Skip to content


  • Research Article
  • Open Access

Noniterative Design of 2-Channel FIR Orthogonal Filters

EURASIP Journal on Advances in Signal Processing20062007:045816

  • Received: 1 January 2006
  • Accepted: 26 August 2006
  • Published:


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.


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

Authors’ Affiliations

TACA Research Group, ETSI Industriales, Universidad Politécnica de Madrid, Madrid, 28006, Spain


  1. Daubechies I: Ten Lectures on Wavelets. SIAM, Philadelphia, Pa, USA; 1992.View ArticleGoogle Scholar
  2. Vaidyanathan PP: Multirate Systems and Filter Banks. Prentice-Hall, Englewood Cliffs, NJ, USA; 1993.MATHGoogle Scholar
  3. Vetterli M, Kovacevic J: Wavelets and Subband Coding. Prentice-Hall, Englewood Cliffs, NJ, USA; 1995.MATHGoogle Scholar
  4. Strang G, Nguyen T: Wavelets and Filter Banks. Wellesley-Cambridge Press, Wellesley, Mass, USA.; 1996.MATHGoogle Scholar
  5. Daubechies I, Sweldens W: Factoring wavelet transforms into lifting steps. Journal of Fourier Analysis and Applications 1998,4(3):247-269. 10.1007/BF02476026MathSciNetView ArticleGoogle Scholar
  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. 10.1109/29.32282View ArticleGoogle Scholar
  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. 10.1109/78.370620View ArticleGoogle Scholar
  8. Kovacevic J, Sweldens W: Wavelet families of increasing order in arbitrary dimensions. IEEE Transactions on Image Processing 2000,9(3):480–496. 10.1109/83.826784View ArticleGoogle Scholar
  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


© M. Elena Domínguez Jiménez. 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.