Design of Two Channel Quadrature Mirror Filter Bank: A Multi-Objective Approach
- 1.3k Downloads
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.
KeywordsDifferential Evolution Multiobjective Optimization Stop Band Multiobjective Evolutionary Algorithm Quadrature Mirror Filter
Unable to display preview. Download preview PDF.
- 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
- 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
- 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
- 11.Golberg, D.E.: Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley, Massachusetts (1989)Google Scholar
- 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.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
- 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.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
- 24.Zhang, Q., Li, H.: MOEA/D: A Multiobjective Evolutionary Algorithm Based on Decomposition. IEEE Trans. Evolutionary Computation, 712–731 (2007)Google Scholar