band (MSEP), Mean Square Error in Stop Band (MSES), Square error of the overall transfer function of the QMF bank at the quadrature frequency and Measure of Ripple (mor). In contrast to the existing optimization-based methods that attempt to minimize a weighted sum of the four objectives considered here, in this article we consider these as four distinct objectives that are to be optimized simultaneously in a multi-objective framework. To the best of our knowledge, this is the first time to apply MO approaches to solve this problem. We use one of the best known Multi-Objective Evolutionary Algorithms (MOEAs) of current interest called NSGA-II as the optimizer. The multiobjective optimization (MO) approach provides greater flexibility in design by producing a set of equivalent final solutions from which the designer can choose any solution as per requirements. Extensive simulations reported shows that results of NSGA-II is superior to that obtained by two state-of-the-art single objective optimization algorithms namely DE and PSO.

Keywords

Differential Evolution Multiobjective Optimization Stop Band Multiobjective Evolutionary Algorithm Quadrature Mirror Filter 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Johnston, J.D.: A filter family designed for use in quadrature mirror filter banks. In: Proc. IEEE Int. Conf. Acoustics, Speech, Signal Processing, pp. 291–294 (1980)Google Scholar
  2. 2.
    Bellanger, M.G., Daguet, J.L.: TDM-FDM transmultiplexer: Digital Poly phase and FFT. IEEE Trans. Commun. 22(9), 1199–1204 (1974)CrossRefGoogle Scholar
  3. 3.
    Gu, G., Badran, E.F.: Optimal design for channel equalization via the filter bank approach. IEEE Trans. Signal Process 52(2), 536–544 (2004)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Esteban, D., Galand, C.: Application of quadrature mirror filter to split band voice coding schemes. In: Proc. IEEE International Conference on Acoustics, Speech, and Signal Processing (ASSP), pp. 191–195 (1977)Google Scholar
  5. 5.
    Liu, Q.G., Champagne, B., Ho, D.K.C.: Simple design of over sampled uniform DFT filter banks with application to sub-band acoustic echo cancellation. Signal Process 80(5), 831–847 (2000)CrossRefMATHGoogle Scholar
  6. 6.
    Chen, C.K., Lee, J.H.: Design of quadrature mirror filters with linear phase in the frequency domain. IEEE Trans. Circuits Syst. 39(9), 593–605 (1992)CrossRefMATHGoogle Scholar
  7. 7.
    Jou, Y.D.: Design of two-channel linear-phase quadrature mirror filter banks based on neural networks. Signal Process 87(5), 1031–1044 (2007)CrossRefMATHGoogle Scholar
  8. 8.
    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
  9. 9.
    Haddad, K.C., Stark, H., Galatsanos, N.P.: Design of two-channel equiripple FIR linear-phase quadrature mirror filters using the vector space projection method. IEEE Signal Process. Lett. 5(7), 167–170 (1998)CrossRefGoogle Scholar
  10. 10.
    Bregovic, R., Saramaki, T.: A general purpose optimization approach for designing two-channel FIR filter banks. IEEE Trans. Signal Process. 51(7), 1783–1791 (2003)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Golberg, D.E.: Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley, Massachusetts (1989)Google Scholar
  12. 12.
    Kennedy, J., Eberhart, R.: Particle swarm optimization. In: Proceedings of the IEEE International Conference Neural Networks, vol. 4, pp. 1942–1948 (1995)Google Scholar
  13. 13.
    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), http://http.icsi.berkeley.edu/~storn/litera.html
  14. 14.
    Das, S., Suganthan, P.N.: Differential Evolution: A Survey of the State-of-the-Art. IEEE Trans. Evolutionary Computation 15(1), 4–31 (2011)CrossRefGoogle Scholar
  15. 15.
    Zhao, S.Z., Willjuice, M.I., Baskar, S., Suganthan, P.N.: Multi-objective Robust PID Controller Tuning using Two Lbests Multi-objective Particle Swarm Optimization. Information Sciences 181(16), 3323–3335 (2011)CrossRefGoogle Scholar
  16. 16.
    Pal, S., Das, S., Basak, A., Suganthan, P.N.: Synthesis of difference patterns for monopulse antennas with optimal combination of array-size and number of subarrays - A multiobjective optimization approach. Progress in Electromagnetics Research, PIER B 21, 257–280 (2010)Google Scholar
  17. 17.
    Upender, J.P., Gupta, C.P., Singh, G.K.: Design of two-channel quadrature mirror filter bank using particle swarm optimization. Signal Processing 20, 304–313 (2010), doi:10.1016/j.dsp.2009.06.014Google Scholar
  18. 18.
    Zhou, A., Qu, B.-Y., Li, H., Zhao, S.-Z., Suganthan, P.N., Zhang, Q.: Multi-objective Evolutionary Algorithms: A Survey of the State-of-the-art. Swarm and Evolutionary Computation 1(1), 32–49 (2011)CrossRefGoogle Scholar
  19. 19.
    Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation 6(2), 182–197 (2002)CrossRefGoogle Scholar
  20. 20.
    Abido, M.A.: A novel multiobjective evolutionary algorithm for environmental/economic power dispatch. Electric Power Systems Research 65, 71–81 (2003)CrossRefGoogle Scholar
  21. 21.
    Swaminathan, K., Vaidyanathan, P.P.: Theory and design of uniform DFT, parallel QMF banks. IEEE Trans. Circuits Syst. 33(12), 1170–1191 (1986)CrossRefGoogle Scholar
  22. 22.
    Zhao, S.Z., Suganthan, P.N.: Two-lbests Based Multi-objective Particle Swarm Optimizer. Engineering Optimization 43(1), 1–17 (2011), doi:10.1080/03052151003686716MathSciNetCrossRefGoogle Scholar
  23. 23.
    Qu, B.Y., Suganthan, P.N.: Multi-Objective Evolutionary Algorithms based on the Summation of Normalized Objectives and Diversified Selection. Information Sciences 180(17), 3170–3181 (2010)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Zhang, Q., Li, H.: MOEA/D: A Multiobjective Evolutionary Algorithm Based on Decomposition. IEEE Trans. Evolutionary Computation, 712–731 (2007)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Subhrajit Roy
    • 1
  • Sk. Minhazul Islam
    • 1
  • Saurav Ghosh
    • 1
  • Shizheng Zhao
    • 2
  • Ponnuthurai Nagaratnam Suganthan
    • 2
  • Swagatam Das
    • 1
  1. 1.Dept. of Electronics and Telecommunication Engg.Jadavpur UniversityKolkataIndia
  2. 2.Dept. of Electronics and Electrical Engg.Nanyang Technological UnivrsitySingapore

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