Skip to main content
SpringerLink
Log in

Closed-Form FIR Filter Design with Accurately Controllable Cut-Off Frequency

  • Published:
Circuits, Systems, and Signal Processing Aims and scope Submit manuscript

Abstract

To enhance the efficiency of designing finite impulse response (FIR) filters with a controllable cut-off frequency that possess excellent transfer characteristics, this paper proposes a closed-form filter design based on transfer characteristic compensation. First, a novel filter design based on a convolution window is presented, and the relationship between the spectrum of this window and the filter performance is elaborated. We then derive a three-stage filter design scheme that describes the design of an irregular filter, design of a compensation filter and filter summation. This scheme can be simplified into a closed-form design characterized by two analytic formulas by merging the intermediate steps. The configuration of a vital Kaiser window parameter is also derived. Numerical results show that the proposed closed-form design accurately controls the cut-off frequencies and exhibits a transfer performance comparable to the Remez design and the closed-form weighted least square (WLS) design. Moreover, our method is more efficiency than the closed-form WLS method for the design of high-order FIR filters.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  1. C.K. Ahn, Passive and exponential filter design for fuzzy neural networks. Inf. Sci. 238, 126–137 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  2. D. Bhattacharya, A. Antoniou, Real-time design of FIR filters by feedback neural networks. IEEE Signal Process. Lett. 3(5), 158–161 (1996)

    Article  Google Scholar 

  3. Q. Ding, M. Zhong, On designing H\(\infty \) fault detection filter for Markovian jump linear systems with polytopic uncertainties. Int. J. Innov. Comput. Inf. Control 6(3), 995–1004 (2010)

    Google Scholar 

  4. H. Han, Y.S. Ding, K.R. Hao, X. Liang, An evolutionary particle filter with the immune genetic algorithm for intelligent video target tracking. Comput. Math. Appl. 62(7), 2685C2695 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  5. K. Kaur, J.S. Dhillon, Design of digital IIR filters using integrated cat swarm optimization and differential evolution. Int. J. Comput. Appl. 99(4), 28–43 (2014)

    Google Scholar 

  6. S.S. Kidambi, An efficient closed-form approach to the design of linear-phase FIR digital filters with variable-bandwidth characteristics. Signal Process. 86, 1656C1669 (2006)

    Article  MATH  Google Scholar 

  7. A. Kumar, S. Suman, G.K. Singh, A new closed form method for design of variable bandwidth linear phase FIR filter using different polynomials. AEU Int. J. Electron. Commun. 68(4), 351C360 (2014)

    Article  Google Scholar 

  8. Z. Li, C. He, H.Z. Tan, Ainet-sl: artificial immune network with social learning and its application in FIR filter designing. Appl. Soft Comput. 13(12), 4557C4569 (2013)

    Article  Google Scholar 

  9. J.P. Magalhaes, J.M.N. Vieira, R. Gomez-Garcia, N.B. Carvalho, Bio-inspired hybrid filter bank for software-defined radio receivers. IEEE Trans. Microw. Theory Tech. 61(4), 1455–1466 (2013)

    Article  Google Scholar 

  10. R. Mahesh, A.P. Vinod, Reconfigurable low area complexity filter bank architecture based on frequency response masking for nonuniform channelization in software radio receivers. IEEE Trans. Aerosp. Electron. Syst. 47(2), 1241–1255 (2011)

    Article  Google Scholar 

  11. M. Mahrooghy, N.H. Younan, V.G. Anantharaj, J. Aanstoos, S. Yarahmadian, On the use of the genetic algorithm filter-based feature selection technique for satellite precipitation estimation. IEEE Geosci. Remote Sens. Lett. 9(5), 963–967 (2012)

    Article  Google Scholar 

  12. S. Mandal, S.P. Ghoshal, R. Kar, D. Mandal, Optimal linear phase finite impulse response band pass filter design using craziness based particle swarm optimization algorithm. J. Shanghai Jiaotong Univ. 16(6), 696–703 (2011)

    Article  Google Scholar 

  13. J.H. Mcclellan, T.W. Parks, L. Rabiner, A computer program for designing optimum FIR linear phase digital filters. IEEE Trans. Audio Electroacoust. 21(6), 506–526 (1973)

    Article  Google Scholar 

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

    Google Scholar 

  15. P. Mohindru, R. Khanna, S.S. Bhatia, A novel design technique for variable non-recursive digital filter based on FrFT. Electron. Electr. Eng. 121(5), 89–92 (2012)

    Google Scholar 

  16. A. Oppenheim, R. Schafer, J.R. Buck, Discrete-Time Signal Processing (Prentice-hall, Englewood Cliffs, 1989)

    MATH  Google Scholar 

  17. S.T. Pan, A canonic-signed-digit coded genetic algorithm for designing finite impulse response digital filter. Digit. Signal Process. 20(2), 314C327 (2010)

    Article  Google Scholar 

  18. T. Parks, J. Mcclellan, Chebyshev approximation for nonrecursive digital filters with linear phase. IEEE Trans. Circuit Theory 19(2), 189–194 (1972)

    Article  Google Scholar 

  19. M. Renfors, J. Yli-Kaakinen, F.J. Harris, Analysis and design of efficient and flexible fast-convolution based multirate filter banks. IEEE Trans. Signal Process. 62(15), 3768–3783 (2014)

    Article  MathSciNet  Google Scholar 

  20. S.K. Saha, S.P. Ghoshal, R. Kar, D. Mandal, Cat swarm optimization algorithm for optimal linear phase FIR filter design. ISA Trans. 52(6), 781–794 (2013)

    Article  Google Scholar 

  21. S.K. Saha, R. Kar, D. Mandal, S.P Ghoshal, Adaptive particle swarm optimization for low pass finite impulse response filter design. In 2013 International Conference on Communications and Signal Processing (ICCSP) (2013)

  22. B. Soltanian, A. Hagh Ghadam, M. Renfors, Utilization of multi-rate signal processing for GNSS-SDR receivers. EURASIP J. Adv. Signal Process. 2014(1), 1–13 (2014)

  23. S. Suman, A. Kumar, G.K. Singh, A new closed form method for design of variable bandwidth linear phase FIR filter using Bernstein multiwavelets. Int. J. Electron. 102(4), 635–650 (2015)

    Article  Google Scholar 

  24. P. Vaidyanathan, T.Q. 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)

    Article  Google Scholar 

  25. W.B. Ye, Y.J. Yu, Single-stage and cascade design of high order multiplierless linear phase FIR filters using genetic algorithm. IEEE Trans. Circuits Syst. I Regul. Pap. 60(11), 2987–2997 (2013)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Electronic Information Engineering, Tianjin University, Tianjin, 300072, China

    Xiangdong Huang, Yuedong Wang, Ziyang Yan, Hongyu Xian & Mingzhuo Liu

Authors
  1. Xiangdong Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yuedong Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ziyang Yan
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Hongyu Xian
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Mingzhuo Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xiangdong Huang.

Additional information

This work was supported by the National Natural Science Foundation of China under Grant 61271069.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Huang, X., Wang, Y., Yan, Z. et al. Closed-Form FIR Filter Design with Accurately Controllable Cut-Off Frequency. Circuits Syst Signal Process 36, 721–741 (2017). https://doi.org/10.1007/s00034-016-0330-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-016-0330-7

Keywords

Search

Navigation