Enriching the art of FIR filter design via convex optimization

IEEE Signal Processing Magazine

Volumn 27, Issue 3, 2010, Pages 89-101

  Davidson, Timothy ^a  

^a MCMASTER UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION ALGORITHMS; BANDPASS FILTERS; CONVEX OPTIMIZATION; DESIGN; DIGITAL SIGNAL PROCESSING; IMPULSE RESPONSE; LEAST SQUARES APPROXIMATIONS; LINEAR PROGRAMMING; LOW PASS FILTERS; OPTIMIZATION; QUADRATIC PROGRAMMING; SIGNAL FILTERING AND PREDICTION; SIGNAL PROCESSING;

COMPUTING RESOURCE; EXCHANGE ALGORITHMS; FREQUENCY SAMPLING TECHNIQUE; LINEAR CONSTRAINTS; LINEAR PHASE FIR FILTER; OPTIMIZATION-BASED TECHNIQUES; PARKS-MCCLELLAN ALGORITHM; PEAK CONSTRAINED LEAST SQUARES;

FIR FILTERS;

EID: 85032751923     PISSN: 10535888     EISSN: None     Source Type: Journal    
DOI: 10.1109/MSP.2010.936040     Document Type: Conference Paper

References (71)

1. T. W. Parks and C. S. Burrus, Digital Filter Design. New York: Wiley, 1987.
2. A. Antoniou, Digital Filters. Analysis, Design, and Applications, 2nd ed. New York: McGraw-Hill, 1993.
3. T. Saramäki, "Finite impulse response filter design," in Handbook for Digital Signal Processing, S. K. Mitra and J. F. Kaiser, Eds. New York: Wiley, 1993, ch. 4, pp. 155-277.
4. L. J. Karam, J. H. McClellan, I. W. Selesnick, and C. S. Burrus, "Digital filtering," in The Digital Signal Processing Handbook, V. K. Madisetti and D. B. Williams, Eds. Boca Raton, FL: CRC, 1998, ch. 11, pp. 1-86.
5. T. I. Laakso, V. Välimäki, M. Karjalainen, and U. K. Laine, "Splitting the unit delay," IEEE Signal Processing Mag., vol.13, pp. 30-60, Jan. 1996.
6. W.-S. Lu, "Design of digital filters and filter banks by optimization: A state of the art review," in Proc. European Signal Processing Conf., Tampere, Finland, Sept. 2000, pp. 351-354.
7. A. Tkacenko, P. P. Vaidyanathan, and T. Q. Nguyen, "On the eigenfilter design method and its applications: A tutorial," IEEE Trans. Circuits Syst. II, vol.50, pp. 497-517, Sept. 2003.
8. T. W. Parks and J. H. McClellan, "Chebyshev approximation for nonrecursive digital filters with linear phase," IEEE Trans. Circuit Theory, vol.CT-19, no.2, pp. 189-194, 1972.
9. J. H. McClellan and T. W. Parks, "A personal history of the Parks-McClellan algorithm," IEEE Signal Processing Mag., vol.22, pp. 82-86, Mar. 2005.
10. K. Steiglitz, T. W. Parks, and J. F. Kaiser, "METEOR: A constraint-based FIR filter design program," IEEE Trans. Signal Processing, vol.40, pp. 1901-1909, Aug. 1992.
11. J. W. Adams and J. L. Sullivan, "Peak-constrained least-squares optimiza tion," IEEE Trans. Signal Processing, vol.46, pp. 306-321, Feb. 1998.
12. I. W. Selesnick, M. Lang, and C. S. Burrus, "Constrained least square design for FIR filters without specified transition bands," IEEE Trans. Signal Processing, vol.44, pp. 1879-1892, Aug. 1996.
13. S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge, U.K.: Cambridge Univ. Press, 2004.
14. J. F. Sturm. (1999). Using SeDuMi 1.02, a Matlab toolbox for optimization over symmetric cones. Optim. Methods and Software vol. 11-12, pp. 625-653 [Online]. Available: http://sedumi.ie.lehigh.edu
15. K. C. Toh, M. J. Todd, and R. H. Tutuncu. (1999). SDPT3\A Matlab software package for semidefinite programming, version 2.1. Optim. Methods and Software, vol.11-12, pp. 545-581 [Online]. Available: http://www.math.nus.edu.sg/ mattohkc/sdpt3.html
16. J. Löfberg. (2004, Sept.). YALMIP: A toolbox for modeling and optimization in MATLAB. Proc. IEEE Int. Symp. Computer-Aided Control System Design, Taipei [Online]. Available: http://control.ee.ethz.ch/̃joloef/ yalmip.php
17. M. Grant and S. Boyd. (2008). Graph implementations for nonsmooth convex programs. Recent Advances in Learning and Control, V. Blondel, S. Boyd, and H. Kimura, Eds. New York: Springer, pp. 95-110 [Online]. Available: http://stanford.edu/̃boyd/cvx
18. J. O. Coleman and D. P. Scholnik, "Design of nonlinear-phase FIR filters with second-order cone programming," in Proc. Midwest Symp. Circuits Systems, Las Cruces, NM, Aug. 1999, pp. 409-412.
19. W.-S. Lu, "A unified approach for the design of 2-D digital filters via semi-definite programming," IEEE Trans. Circuits Syst. I, vol.49, pp. 814-826, June 2002.
20. K. M. Tsui, S. C. Chan, and K. S. Yeung, "Design of FIR digital filters with prescribed flatness and peak error constraints using second-order cone programming," IEEE Trans. Circuits Syst. II, vol.52, pp. 601-605, Sept. 2005.
21. K. H. Afkhamie, H. Latchman, L. Yonge, T. N. Davidson, and R. Newman, "Joint optimization of transmit pulse shaping, guard interval length, and receiver side narrow-band interference mitigation in the HomePlugAV OFDM system," in Proc. IEEE Workshop Signal Processing Advances Wireless Communications, New York, June 2005, pp. 996-1000.
22. E. L. Lawler and D. E. Wood, "Branch-and-bound methods: A survey," Oper. Res., vol.14, no.4, pp. 699-719, 1966.
23. J. Nocedal and S. J. Wright, Numerical Optimization. New York: Springer, 1999.
24. O. Herrmann and H. W. Schüssler, "Design of non-recursive digital filters with minimum phase," Electron. Lett., vol.6, pp. 329-330, May 1970.
25. S.-P. Wu, S. Boyd, and L. Vandenberghe, "FIR filter design via spectral factorization and convex optimization," in Applied and Computational Control, Signals, and Circuits, vol 1, B. Datta, Ed. Cambridge, MA: Birkhauser, May 1999, ch. 5, pp. 215-245.
26. T. N. Davidson, Z.-Q. Luo, and K. M. Wong, "Design of orthogonal pulse shapes for communications via semidefinite programming," IEEE Trans. Signal Processing, vol.48, pp. 1433-1445, May 2000.
27. T. N. Davidson, "Efficient design of waveforms for robust pulse amplitude modulation," IEEE Trans. Signal Processing, vol.49, pp. 3098-3111, Dec. 2001.
28. P. Moulin, M. Anitescu, K. O. Kortanek, and F. A. Potra, "The role of linear semi-infinite programming in signal adapted QMF bank design," IEEE Trans. Signal Processing, vol.45, pp. 2160-2174, Sept. 1997.
29. J. Tuqan and P. P. Vaidyanathan, "A state space approach to the design of globally optimal FIR energy compaction filters," IEEE Trans. Signal Processing, vol.48, pp. 2822-2838, Oct. 2000.
30. B. Dumitrescu and C. Popeea, "Accurate computation of compaction filters with high regularity," IEEE Signal Processing Lett., vol.9, pp. 278-281, Sept. 2002.
31. J.-K. Zhang, T. N. Davidson, and K. M. Wong, "Efficient design of orthonor-mal wavelet bases for signal representation," IEEE Trans. Signal Processing, vol.52, pp. 1983-1996, July 2004.
32. T. N. T. Goodman, C. A. Micchelli, G. Rodriguez, and S. Seatzu, "Spectral factorization of Laurent polynomials," Advances Comput. Math., vol.7, no.4, pp. 429-454, 1997.
33. C. Taswell, "Constraint-selected and search-optimized families of Daubechies wavelet filters computable by spectral factorization," J. Comput. Appl. Math., vol.121, pp. 179-195, Sept. 2000.
34. T. N. Davidson, Z.-Q. Luo, and J. F. Sturm, "Linear matrix inequality formulation of spectral mask constraints with applications to FIR filter design," IEEE Trans. Signal Processing, vol.50, pp. 2702-2715, Nov. 2002.
35. R. Hettich and K. O. Kortanek, "Semi-infinite programming: Theory, methods and applications," SIAM Rev., vol.35, pp. 380-429, Sept. 1993.
36. H. H. Dam, K. L. Teo, S. Nordebo, and A. Cantoni, "The dual parameterization approach to optimal least square FIR filter design subject to maximum error constraints," IEEE Trans. Signal Processing, vol.48, pp. 2314-2320, Aug. 2000.
37. B. Alkire and L. Vandenberghe, "Convex optimization problems involving finite autocorrelation sequences," Math. Program., vol.93, pp. 331-359, Dec. 2002.
38. B. Dumitrescu, Positive Trigonometric Polynomials and Signal Processing Applications. New York: Springer, 2007.
39. H. D. Tuan, T. T. Son, B.-N. Vo, and T. Q. Nguyen, "Efficient large-scale filter/filterbank design via LMI characterization of trigonometric curves," IEEE Trans. Signal Processing, vol.55, pp. 4394-4404, Sept. 2007.
40. B. Dumitrescu, I. Tabus, and P. Stoica, "On the parameterization of positive real sequences and MA parameter estimation," IEEE Trans. Signal Processing, vol.49, pp. 2630-2639, Nov. 2001.
41. M. C. Lang, "Design of nonlinear phase FIR digital filters using quadratic programming," in Proc. Int. Conf. Acoustics, Speech, Signal Processing, Munich, Apr. 1997, pp. 2169-2172.
42. X. Lai, "Optimal design of non-linear-phase FIR filters with prescribed phase error," IEEE Trans. Signal Processing, vol.57, pp. 3399-3410, Sept. 2009.
43. B. A. Weisburn, T. W. Parks, and R. G. Shenoy, "Error criteria for filter design," in Proc. Int. Conf. Acoustics, Speech, Signal Processing, Adelaide, Apr. 1994, vol.3, pp. 565-568.
44. S. Boyd and C. Barratt, Linear Controller Design: Limits of Performance. Englewood Cliffs, NJ: Prentice-Hall, 1991.
45. J. C. Doyle, B. A. Francis, and A. R. Tannenbaum, Feedback Control Theory. New York: MacMillan, 1992.
46. A. Potchinkov and R. Reemsten, "The design of FIR filters in the complex plane by convex optimization," Signal Process., vol.46, pp. 127-146, Oct. 1995.
47. D. Burnside and T. W. Parks, "Optimal design of FIR filters with the complex Chebyshev error criteria," IEEE Trans. Signal Processing, vol.43, pp. 605-616, Mar. 1995.
48. C. S. Burrus, J. A. Barreto, and I. W. Selesnick, "Iterative reweighted least-squares design of FIR filters," IEEE Trans. Signal Processing, vol.42, pp. 2926-2936, Nov. 1994.
49. 1- approximation based method for synthesizing FIR filters," IEEE Trans. Circuits Syst. II, vol.39, pp. 578-581, Aug. 1992.
50. 1-method for the design of linear-phase FIR digital filters," IEEE Trans. Signal Processing, vol.55, pp. 5253-5266, Nov. 2007. (Pubitemid 350130738)
51. B.-N. Vo, A. Cantoni, and K. L. Teo, Filter Design with Time Domain Mask Constraints: Theory and Applications. New York: Springer, 2001.
52. T. Baran, D. Wei, and A. V. Oppenheim, "Linear programming algorithms for sparse filter design," IEEE Trans. Signal Processing, vol.58, no.3, pp. 1605-1617, Mar. 2010.
53. T. Q. Nguyen, "Digital filter bank design quadratic-constrained formulation," IEEE Trans. Signal Processing, vol.43, pp. 2103-2108, Sept. 1995.
54. M. R. Wilbur, T. N. Davidson, and J. P. Reilly, "Efficient design of over-sampled NPR GDFT filter banks," IEEE Trans. Signal Processing, vol.52, pp. 1947-1963, July 2004.
55. B. Borna and T. N. Davidson, "Efficient design of FMT systems," IEEE Trans. Commun., vol.54, pp. 794-797, May 2006. (Pubitemid 43792581)
56. M. Harteneck, S. Weiss, and R. W. Stewart, "Design of near perfect reconstruction oversampled filter banks for subband adaptive filters," IEEE Trans. Circuits Syst. II, vol.46, pp. 1081-1085, Aug. 1999.
57. B. Farhang-Boroujeny, "A square-root Nyquist (M) filter design for digital communication systems," IEEE Trans. Signal Processing, vol.56, pp. 2127-2132, May 2008.
58. H. H. Dam, S. Nordholm, and A. Cantoni, "Uniform FIR filterbank optimization with group delay specifications," IEEE Trans. Signal Processing, vol.53, pp. 4249-4260, Nov. 2005. (Pubitemid 41622556)
59. W.-S. Lu, T. Saramäki, and R. Bregović, "Design of practically perfect-reconstruction cosine-modulated filter banks: A second-order cone programming approach," IEEE Trans. Circuits Syst. I, vol.51, pp. 552-563, Mar. 2004.
60. Z. Lin and Y. Liu, "Design of arbitrary complex coefficient WLS FIR filters with group delay constraints," IEEE Trans. Signal Processing, vol.57, pp. 3274-3279, Aug. 2009.
61. D. Kodek and K. Steiglitz, "Comparison of optimal and local search methods for designing finite wordlength FIR digital filters," IEEE Trans. Circuits Syst., vol.CAS-28, pp. 28-32, Jan. 1981. (Pubitemid 11466331)
62. Y. C. Lim and S. R. Parker, "Discrete coefficient FIR digital filter design based upon an LMS criteria," IEEE Trans. Circuits Syst., vol.CAS-30, pp. 723-739, Oct. 1983.
63. U. Heute, A. Srivastav, V. Sauerland, and J. Kliewer, "Fixed-point-coefficient FIR filters and filter banks: Improved design by randomized quantizations," in Proc. Int. Symp. Signal Processing and Applications, Sharjah, Feb. 2007.
64. H. Lebret and S. Boyd, "Antenna array pattern synthesis via convex optimization," IEEE Trans. Signal Processing, vol.45, pp. 526-532, Mar. 1997. (Pubitemid 127765940)
65. S. Nordebo and Z. Zang, "Semi-infinite linear programming: A unified approach to digital filter design with time-and frequency-domain specifications," IEEE Trans. Circuits Syst. II, vol.46, pp. 765-775, June 1999.
66. H. H. Dam, A. Cantoni, S. Nordholm, and K. L. Teo, "Digital Laguerre filter design with maximum passband-to-stopband energy ratio subject to peak and group delay constraints," IEEE Trans. Circuits Syst. I, vol.53, pp. 1108-1118, May 2006.
67. A. Tarczyński, G. D. Cain, E. Hermanowicz, and M. Rojewski, "A WISE method for designing IIR filters," IEEE Trans. Signal Processing, vol.49, pp. 1421-1432, July 2001. (Pubitemid 32615805)
68. M. C. Lang, "Least-squares design of IIR filters with prescribed magnitude and phase responses and a pole radius constraint," IEEE Trans. Signal Processing, vol.48, pp. 3109-3121, Nov. 2000.
69. W.-S. Lu and T. Hinamoto, "Optimal design of IIR digital filters with robust stability using conic-quadratic-programming updates," IEEE Trans. Signal Processing, vol.51, pp. 1581-1592, June 1998.
70. B. Dumitrescu and R. Niemistö, "Mutistage IIR filter design using convex stability domains defined by positive realness," IEEE Trans. Signal Processing, vol.52, pp. 962-974, Apr. 2004.
71. A. Jiang and H. K. Kwan, "Minimax design of IIR digital filters using iterative SOCP," IEEE Trans. Circuits Syst. I, to be published.