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Link to original content: https://doi.org/10.1007/s11760-015-0856-3
A new method for higher-order linear phase FIR digital filter using shifted Chebyshev polynomials | Signal, Image and Video Processing Skip to main content
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A new method for higher-order linear phase FIR digital filter using shifted Chebyshev polynomials

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Abstract

In this work, a new method for the design of linear phase finite impulse response (FIR) filters using shifted Chebyshev polynomial is proposed. In this method, magnitude response of FIR filter is approximated with the help of shifted Chebyshev polynomials. The number of polynomials used for approximation depends upon the order of filter. Design problem of filter is constructed as minimization of integral mean-square error between the ideal response and actual response through differentiating it with respect to its coefficients, which leads to a system of linear equations. The simulation results included in this paper show the efficiency of proposed method. It is also evident from the results that the proposed method is suitable for higher filter taps.

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References

  1. Mitra, S.K.: Digital Signal Processing: A Computer-Based Approach. McGraw-Hill School Education Group, New York (2001)

    Google Scholar 

  2. Chan, S.C., Pun, C.K.S., Ho, K.L.: A new method for designing FIR filters with variable characteristics. IEEE Signal Process. Lett. 11(2), 274–277 (2004)

    Article  Google Scholar 

  3. Kidambi, S.S.: An efficient closed-form approach to the design of linear-phase FIR digital filters with variable-bandwidth characteristics. Signal Process. 86(7), 1656–1669 (2006)

    Article  MATH  Google Scholar 

  4. Suman, S., Kumar, A., Singh, G.K.: 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 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  7. Karaboga, N., Cetinkaya, B.: Design of digital FIR filters using differential evolution algorithm. Circuits Syst. Signal Process. 25(5), 649–660 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  8. Oliveira Jr, H.A., Petraglia, A., Petraglia, M.R., Oliveira, H.A.: Frequency domain FIR filter design using fuzzy adaptive simulated annealing. Circuits Syst. Signal Process. 28(6), 899–911 (2009)

    Article  MATH  Google Scholar 

  9. Joaquim, M.B., Lucietto, C.A.S.: A nearly optimum linear-phase digital FIR filters design. Digit. Signal Process. 21(6), 690–693 (2011)

    Article  Google Scholar 

  10. Wang, X.H., He, Y.G.: A neural network approach to FIR filter design using frequency-response masking technique. Signal Process. 88(12), 2917–2926 (2008)

    Article  MATH  Google Scholar 

  11. Suckley, D.: Genetic algorithm in the design of FIR filters. IEEE Proc. G IET Circuits Devices Syst. 138(2), 234–238 (1991)

    Article  Google Scholar 

  12. Ababneh, J.I., Bataineh, M.H.: Linear phase FIR filter design using particle swarm optimization and genetic algorithms. Digit. Signal Process. 18(4), 657–668 (2008)

    Article  Google Scholar 

  13. Boudjelaba, K., Ros, F., Chikouche, D.: An efficient hybrid genetic algorithm to design finite impulse response filters. Expert Syst. Appl. 41(13), 5917–5937 (2014)

    Article  Google Scholar 

  14. Sarangi, A., Sarangi, S.K., Padhy, S.K., Panigrahi, S.P., Panigrahi, B.K.: Swarm intelligence based techniques for digital filter design. Appl. Soft Comput. 25, 530–534 (2014)

    Article  Google Scholar 

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

    Article  Google Scholar 

  16. Chen, L.W., Jou, Y.D., Chen, F.K., Hao, S.S.: Eigenfilter design of linear-phase FIR digital filters using neural minor component analysis. Digit. Signal Process. 32, 146–155 (2014)

    Article  Google Scholar 

  17. Algazi, V.R., Suk, M.: On the frequency weighted least-square design of finite duration filters. IEEE Trans. Circuits Syst. 22(12), 943–953 (1975)

    Article  Google Scholar 

  18. Algazi, V.R., Suk, M., Rim, C.S.: Design of almost minimax FIR filters in one and two dimensions by WLS techniques. IEEE Trans. Circuits Syst. 33(6), 590–596 (1986)

    Article  Google Scholar 

  19. Lim, Y.C., Lee, J.H., Chen, C.K., Yang, R.H.: A weighted least squares algorithm for quasi-equiripple FIR and IIR digital filter design. IEEE Trans. Signal Process. 40, 551–558 (1992)

    Article  Google Scholar 

  20. Sunder, S., Ramachandran, V.: Design of equiripple nonrecursive digital differentiators and Hilbert transformers using a weighted least-squares technique. IEEE Trans. Signal Process. 42(9), 2504–2509 (1994)

    Article  Google Scholar 

  21. Sunder, S.: An efficient weighted least-squares design of linear-phase nonrecursive filters. IEEE Trans. Circuits Syst. II Analog Digit. Signal Process. 42(5), 359–361 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  22. Burrus, C.S., Barreto, J.A., Selesnick, I.W.: Iterative reweighted least-squares design of FIR filters. IEEE Trans. Signal Process. 42(11), 2926–2936 (1994)

    Article  Google Scholar 

  23. Brandenstein, H., Unbehauen, R.: Weighted least-squares approximation of FIR by IIR digital filters. IEEE Trans. Signal Process. 49(3), 558–568 (2001)

    Article  MathSciNet  Google Scholar 

  24. Deng, T.B., Lian, Y.: Weighted-least-squares design of variable fractional-delay FIR filters using coefficient symmetry. IEEE Trans. Signal Process. 54(8), 3023–3038 (2006)

    Article  Google Scholar 

  25. Lee, W.R., Rehbock, V., Teo, K.L., Caccetta, L.: A weighted least-square-based approach to FIR filter design using the frequency-response masking technique. IEEE Signal Process. Lett. 11(7), 593–596 (2004)

    Article  Google Scholar 

  26. Lim, Y.C., Parker, S.: Discrete coefficient FIR digital filter design based upon an LMS criteria. IEEE Trans. Circuits Syst. 30(10), 723–739 (1983)

    Article  MATH  Google Scholar 

  27. Shyu, J.J., Lin, Y.C.: A new approach to the design of discrete coefficient FIR digital filters. IEEE Trans. Signal Process. 43(1), 310–314 (1995)

    Article  Google Scholar 

  28. Okuda, M., Yoshida, M., Kiyose, K., Ikehara, M., Takahashi, S.: Complex approximation of FIR digital filters by updating desired responses. IEEE Trans. Signal Process. 53(8), 2948–2953 (2005)

    Article  MathSciNet  Google Scholar 

  29. Lim, Y.C., Parker, S.R.: FIR filter design over a discrete powers-of-two coefficient space. IEEE Trans. Acoust. Speech Signal Process. 31(3), 583–591 (1983)

    Article  Google Scholar 

  30. Feng, Z.G., Teo, K.L.: A discrete filled function method for the design of FIR filters with signed-powers-of-two coefficients. IEEE Trans. Signal Process. 56(1), 134–139 (2008)

  31. Xu, F., Chang, C.H., Jong, C.C.: Design of low-complexity FIR filters based on signed-powers-of-two coefficients with reusable common subexpressions. IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 26(10), 1898–1907 (2007)

    Article  Google Scholar 

  32. Mason, J.C., Handscom, D.C.: Chebyshev Polynomials. CRC Press, Boca Raton (2003)

    Google Scholar 

  33. Cintra, R.J., de Oliveira, H.M., Soares, L.R.: On filter banks and wavelets based on Chebyshev polynomials. arXiv:1411.2389 (2014)

  34. Kumar, A., Suman, S., Singh, G.K.: A new closed form method for design of variable bandwidth linear phase FIR filter using different polynomials. Int. J. Electron. Commun. 68(4), 351–360 (2014)

    Article  Google Scholar 

  35. Zou, A.M., Kumar, K.D., Hou, Z.G., Liu, X.: Finite-time attitude tracking control for spacecraft using terminal sliding mode and chebyshev neural network. IEEE Trans. Syst. Man Cybern. Part B Cybern. 41(4), 950–963 (2011)

    Article  Google Scholar 

  36. Sedaghat, S.Y., Ordokhani, Y., Dehghan, M.: Numerical solution of the delay differential equations of pantograph type via Chebyshev polynomials. Commun. Nonlinear Sci. Numer. Simul. 17(12), 4815–4830 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  37. Gerek, O.N., Yardimci, Y.: Equiripple FIR filter design by the FFT algorithm. IEEE Signal Process. Mag. 14(2), 60–64 (1997)

    Article  Google Scholar 

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Authors and Affiliations

  1. PDPM Indian Institute of Information Technology Design and Manufacturing, Jabalpur, MP, 482005, India

    S. Suman & A. Kumar

  2. Indian Institute of Information Technology Patna, Patna, India

    S. Suman

  3. Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, 247667, India

    G. K. Singh

Authors
  1. S. Suman
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  2. A. Kumar
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  3. G. K. Singh
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Correspondence to A. Kumar.

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Suman, S., Kumar, A. & Singh, G.K. A new method for higher-order linear phase FIR digital filter using shifted Chebyshev polynomials. SIViP 10, 1041–1048 (2016). https://doi.org/10.1007/s11760-015-0856-3

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