Linear matrix inequality formulation of spectral mask constraints with applications to FIR filter design

IEEE Transactions on Signal Processing

Volumn 50, Issue 11, 2002, Pages 2702-2715

  Davidson, Timothy N ^a,b   Luo, Zhi Quan ^a,b   Sturm, Jos F ^c  

^a IEEE   (Canada)

^b MCMASTER UNIVERSITY   (Canada)

^c TILBURG UNIVERSITY   (Netherlands)

Author keywords

Beamforming; FIR digital filter design; Optimization; Spectral masks

Indexed keywords

BEAMFORMING; FIR FILTER DESIGN; LINEAR MATRIX INEQUALITY; SPECTRAL MASKS;

ALGORITHMS; ANTENNA ARRAYS; LINEAR CONTROL SYSTEMS; MATRIX ALGEBRA; OPTIMIZATION; SIGNAL FILTERING AND PREDICTION; SYSTEM THEORY; WIRELESS TELECOMMUNICATION SYSTEMS;

FIR FILTERS;

EID: 0036842590     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2002.804079     Document Type: Article

References (34)

1. T. W. Parks and C. S. Burrus, Digital Filter Design. New York: Wiley, 1987.
2. 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.
3. 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.
4. J. W. Adams and J. L. Sullivan, "Peak-constrained least-squares optimization," IEEE Trans. Signal Processing, vol. 46, pp. 306-321, Feb. 1998.
5. P. Leister and T. W. Parks, "On the design of digital FIR filters with optimum magnitude and minimum phase," Arch. El. Übertr., vol. 29, pp. 270-274, 1975.
6. O. Herrmann and W. Schuessler, "Design of nonrecursive digital filters with minimum phase," Electron. Lett., vol. 6, no. 11, pp. 329-330, June 1970.
7. X. Chen and T. W. Parks, "Design of optimal minimum phase FIR filters by direct factorization," Signal Process., vol. 10, pp. 369-383, June 1986.
8. S.-P. Wu, S. Boyd, and L. Vandenberghe, "FIR filter design via semidefinite programming and spectral factorization," in Proc. IEEE Conf. Dec. Contr., 1996 pp. 271-276.
9. ____, "FIR filter design via spectral factorization and convex optimization," in Applied and Computational Control, Signals and Circuits, B. Datta, Ed. Boston, MA: Birkhauser, 1999, vol. 1.
10. 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.
11. T. N. T. Goodman, C. A. Micchelli, G. Rodriguez, and S. Seatzu, "Spectral factorization of Laurent polynomials," Adv. Comput. Math., vol. 7, no. 4, pp. 429-454, 1997.
12. R. Hettich and K. O. Kortanek, "Semi-infinite programming: Theory, methods and applications," SIAM Rev., vol. 35, no. 3, pp. 380-429, Sept. 1993.
13. 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.
14. O Rioul and P. Duhamel, "A Remez exchange algorithm for orthonormal wavelets," IEEE Trans. Circuits Syst. II, vol. 41, pp. 550-560, Aug. 1994.
15. 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.
16. B. D. O. Anderson, K. L. Hitz, and N. D. Diem, "Recursive algorithm for spectral factorization," IEEE Trans. Circuits Syst., vol. CAS-21, pp. 742-750, Nov. 1974.
17. ∞ Theories. Philadelphia, PA: SIAM, 1999.
18. P. P. Vaidyanathan, "The discrete-time Bounded-Real Lemma in digital filtering," IEEE Trans. Circuits Syst., vol. CAS-32, pp. 918-924, Sept. 1985.
19. J. E. Marsden, Basic Complex Variables, San Francisco, CA: W. H. Freeman, 1973.
20. A. V. Oppenheim and R. W. Schafer, Discrete-Time Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 1989.
21. A. A. Markov, "Lecture notes on functions with the least deviation from zero" (in Russian), in A. A. Markov, Selected Papers, N. Achiezer, Ed. Moscow, Russia: GosTechIzdat, pp. 244-91.
22. Lukacs, "Verscharfung der ersten mittelwertsatzes der integralrechnung fur rationale polynome," Math. Zeitschrift, vol. 2, pp. 229-305, 1918.
23. V. Powers and B. Reznick, "Polynomials that are positive on an interval," Trans. Amer. Math. Soc., vol. 352, no. 10, pp. 4677-4692, June 2000.
24. Yu. Nesterov, "Squared functional systems and optimization problems," in High Performance Optimization, H. Frenk, K. Roos, T. Terlaky, and S. Zhang, Eds. Dordrecht, The Netherlands: Kluwer, 2000, pp. 405-440.
25. Yu. Nesterov and A. Nemirovsky, Interior Point Polynomial Algorithms in Convex Programming. Philadelphia, PA: SIAM, 1994.
26. J. F. Sturm, "Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones," Optimiz. Methods Softw., pp. 11 625-12 653, 1999.
27. L. Vandenberghe and S. Boyd, "Semidefinite programming," SIAM Rev., vol. 31, no. 1, pp. 49-95, Mar. 1996.
28. M. S. Lobo, L. Vandenberghe, S. Boyd, and H. Lebret, "Applications of second-order cone programming," Linear Algebra Applicat., vol. 284, no. 1-3, pp. 193-228, Nov. 1998.
29. Y. Ye, Interior Point Algorithms: Theory and Analysis. New York: Wiley, 1997.
30. "Proposed EIA/TIA Interim Standard. Wideband Spread Spectrum Digital Cellular System Dual-Mode Mobile Station-Base Station Compatibility Standard," QUALCOMM, Inc., San Diego, CA, TR45.5, 1992.
31. T. N. Davidson, "Efficient design of waveforms for robust pulse amplitude modulation," IEEE Trans. Signal Processing, vol. 49, pp. 3098-3111, Dec. 2001.
32. B. D. Van Veen and K. M. Buckley, "Beamforming: A versatile approach to spatial filtering," IEEE Acoust., Speech, Signal Process. Mag., pp. 4-24, Apr. 1988.
33. Y. Genin, Y. Hachez, Yu. Nesterov, and P. Van Dooren, "Convex optimization over positive polynomials and filter design," in Proc. UKACC Int. Conf. Contr., Cambridge, U.K., Sept. 2000.
34. B. Alkire and L. Vandenberghe, "Interior point methods for magnitude filter design," in Proc. Int. Conf. Acoust., Speech, Signal Process., Salt Lake City, UT, May 2001.