Skip to main content

Noniterative Design of 2-Channel FIR Orthogonal Filters

Abstract

This paper addresses the problem of obtaining an explicit expression of all real FIR paraunitary filters. In this work, we present a general parameterization of 2-channel FIR orthogonal filters. Unlike other approaches which make use of a lattice structure, we show that our technique designs any orthogonal filter directly, with no need of iteration procedures. Moreover, in order to design an-tap 2-channel paraunitary filterbank, it suffices to choose independent parameters, and introduce them in a simple expression which provides the filter coefficients directly. Some examples illustrate how this new approach can be used for designing filters with certain desired properties. Further conditions can be eventually imposed on the parameters so as to design filters for specific applications.

References

  1. 1.

    Daubechies I: Ten Lectures on Wavelets. SIAM, Philadelphia, Pa, USA; 1992.

    Google Scholar 

  2. 2.

    Vaidyanathan PP: Multirate Systems and Filter Banks. Prentice-Hall, Englewood Cliffs, NJ, USA; 1993.

    Google Scholar 

  3. 3.

    Vetterli M, Kovacevic J: Wavelets and Subband Coding. Prentice-Hall, Englewood Cliffs, NJ, USA; 1995.

    Google Scholar 

  4. 4.

    Strang G, Nguyen T: Wavelets and Filter Banks. Wellesley-Cambridge Press, Wellesley, Mass, USA.; 1996.

    Google Scholar 

  5. 5.

    Daubechies I, Sweldens W: Factoring wavelet transforms into lifting steps. Journal of Fourier Analysis and Applications 1998,4(3):247-269. 10.1007/BF02476026

    MathSciNet  Article  Google Scholar 

  6. 6.

    Vaidyanathan PP, Nguyen TQ, Doganata Z, Saramaki T: Improved technique for design of perfect reconstruction FIR QMF banks with lossless polyphase matrices. IEEE Transactions on Acoustics, Speech, and Signal Processing 1989,37(7):1042–1056. 10.1109/29.32282

    Article  Google Scholar 

  7. 7.

    Phoong S-M, Kim CW, Vaidyanathan PP, Ansari P: A new class of two-channel biorthogonal filter banks and wavelet bases. IEEE Transactions on Signal Processing 1995,43(3):649–665. 10.1109/78.370620

    Article  Google Scholar 

  8. 8.

    Kovacevic J, Sweldens W: Wavelet families of increasing order in arbitrary dimensions. IEEE Transactions on Image Processing 2000,9(3):480–496. 10.1109/83.826784

    Article  Google Scholar 

  9. 9.

    Domínguez Jiménez ME: New technique for design of 2-channel FIR paraunitary filter banks. Proceedings of the 7th IASTED International Conference on Signal and Image Processing (SIP '05), August 2005, Honolulu, Hawaii, USA 220–225.

    Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to M. Elena Domínguez Jiménez.

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://doi.org/creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reprints and Permissions

About this article

Cite this article

Jiménez, M.E.D. Noniterative Design of 2-Channel FIR Orthogonal Filters. EURASIP J. Adv. Signal Process. 2007, 045816 (2006). https://doi.org/10.1155/2007/45816

Download citation

Keywords

  • Information Technology
  • Explicit Expression
  • Quantum Information
  • Lattice Structure
  • Independent Parameter