Skip to main content
SpringerLink
Log in

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

  • Original Paper
  • Published:
Signal, Image and Video Processing Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Painter T., Spanias A.: Perceptual coding of digital audio. Proc. IEEE 88(4), 451–513 (2000)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  4. Vaidyanathan P.P.: Multirate systems and filter banks. Prentice-Hall, Englewood Cliffs (1993)

    MATH  Google Scholar 

  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)

    MathSciNet  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

  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)

    Article  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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. 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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  20. Jou Y.D.: Design of two channel linear phase QMF bank based on neural networks. Signal Process. 87(5), 1031–1044 (2007)

    Article  MATH  Google Scholar 

  21. Kok C.W., Siu W.C., Law Y.M.: Peak constrained least QMF banks. Signal Process. 88(10), 2363–2371 (2008)

    Article  MATH  Google Scholar 

  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, Germany

  23. Mitra S.K.: Digital Signal Processing: A Computer Based Approach. McGraw-Hill, New York (2006)

    Google Scholar 

  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)

  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)

  26. Dolecek G.J.: Multirate Systems: Design and Applications. Idea group of publishing, Hershey (2002)

    Google Scholar 

  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)

    Article  Google Scholar 

  28. Vetterli M.: Multi-dimensional sub-band coding: some theory and algorithms. Signal Process. 6, 97–112 (1984)

    Article  MathSciNet  Google Scholar 

  29. Woods J.W., O’Neil S.D.: Subband coding of images. IEEE Trans. Acoustics Speech Signal Process. ASSP-34(5), 1278–1288 (1986)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  31. Husqy J.H., Gjerde T.: Computationally efficient sub-band coding of ECG signals. Med. Eng. Phys. 18(2), 132–142 (1996)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electrical Engineering, Indian Institute of Technology, Roorkee, 247667, Uttrakhand, India

    Anil Kumar, G. K. Singh & R. S. Anand

Authors
  1. Anil Kumar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. K. Singh
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. R. S. Anand
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Anil Kumar.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kumar, A., Singh, G.K. & Anand, R.S. A closed form design method for the two-channel quadrature mirror filter banks. SIViP 5, 121–131 (2011). https://doi.org/10.1007/s11760-009-0147-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11760-009-0147-y

Keywords

Search

Navigation