Hybrid filter banks with fractional delays: Minimax design and application to multichannel sampling

IEEE Transactions on Signal Processing

Volumn 56, Issue 7 II, 2008, Pages 3180-3190

  Nguyen, Ha Thai ^a   Do, Minh N ^a  

^a United States of America   (United States)

Author keywords

Filter design; Fractional delay; H optimization; Hybrid filter banks; Linear matrix inequality; Model matching; Multichannel sampling; Polyphase; Sampled data control

Indexed keywords

AUTOMATION; CONTROL SYSTEM SYNTHESIS; DIGITAL ARITHMETIC; DIGITAL FILTERS; ELECTRIC FILTERS; ERROR ANALYSIS; FILTER BANKS; FIR FILTERS; LINEAR CONTROL SYSTEMS; LINEAR MATRIX INEQUALITIES; MATHEMATICAL OPERATORS; MATRIX ALGEBRA; MILITARY DATA PROCESSING; WAVE FILTERS;

(E ,2E) THEORY; A/D CONVERTERS; ANTI-ALIASING FILTERS; DIGITAL SYNTHESIS; DIGITAL SYSTEMS; ERROR SYSTEMS; FRACTIONAL DELAY (FD); HYBRID FILTERING; LINEAR MATRICES; MAXIMUM GAIN; MINIMAX DESIGN; MODEL-MATCHING; MULTI-CHANNEL SAMPLING; NUMERICAL EXPERIMENTS; SYNTHESIS FILTERS;

CONTROL THEORY;

EID: 46649085240     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2008.920489     Document Type: Article

References (32)

1. V. Balakrishnan and L. Vandenberghe, "Linear matrix inequalities for signal processing: An overview," presented at the 32nd Annual Conf. Information Sciences and Systems, Princeton, NJ, Mar. 1998.
2. J. Benesty, J. Chen, and Y. Huang, "Time-delay estimation via linear interpoation and cross correlation," IEEE Trans. Speech Audio Process., vol. 12, no. 5, pp. 509-519, Sep. 2004.
3. S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory. Philadelphia, PA: SIAM, 1994.
4. T. Chen and B. Francis, "Design of multirate filter banks by H∞ optimization," IEEE Trans. Signal Process., vol. 43, no. 12, pp. 2822-2830, Dec. 1995.
5. T. Chen and B. Francis, Optimal Sampled-Data Control Systems. London, U.K.: Springer-Verlag, 1995.
6. R. Y. Chiang and M. G. Safonov, MATLAB - Robust Control Toolbox, 2005 Online. Available: http://www.mathworks.com
7. G. E. Dullerud and F. Paganini, A Course in Robust Control Theory: A Convex Approach. New York: Springer-Verlag, 2000.
8. J. Franca, A. Petraglia, and S. K. Mitra, "Multirate analog-digital systems for signal processing and conversion," Proc. IEEE, vol. 35, pp. 242-262, Feb. 1997.
9. B. Francis, A Course in H∞ Control Theory. Heidelberg, Germany: Springer-Verlag, 1987.
10. P. Gahinet and P. Apkarian, "A linear matrix inequality approach to H∞ control," Int. J. Robust Nonlinear Contr., vol. 4, pp. 421-448, 1994.
11. P. Gahinet, A. Nemirovski, A. J. Laub, and M. Chilali, LMI Control Toolbox 1995 [Online]. Available: http://www.mathworks.com
12. M. Green and D. J. N. Limebeer, Linear Robust Control. Upper Saddle River, NJ: Prentice-Hall, Inc., 1995.
13. C. Herley and P. W. Wong, "Minimum rate sampling and reconstruction of signals with arbitrary frequency support," IEEE Trans. Inf. Theory vol. 45, no. 5, pp. 1555-1564, Jul. 1999.
14. O. S. Jahromi and P. Aarabi, "Theory and design of multirate sensor arrays," IEEE Trans. Signal Process., vol. 53, no. 5, May 2005.
15. C. H. Knapp and G. C. Carter, "The generalized correlation method for estimation of time delay," IEEE Trans. Acoust., Speech, Signal Process., vol. ASSP-24, no. 4, pp. 320-327, Aug. 1976.
16. T. I. Laakso, V. Valimaki, M. Karjalainen, and U. K. Lame, "Splitting the unit delay - Tools for fractional delay filter design," IEEE Signal Process. Mag., vol. 13, no. 1, pp. 30-60, 1996.
17. J. Lam, "Model reduction of delay systems using Pade approximation," Int. J. Contr., vol. 57, no. 2, pp. 377-391, Feb. 1993.
18. B. P. Lathi, Linear Systems and Signals, 2nd ed. New York: Oxford University Press, 1992.
19. C. F. V. Loan, "Computing integrals involving the matrix exponential," IEEE Trans. Autom. Contr., vol. 23, no. 3, pp. 395-404, Jun. 1978.
20. P. Marziliano and M. Vetterli, "Reconstruction of irregularly sampled discrete-time bandlimited signals with unknown sampling locations," IEEE Trans. Signal Process., vol. 48, no. 12, pp. 3462-3471, Dec. 2000.
21. M. Nagahara and Y. Yamamoto, "Optimal design of fractional delay filters," in Proc. IEEE Conf. Decision and Control, Dec. 2003, vol. 6, pp. 6539-6544.
22. M. Nagahara and Y. Yamamoto, "Optimal design of fractional delay FIR filters without band-limiting assumption," in Proc. IEEE Int. Conf. Acoust., Speech, Signal Process., Mar. 2005, vol. 4, pp. 221-224.
23. H. T. Nguyen and M. N. Do, "Signal reconstruction from a periodic nonuniform set of samples using H∞ optimization," in Proc. SPIE, San Jose, CA, Feb. 2007, vol. 6498.
24. L. D. Philipp, A. Mahmood, and B. L. Philipp, "An improved refinable rational approximation to the ideal time delay," IEEE Trans. Circuits Syst., vol. 46, no. 5, pp. 637-640, May 1999.
25. R. G. Shenoy, D. Burnside, and T. W. Parks, "Linear periodic systems and multirate filter design," IEEE Trans. Signal Process., vol. 42, no. 9, pp. 2242-2256, Sep. 1994.
26. H. Shu, T. Chen, and B. Francis, "Minimax design of hybrid multirate filter banks," IEEE Trans. Circuits Syst., vol. 44, no. 2, pp. 120-128, Feb. 1997.
27. D. Slepian, "On bandwidth," Proc. IEEE, vol. 64, pp. 292-300, 1976.
28. P. P. Vaidyanathan, Multirate Systems and Filter Banks. Englewood Cliffs, NJ: Prentice Hall, 1993.
29. M. Vetterli and J. Kovačević, Wavelets and Subband Coding. Englewood Cliffs, NJ: Prentice-Hall, 1995.
30. F. Viola and W. F. Walker, "A spline-based algorithm for continuous time-delay estimation using sampled data," IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 52, no. 1, pp. 80-93, Jan. 2005.
31. Y. Yamamoto, B. D. O. Anderson, M. Nagahara, and Y. Koyanagi, "Optimal FIR approximation for discrete-time IIR filters," IEEE Signal Process. Lett., vol. 10, no. 9, pp. 273-276, Sep. 2003.
32. M. G. Yoon and B. H. Lee, "A new approximation method for time-delay systems," IEEE Trans. Autom. Contr., vol. 42, no. 7, pp. 1008-1012, Jul. 1997.