Circuits, Systems, and Signal Processing

, Volume 36, Issue 11, pp 4441–4452 | Cite as

On the Design of Arbitrary Shape Two-Channel Filter Bank Using Eigenfilter Approach

  • Swati P. MadheEmail author
  • Bhushan D. Patil
  • Raghunath S. Holambe


In our paper, we have extended an eigenfilter-based approach for the design of arbitrary shape two-channel filter bank. The method is based on designing arbitrary shape analysis filter, followed by the design of complementary arbitrary shape synthesis filter. In eigenfilter designing, eigenvector is computed corresponding to the minimum eigenvalue of a real, symmetric and positive-definite matrix. In our case, this matrix is formulated using the combination of pass-band and stop-band errors between frequency response of desired and designed arbitrary shape filters. After designing the arbitrary shape analysis filter, same is used in perfect-reconstruction constraint, for the design of complementary arbitrary shape synthesis filter. The length of this arbitrary shape synthesis filter should satisfy certain condition depending on the length of the pre-designed arbitrary shape analysis filter. This ensures the existence of the solution for the complementary arbitrary shape synthesis filter. We have demonstrated the usefulness of this method in designing the arbitrary shapes such as, differentiator, integrator and comb shape.


Arbitrary shape filter bank Eigenfilter Perfect reconstruction Pass-band error Stop-band error 


  1. 1.
    L. Andrew, V.T. Franques, V.K. Jain, Eigen design of quadrature mirror filters. IEEE Trans. Circuits Syst. II Analog Digit. Signal Process. 44(9), 754–757 (1997). doi: 10.1109/82.625010 CrossRefGoogle Scholar
  2. 2.
    R.A. Horn, C.R. Johnson, Matrix Analysis (Cambridge University Press, 2012)Google Scholar
  3. 3.
    T. Q. Nguyen. The eigenfilter for the design of linear-phase filters with arbitrary magnitude response. in 1991, ICASSP-91., 1991 International Conference on Acoustics, Speech, and Signal Processing, vol. 3, pp. 1981–1984 April 1991. doi: 10.1109/ICASSP.1991.150785
  4. 4.
    B.D. Patil, P.G. Patwardhan, V.M. Gadre, Eigenfilter approach to the design of one-dimensional and multidimensional two-channel linear-phase fir perfect reconstruction filter banks. IEEE Trans. Circuits Syst. I: Regul. Pap. 55(11), 3542–3551 (2008)MathSciNetCrossRefGoogle Scholar
  5. 5.
    J. Reger, A. Amthor, B. Schmidt, FIR-Filter Design for Derivative Estimation in a Nanopositioning System, in Proceedings 55th International Scientific Colloquium, vol. 1 (2010), pp. 424–429Google Scholar
  6. 6.
    M. Sharma, Vikram M. Gadre, S. Porwal, An eigenfilter-based approach to the design of time-frequency localization optimized two-channel linear phase biorthogonal filter banks. Circuits Syst. Signal Process. 34(3), 931–959 (2014). doi: 10.1007/s00034-014-9885-3 CrossRefGoogle Scholar
  7. 7.
    A. Tkacenko, P.P. Vaidyanathan, T.Q. Nguyen, On the eigenfilter design method and its applications: a tutorial. IEEE Trans. Circuits Syst. II Analog Digit. Signal Process. 50(9), 497–517 (2003). doi: 10.1109/TCSII.2003.816942 CrossRefGoogle Scholar
  8. 8.
    P. Vaidyanathan, Truong Nguyen, Eigenfilters: a new approach to least-squares fir filter design and applications including nyquist filters. IEEE Trans. Circuits Syst. 34(1), 11–23 (1987). doi: 10.1109/TCS.1987.1086033 CrossRefGoogle Scholar
  9. 9.
    P.P. Vaidyanathan, Multirate Systems and Filter Banks, 2nd edn. (Prentice Hall, Englewood Cliffs, 1992)zbMATHGoogle Scholar
  10. 10.
    P. Zahradnik, M. Vlcek, Analytical design method for optimal equiripple comb fir filters. IEEE Trans. Circuits Syst. II Express Br. 52(2), 112–115 (2005). doi: 10.1109/TCSII.2001.840117 CrossRefGoogle Scholar
  11. 11.
    W.-P. Zhu, M. Omair Ahmad, M.N.S. Swamy, A least-square design approach for 2d fir filters with arbitrary frequency response. IEEE Trans. Circuits Syst. II Analog Digit. Signal Process. 46(8), 1027–1034 (1999). doi: 10.1109/82.782044 CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  • Swati P. Madhe
    • 1
    Email author
  • Bhushan D. Patil
    • 2
  • Raghunath S. Holambe
    • 3
  1. 1.Cummins College of EngineeringPuneIndia
  2. 2.BangaloreIndia
  3. 3.SGGS Institute of Engineering and TechnologyNandedIndia

Personalised recommendations