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An Alternating Variable Technique for the Constrained Minimax Design of Frequency-Response-Masking Filters

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Abstract

The frequency-response-masking (FRM) technique is one of the most efficient approaches to the design of narrow transition band FIR filters. The constrained minimax design of linear-phase FRM FIR filters in the frequency domain is considered in this paper. The corresponding optimization problem is a nonconvex one. To deal with the nonconvex design problem and improve the FRM filter performance, we propose an algorithm to alternately optimize different subsets of the design variables by fixing the remaining ones. In this way, the nonconvex optimization problem is converted into a series of linear programming subproblems defined on different frequency bands, which are then solved alternately and iteratively. Moreover, the new algorithm converges to a better FRM filter than those obtained by several competitive methods and is flexible to incorporate linear constraints in the design. Several design examples are provided to demonstrate the advantages of the proposed algorithm.

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References

  1. L.C.R. Barcellos, S.L. Netto, P.S.R. Diniz, Optimization of FRM filters using the WLS–Chebyshev approach. Circuits Syst. Signal Process. 22(2), 99–113 (2003)

    Article  MATH  Google Scholar 

  2. S. Boyd, L. Vandenberghe, Convex Optimization (Cambridge University Press, Cambridge, 2004)

    Book  MATH  Google Scholar 

  3. R. Bregovic, Y.C. Lim, T. Saramäki, Frequency-response masking-based design of nearly perfect-reconstruction two-channel FIR filterbanks with rational sampling factors. IEEE Trans. Circuits Syst. I 55(7), 2002–2012 (2008)

    Article  MathSciNet  Google Scholar 

  4. N. Haridas, E. Elias, Reconfigurable Farrow structure-based FRM filters for wireless communication systems. Circuits Syst. Signal Process. 36(1), 315–338 (2017)

    Article  Google Scholar 

  5. X.P. Lai, R.J. Zhao, On Chebyshev design of linear-phase FIR filters with frequency inequality constraints. IEEE Trans. Circuits Syst. II 53(2), 120–124 (2006)

    Article  Google Scholar 

  6. M. Lang, Algorithms for the constrained design of digital filters with arbitrary magnitude and phase responses. Ph.D. Thesis, Vienna University of Technology (1999)

  7. W.R. Lee, L. Caccetta, K.L. Teo, V. Rehbock, A unified approach to multistage frequency-response masking filter design using the WLS technique. IEEE Trans. Signal Process. 54(9), 3459–3467 (2006)

    Article  MATH  Google Scholar 

  8. W.R. Lee, L. Caccetta, K.L. Teo, V. Rehbock, A weighted least squares approach to the design of FIR filters synthesized using the modified frequency response masking structure. IEEE Trans. Circuits Syst. II 53(5), 379–383 (2006)

    Article  Google Scholar 

  9. W.R. Lee, V. Rehbock, K.L. Teo, L. Caccetta, An alternating variable approach to FIR filter design with power-of-two coefficients using the frequency-response masking technique, in IEEE International Symposium on Circuits and Systems, Bangkok, Thailand (2003), pp. 886–889

  10. W.R. Lee, V. Rehbock, K.L. Teo, S. Member, L. Caccetta, A weighted least-square-based approach to FIR filter design using the frequency-response masking technique. IEEE Trans. Circuits Syst. II 11(7), 593–596 (2004)

    Google Scholar 

  11. Y. Lian, Complexity reduction for FRM-based FIR filters using the prefilter–equalizer technique. Circuits Syst. Signal Process. 22(2), 137–155 (2003)

    MATH  Google Scholar 

  12. Y. Lian, A modified frequency-response masking structure for high-speed FPGA implementation of sharp FIR filter. J. Circuits Syst. Comput. 12(5), 643–654 (2003)

    Article  Google Scholar 

  13. Y. Lian, Y.C. Lim, Reducing the complexity of frequency-response masking filters using half band filter. Signal Process. 42(3), 227–230 (1995)

    Article  MATH  Google Scholar 

  14. Y. Lian, C.Z. Yang, Complexity reduction by decoupling the masking filters from the bandedge shaping filter in the FRM technique. Circuits Syst. Signal Process. 22(2), 115–135 (2003)

    MATH  Google Scholar 

  15. Y. Lian, L. Zhang, C.C. Ko, An improved frequency response masking approach for designing sharp FIR filters. Signal Process. 81(12), 2573–2581 (2001)

    Article  MATH  Google Scholar 

  16. Y.C. Lim, A digital filter bank for digital audio systems. IEEE Trans. Circuits Syst. 33(8), 848–849 (1986)

    Article  Google Scholar 

  17. Y.C. Lim, Frequency-response masking approach for the synthesis of linear phase digital filters. IEEE Trans. Circuits Syst. 33(4), 357–364 (1986)

    Article  Google Scholar 

  18. Y.C. Lim, Y. Lian, The optimum design of one- and two-dimensional FIR filters using the frequency response masking technique. IEEE Trans. Circuits Syst. II 40(2), 88–95 (1993)

    Article  MATH  Google Scholar 

  19. Y.C. Lim, Y. Lian, Frequency-response masking approach for digital filter design: complexity reduction via masking filter factorization. IEEE Trans. Circuits Syst. II 41(8), 518–525 (1994)

    Article  Google Scholar 

  20. Y.C. Lim, R. Yang, On the synthesis of very sharp decimators and interpolators using the frequency-response masking technique. IEEE Trans. Signal Process. 53(4), 1387–1397 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  21. Y.C. Lim, Y.J. Yu, T. Saramäki, Optimum masking levels and coefficient sparseness for hilbert transformers and half-band filters designed using the frequency-response masking technique. IEEE Trans. Circuits Syst. I 52(11), 2444–2453 (2005)

    Article  Google Scholar 

  22. Y.Z. Liu, Z.P. Lin, On the applications of the frequency-response masking technique in array beamforming. Circuits Syst. Signal Process. 25(2), 201–224 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  23. Y.Z. Liu, Z.P. Lin, Optimal design of frequency-response masking with reduced group delays. IEEE Trans. Circuits Syst. I 55(6), 1560–1570 (2008)

    Article  MathSciNet  Google Scholar 

  24. W.S. Lu, T. Hinamoto, Optimal design of FIR frequency-response-masking filters using second-order cone programming, in IEEE International Symposium on Circuits and Systems, Bangkok, Thailand (2003), pp. 878–881

  25. W.S. Lu, T. Hinamoto, Optimal design of frequency-response-masking filters using semidefinite programming. IEEE Trans. Circuits Syst. I 50(4), 557–568 (2003)

    Article  MATH  Google Scholar 

  26. W.S. Lu, T. Hinamoto, A unified approach to the design of interpolated and frequency-response-masking FIR filters. IEEE Trans. Circuits Syst. I 63(12), 2257–2266 (2016)

    Article  Google Scholar 

  27. J.H. McClellan, T.W. Parks, A computer program for designing optimum FIR linear phase digital filters. IEEE Trans. Audio Electroacoust. 21(12), 506–526 (1973)

    Article  Google Scholar 

  28. G. Meinardus, Approximation of Functions: Theory and Numerical Methods (Springer, New York, 1967)

    Book  MATH  Google Scholar 

  29. T. Saramäki, Y.C. Lim, Use of the Remez algorithm for designing FRM based FIR filters. Circuits Syst. Signal Process. 22(2), 77–97 (2003)

    MATH  Google Scholar 

  30. T. Saramäki, Y.C. Lim, R. Yang, The synthesis of half-band filter using frequency-response masking technique. IEEE Int. Symp. Circuits Syst. II 42(1), 58–60 (1995)

    Google Scholar 

  31. T. Saramäki, J. Yli-Kaakinen, Optimization of frequency-response-masking based FIR filters with reduced complexity, in IEEE International Symposium on Circuits and Systems, Phoenix, AZ (2002), pp. 225–228

  32. T. Saramäki, J. Yli-Kaakinen, Optimization of frequency-response masking based FIR filters. J. Circuits Syst. Comput. 12(5), 563–590 (2003)

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  34. Y. Wei, S.G. Huang, X.J. Ma, A novel approach to design low-cost two-stage frequency-response masking filters. IEEE Trans. Circuits Syst. II 62(10), 982–986 (2015)

    Article  Google Scholar 

  35. Y. Wei, Y. Lian, Frequency-response masking filters based on serial masking schemes. Circuits Syst. Signal Process. 29(1), 7–24 (2010)

    Article  MATH  Google Scholar 

  36. Y. Wei, D.B. Liu, Improved design of frequency-response masking filters using band-edge shaping filter with non-periodical frequency response. IEEE Trans. Singal Process. 61(13), 3269–3278 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  37. J. Yli-Kaakinen, T. Saramäki, An efficient algorithm for the optimization of FIR filters synthesized using the multistage frequency-response masking approach. Circuits Syst. Signal Process. 30(1), 157–183 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  38. J.H. Yu, Y. Lian, Design equations for jointly optimized frequency-response masking filters. Circuits Syst. Signal Process. 26(1), 27–42 (2007)

    Article  MATH  Google Scholar 

  39. Y.J. Yu, Y.C. Lim, FRM based FIR filter design—the WLS approach, in IEEE International Symposium on Circuits and Systems, Phoenix, AZ (2002), pp. 221–224

  40. Y.J Yu, T. Saramäki, Y.C. Lim, An iterative method for optimizing FIR filters synthesized using the two-stage frequency-response masking technique, in IEEE International Symposium on Circuits and Systems, Bangkok, Thailand (2003), pp. 874–877

  41. Y.J. Yu, K.L. Teo, Y.C. Lim, G.H. Zhao, Extrapolated impulse response filter and its application in the synthesis of digital filters using the frequency-response masking technique. Signal Process. 85, 581–590 (2005)

    Article  MATH  Google Scholar 

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Acknowledgements

This work was supported partially by the Singapore Academic Research Fund (AcRF) Tier 1 under Project RG 31/16, and partially by the National Nature Science Foundation of China under Grants 61573123 and 61427808.

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Correspondence to Zhiping Lin.

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Zhao, R., Lai, X., Tay, D.B.H. et al. An Alternating Variable Technique for the Constrained Minimax Design of Frequency-Response-Masking Filters. Circuits Syst Signal Process 38, 827–846 (2019). https://doi.org/10.1007/s00034-018-0890-9

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  • DOI: https://doi.org/10.1007/s00034-018-0890-9

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