Signal, Image and Video Processing

, Volume 5, Issue 1, pp 121–131 | Cite as

A closed form design method for the two-channel quadrature mirror filter banks

  • Anil Kumar
  • G. K. Singh
  • R. S. Anand
Original Paper


This paper presents a simple and efficient closed form method for designing two-channel linear phase quadrature mirror filter (QMF) banks with prescribed stopband attenuation and channel overlap. The proposed method is based on optimum passband edge frequency, which is calculated using empirical formulas instead of using optimization algorithm. Different window functions are used to design the prototype filter for QMF banks. When compared to other existing methods, the proposed method reduces computation time (CPU time) and amplitude distortion (e am ), which results in a simpler and efficient design procedure for the applications where the design must be carried out in real or quasi-real-time. Several design examples are included to illustrate the proposed method and its improved performances over other exiting methods. An application of the proposed method is considered in the area of subband coding of ultrasound image.


Closed form Filter banks Multirate filter banks QMF bank 


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  1. 1.
    Painter T., Spanias A.: Perceptual coding of digital audio. Proc. IEEE 88(4), 451–513 (2000)CrossRefGoogle Scholar
  2. 2.
    Afonso V.X., Tompkins W.J., Nguyen T.Q., Luo S.: ECG beat detection using filter banks. IEEE Trans. Biomed. Eng. 46(2), 192–202 (1999)CrossRefGoogle Scholar
  3. 3.
    Cruz-Roldan F., Bravo-Santos A.M., Martin P.M., Jimenez– Martinez R.: Design of multi-channel near perfect reconstruction transmultiplexers using cosine modulated filter banks. Signal Process. 83(5), 1079–1091 (2003)zbMATHCrossRefGoogle Scholar
  4. 4.
    Vaidyanathan P.P.: Multirate systems and filter banks. Prentice-Hall, Englewood Cliffs (1993)zbMATHGoogle Scholar
  5. 5.
    Lu H.C., Tzeng S.T.: Two-channel perfect reconstruction linear phase FIR filter banks for subband image coding using genetic algorithm approach. Int. J. Syst. Sci. 1(1), 25–32 (2001)MathSciNetGoogle Scholar
  6. 6.
    Uppalapati H., Rastgar H., Ahmadi M.: Design of QMF banks with canonical signed digit coefficients using genetic algorithm. Proc. IEEE Int. Conf. Commun. Circuits Syst. 2, 682–686 (2005)CrossRefGoogle Scholar
  7. 7.
    Park S.Y., Cho N.I.: Design of signed powers of two coefficient perfect reconstruction QMF bank using Cordic algorithms. IEEE Trans. Circuits Syst. I 53(6), 1254–1265 (2006)CrossRefGoogle Scholar
  8. 8.
    Johnston, J.D.: A filter family designed for use in quadrature mirror filter banks. In: Proceedings IEEE international conference on acoustics, speech, and signal processing, April 1980, pp. 291–294 (1980)Google Scholar
  9. 9.
    Jain V.K., Crochiere R.E.: Quadrature mirror filter design in time domain. IEEE Trans. Acoust. Speech Signal Process. ASSP-32(2), 353–361 (1984)CrossRefGoogle Scholar
  10. 10.
    Chen C.K., Lee J.H.: Design of quadrature mirror filters with linear phase in the frequency domain. IEEE Trans. Circuits Syst. II 39(9), 593–605 (1992)zbMATHCrossRefGoogle Scholar
  11. 11.
    Xu H., Lu W.-S., Antoniou A.: An improved method for the design of FIR quadrature mirror-image filter banks. IEEE Trans. Signal Process. 46(5), 1275–1281 (1998)CrossRefGoogle Scholar
  12. 12.
    Xu H., Lu W.-S., Antoniou A.: A new method for the design of FIR QMF banks. IEEE Trans. Circuits Syst. II Analog Digital Process. 45(7), 922–927 (1998)CrossRefGoogle Scholar
  13. 13.
    Bregovic R., Saramaki T.: A general-purpose optimization approach for designing two-channel FIR filter banks. IEEE Trans. Signal Process. 51(7), 1781–1791 (2003)CrossRefMathSciNetGoogle Scholar
  14. 14.
    Bregovic R., Saramaki T.: Design of Two channel low delay FIR filter banks using constraint optimization. J. Comput. Inf. Technol. 4, 341–348 (2000)CrossRefGoogle Scholar
  15. 15.
    Creusere C.D., Mitra S.K.: A simple method for designing high quality prototype filters for M-band pseudo QMF banks. IEEE Trans. Signal Process. 43(4), 1005–1007 (1995)CrossRefGoogle Scholar
  16. 16.
    Cruz-Roldan F., Lopez P.A., Bascon S.M., Lawson S.S.: An efficient and simple method for designing prototype filters for cosine modulated Pseudo QMF banks. IEEE Signal Process. Lett. 9(1), 29–31 (2002)CrossRefGoogle Scholar
  17. 17.
    Kumar A., Singh G.K., Anand R.S.: Near perfect reconstruction quadrature mirror filter. Int. J. Comput. Sci. Eng. 2(3), 121–123 (2008)Google Scholar
  18. 18.
    Sahu O.P., Soni M.K., Talwar I.M.: Marquardt optimization method to design two-channel quadrature mirror filter banks. Digital Signal Process. 16(6), 870–879 (2006)CrossRefGoogle Scholar
  19. 19.
    Goh C.K., Lim Y.C.: An efficient algorithm to design weighted minimax PR QMF banks. IEEE Trans. Signal Process. 47(12), 3303–3314 (1999)CrossRefGoogle Scholar
  20. 20.
    Jou Y.D.: Design of two channel linear phase QMF bank based on neural networks. Signal Process. 87(5), 1031–1044 (2007)zbMATHCrossRefGoogle Scholar
  21. 21.
    Kok C.W., Siu W.C., Law Y.M.: Peak constrained least QMF banks. Signal Process. 88(10), 2363–2371 (2008)zbMATHCrossRefGoogle Scholar
  22. 22.
    Bregovic, R., Saramaki, T.: Two-channel FIR filter banks—a tutorial review and new results. In: Proceedings of second international workshop transforms filter banks, vol. TICSP 4, pp. 507–558, May 1999, Brandenburg, GermanyGoogle Scholar
  23. 23.
    Mitra S.K.: Digital Signal Processing: A Computer Based Approach. McGraw-Hill, New York (2006)Google Scholar
  24. 24.
    Viholainen, A., Saramaki, T., Renfors, M.: Nearly perfect-reconstruction cosine-modulated filter bank design for VDSL modems. In: Proceeding of international conference on electronics, circuits and systems, pp. 373–376 (1999)Google Scholar
  25. 25.
    Chang, D.C., Lee, D.L.: Prototype filter design for a cosine-modulated filter bank transmultiplexers. In: Proceeding of IEEE international conference, APCCAS 2006, pp. 454–457 (2006)Google Scholar
  26. 26.
    Dolecek G.J.: Multirate Systems: Design and Applications. Idea group of publishing, Hershey (2002)Google Scholar
  27. 27.
    Berger S.W.A., Antoniou A.: An efficient closed form design method for cosine modulated filter banks using window function. Signal Process. 87(5), 811–823 (2007)CrossRefGoogle Scholar
  28. 28.
    Vetterli M.: Multi-dimensional sub-band coding: some theory and algorithms. Signal Process. 6, 97–112 (1984)CrossRefMathSciNetGoogle Scholar
  29. 29.
    Woods J.W., O’Neil S.D.: Subband coding of images. IEEE Trans. Acoustics Speech Signal Process. ASSP-34(5), 1278–1288 (1986)CrossRefGoogle Scholar
  30. 30.
    Smith M.J.T., Eddin S.L.: Analysis/synthesis techniques for subband image coding. IEEE Trans. Acoustics Speech Signal Process. 38(8), 1446–1456 (1990)CrossRefGoogle Scholar
  31. 31.
    Husqy J.H., Gjerde T.: Computationally efficient sub-band coding of ECG signals. Med. Eng. Phys. 18(2), 132–142 (1996)CrossRefGoogle Scholar
  32. 32.
    Wei D., Bovik A.C.: Comments on subband coding of images using asymmetrical filter banks. IEEE Trans Image Process. 8(1), 122–124 (1999)CrossRefGoogle Scholar
  33. 33.
    Cruz-Roldan F., Martin P.M., Landete J.S., Velasco M.B., Saramaki T.: A fast windowing based technique exploiting spline functions for designing modulated filter banks. IEEE Trans. Circuits Syst. I 56(1), 168–176 (2009)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2009

Authors and Affiliations

  1. 1.Department of Electrical EngineeringIndian Institute of TechnologyRoorkeeIndia

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