Near Perfect Reconstruction Quadrature Mirror Filter

Authors: A. Kumar, G. K. Singh, R. S. Anand

Abstract:

In this paper, various algorithms for designing quadrature mirror filter are reviewed and a new algorithm is presented for the design of near perfect reconstruction quadrature mirror filter bank. In the proposed algorithm, objective function is formulated using the perfect reconstruction condition or magnitude response condition of prototype filter at frequency (ω = 0.5π) in ideal condition. The cutoff frequency is iteratively changed to adjust the filters coefficients using optimization algorithm. The performances of the proposed algorithm are evaluated in term of computation time, reconstruction error and number of iterations. The design examples illustrate that the proposed algorithm is superior in term of peak reconstruction error, computation time, and number of iterations. The proposed algorithm is simple, easy to implement, and linear in nature.

Keywords: Aliasing cancellations filter bank, Filter banks, quadrature mirror filter (QMF), subband coding.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1331565

References:

[1] P. P. Vaidyanathan, "Multirate and filter bank," Englewood Cliffs, NJ: Prentice-Hall, 1993.
[2] A. Croisier, D. Esteban, C. Galand, "Perfect channel splitting by use of interpolation /decimation/tree decomposition techniques," International conference on Information Sciences and Systems, Patras, 1976.
[3] D. Esteban and C. Galand, "Application of quadrature mirror filters to split band voice coding schemes," in Proceedings IEEE International Conference on Acoustics, Speech, and Signal Processing, May 1977, pp. 191-195.
[4] J. D. Johnston, "A filter family designed for use in quadrature mirror filter banks," in Proceedings IEEE International Conference on Acoustics, Speech, and Signal Processing, pp. 291-294, April 1980.
[5] R. Hooke and T. Jeaves, "Direct search solution of numerical and statistical problems," J. Ass. Comp. Mach., Vol. 8, pp. 212-229, April 1961.
[6] C. D. Creusere and S.K. Mitra, "A simple method for designing high quality prototype filters for M- band pseudo QMF bank," IEEE Transactions on Signal Processing, 1995, vol. 43, pp. 1005-1007.
[7] A. Jain, R. Saxena, and S. C. Saxena, "A simple alias free QMF system with near perfect reconstruction," Journal of Indian Institute Science, 2005, 85, 1-10.
[8] A. Ramakrishna and M. J. Nigam, "A Simple Method to Design FIR QMF Bank," Fourth International Conference on intelligent sensing and information processing, 2006 ICISIP, pp. 236-239.
[9] http://www.engineer.tamuk.edu/Spark/chap5.pdf.
[10] S. K. Mitra, "Digital signal processing: A computer based approach," Tata McGraw Hill Edition, 2006.