Efficient large-scale filter/filterbank design via LMI characterization of trigonometric curves

IEEE Transactions on Signal Processing

Volumn 55, Issue 9, 2007, Pages 4393-4404

  Tuan, Hoang Duong ^a   Son, Tran Thai ^b   Vo, Ba Ngu ^c   Nguyen, Truong Q ^d  

^a UNIVERSITY OF NEW SOUTH WALES   (Australia)

^b TOYOTA TECHNOLOGICAL INSTITUTE   (Japan)

^c UNIVERSITY OF MELBOURNE   (Australia)

^d UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Filter and filter bank; Semidefinite programming; Trigonometric polynomial

Indexed keywords

FILTER BANKS; LINEAR MATRIX INEQUALITIES; OPTIMIZATION; POLYNOMIALS;

LINEAR MATRIX INEQUALITY; SEMIDEFINITE PROGRAMMING; TRIGONOMETRIC CURVES; TRIGONOMETRIC POLYNOMIAL;

SIGNAL FILTERING AND PREDICTION;

EID: 34548251953     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2007.896285     Document Type: Article

References (39)

1. J. W. Adams, "New optimal window," IEEE Trans. Signal Process., vol. 39, pp. 1753-1769, 1991.
2. J. W. Adams and J. L. Sullivan, "Peak-constrained least squares optimization," IEEE Trans. Signal Process., vol. 46, pp. 306-321, 1998.
3. A. N. Akansu and R. A. Haddad, Mutiresolution Signal Decomposition: Transforms, Subbands, Wavelets. New York: Academic, 2001.
4. B. Alkire and L. Vandenberge, "Handling nonnegative constraints in spectral estimation," in Proc. 34th Asilomar Conf. Signals, Syst., Comput., 2000, pp. 202-206.
5. B. Alkire and L. Vandenberge, "Interior-point methods for magnitude filter design," in Proc. 26th IEEE Int. Conf. Acoust., Speech, Signal Process., 2001.
6. B. Alkire and L. Vandenberge, "Convex optimization problems involving finite autocorrelation sequences," Math. Programm., Ser. A, vol. 93, pp. 331-359, 2002.
7. B. D. O. Anderson and S. Vongpanitlerd, Network Analysis and Synthesis: A Modern System Theory Approach. Englewood Cliffs, NJ: Prentice-Hall, 1973.
8. S. J. Benson, Y.Ye, and X. Zhang, "Solving large-scale sparse semidefinite programs for combinatorial optimization," SIAM J. Optimiz., vol. 10, pp. 443-461, 2000.
9. ∞ norm of a transfer matrix and related problem," Mathematics of Contr., Signal, Syst., vol. 2, pp. 207-219, 1989.
10. T. Davidson, Z. Q. Luo, and J. F. Sturn, "Linear matrix inequality formulation of spectral mask constraints with applications to FIR filter design," IEEE Trans. Signal Process., vol. 50, pp. 2702-2715, 2002.
11. ∞ optimization," IEEE Trans. Signal Process., vol. 43, pp. 2822-2830, 1995.
12. B. Dumitrescu, I. Tabus, and P. Stoica, "On the parameterization of positive real sequences and MA parameter estimation," IEEE Trans. Signal Process., vol. 49, pp. 2630-2639, 2001.
13. M. Fukuda, M. Kojima, and M. Shida, "Lagragian dual interior-point methods for semi-definite programs," SIAM J. Optimiz., vol. 12, pp. 1007-1031, 2002.
14. P. Gahinet, A. Nemirovski, A. Laub, and M. Chilali, LMI Control Toolbox. New York: The Math. Works Inc., 1995.
15. Y. Genin, Y. Hachez, Yu. Nesterov, and P. Van Dooren, "Convex optimization over positive polynomials and filter design," in Proc. 2000 UKACC Int. Conf. Control, 2000, Cambridge Univ..
16. R. Hettich and K. Kortanek, "Semi-infinite programming: Theory methods and applications," SIAM Rev., vol. 35, pp. 380-429, 1993.
17. A. Kirac and P. P. Vaidyanathan, "Theory and design of optimum FIR compaction filters," IEEE Trans. Signal Process., vol. 46, pp. 903-919, 1998.
18. M. Krein and A. Nudel'man, "The Markov moment problem and extremal problems," Transl. Math. Monographs, vol. 50, 1977.
19. J. H. McClellan and T. W. Parks, "A unified approach to the design of optimal FIR linear phase digital filters," IEEE Trans. Circuit Theory, vol. CT-20, pp. 697-701, 1973.
20. P. Moulin, M. Anitescu, K. Kortanek, and F. A. Potra, "The role of linear semi-infinite programming in signal adapted QMF bank design," IEEE Trans. Signal Process., vol. 45, pp. 2160-2174, 1997.
21. P. Moulin and M. K. Mihcak, "Theory and design of signal-adapted FIR paraunitary filterbanks," IEEE Trans. Signal Process., vol. 46, pp. 920-929, 1998.
22. Y. Nesterov, "Squared functional systems and optimization problems," in High Performance Optimization, H. Frenk, Ed. Boston, MA: Kluwer Academic, 2000, pp. 405-440.
23. T. Q. Nguyen and P. P. Vaidyanathan, "Two-channel perfect-reconstruction FIR QMF structures which yield linear-phase analysis and synthesis filters," IEEE Trans. Acoust. Signal Process. vol. 37, pp. 676-690, 1989.
24. R. S. Orr, T. C. Farrell, and G. E. Prescott, "Transform-based low probability of intercept communication," in Wavelet, Subband and Block Transforms in Communications and Multimedia, A. N. Akansu and M. J. Medley, Eds. Boston, MA: Kluwer Academic, 1999, pp. 91-139.
25. J. G. Proakis and D. G. Manolakis, Digital Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 1996.
26. A. Rantzer, "On the Kalman-Yakubovich-Popov lemma," Syst. Contr. Lett., vol. 28, pp. 7-10, 1996.
27. R. Reemtsen and J.-J. Ruckman, Eds., Semi-Inifinite Programming. Dordrecht, Germany: Kluwer Academic, 1998.
28. T. Rockafellar, Convex Analysis. Princeton, NJ, 1970.
29. A. K. Soman, P. P. Vaidyanathan, and T. Q. Nguyen, "Linear phase paraunitary filter banks: Theory, factorizations and designs," IEEE Trans. Signal Process., vol. 41, pp. 3480-3496, 1993.
30. G. Strang and T. Q. Nguyen, Wavelets and Filter Banks. Wellesley, MA: Wellesley-Cambridge Press, 1996.
31. J. Sturm, "Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones," Optimiz. Methods Software, vol. 11-12, pp. 625-653, 1999.
32. H. D. Tuan, L. H. Nam, H. Tuy, and T. Q. Nguyen, "Multicriterion optimized QMF bank design," IEEE Trans. Signal Process., vol. 51, pp. 2582-2591, 2003.
33. H. D. Tuan, T. T. Son, H. Tuy, and T. Q. Nguyen, "New linear programming based filter design," IEEE Trans. Cicruits Syst. II, Digit. Signal Process., vol. 52, pp. 276-281, 2005.
34. J. Tuqan and P. P. Vaidyanathan, "A state-space approach to the design of globally optimal FIR energy compaction filters," IEEE Trans. Signal Process., vol. 48, pp. 2822-2838, 2000.
35. P. P. Vaidyanathan, Multirate Systems and Filter Banks. Englewood Cliffs, NJ: Prentice-Hall, 1993.
36. M. Vetterli and J. Kovacevic, Wavelets and Subband Coding. Englewood Cliffs, NJ: Prentice-Hall, 1995.
37. B. Vo, A. Cantoni, and K. L. Teo, Filter Design with Time Domain Mask Constraints: Theory and Applications. Boston, MA: Kluwer Academic, 2001.
38. S. Wu, S. Boyd, and L. Vandenberge, "FIR filter design via spectral factorization and convex optimization," in Applied and Computational Control, Signals and Circuits, ser. Springer International Series in Engineering and Computer Science, B. Datta, Ed. Berlin, Germany: Springer, ch. 5, pp. 215-245.
39. M. R. Wilbur, T. Davidson, and J. P. Reilly, "Efficient design of over-sampled NPR GDFT filter banks," IEEE Trans. Signal Process., vol. 52, pp. 1947-1963, 2004.