A state space approach to the design of globally optimal FIR energy compaction filters

IEEE Transactions on Signal Processing

Volumn 48, Issue 10, 2000, Pages 2822-2838

  Tuqan, Jamal ^a   Vaidyanathan, P P ^a  

^a IBM T J WATSON RESEARCH CENTER   (United States)

Author keywords

Discrete time positive real lemma; Energy compaction filters; Kaiman yakubovich popov (KYP) lemma; Linear matrix inequality (LMI); Optimum orthonormal subband coder (SBC); Principal components filter bank (PCFB); Semi definite programming (SDP)

Indexed keywords

ALGORITHMS; LEAST SQUARES APPROXIMATIONS; NYQUIST DIAGRAMS; OPTIMIZATION; STATE SPACE METHODS; WAVELET TRANSFORMS;

ENERGY COMPACTION FILTERS; POWER SPECTRUMS; PRINCIPLE COMPONENT FILTER BANKS (PCFB);

FIR FILTERS;

EID: 0034298676     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/78.869032     Document Type: Article

References (47)

1. P. P. Vaidyanathan, Multirate Systems and Filter Banks. Englewood Cliffs, NJ: Prentice-Hall, 1993.
2. P. R. Chevillât and G. Ungerboeck, "Optimum FIR transmitter and receiver filters for data transmission over band-limited channels," IEEE Trans. Commun., vol. COMM-30, pp. 1909-1915, Aug. 1982.
3. J. Tuqan and P. P. Vaidyanathan, "Globally optimal FIR filters with applications in source and channel coding," Proc. Int. Symp. Inform. Theory, Cambridge, MA, 1998, p. 475.
4. J. Tuqan, "Global optimization of orthogonal FIR transmitter and receiver filters for data transmission over noisy channels," Proc. 33rd Asitomar Conf. Signals, Syst., Comput., vol. 1, 1999, pp. 202-206.
5. Q. Jin, Z.-Q. Luo, and K. M. Wong, "Optimum filter banks for signal decomposition and its applications in adaptive echo cancellation," IEEE Trans. Signal Processing, vol. 44, pp. 1669-1689, July 1996.
6. P. P. Vaidyanathan, T. Q. Nguyen, Z. Doganata, and T. Saramaki, "Improved technique for design of perfect reconstruction FIR QMF banks with lossless polyphase matrices," IEEE Trans. Acoust., Speech, Signal Processing, vol. 37, pp. 1042-1056, 1989.
7. J. Tuqan and P. P. Vaidyanathan, "Oversampling PCM techniques and optimum noise shapers for quantizing a class of nonbandlimited signals," IEEE Trans. Signal Processing, vol. 47, pp. 389-407, Feb. 1999.
8. M. K. Tsatsanis and G. B. Giannakis, "Principal component filter banks for optimal multiresolution analysis," IEEE Trans. Signal Processing, vol. 43, pp. 1766-1777, Aug. 1995.
9. K. C. Aas, K. A. Duell, and C. T. Mullis, "Synthesis of extremal waveletgenerating filters using Gaussian quadrature," IEEE Trans. Signal Processing, vol. 43, pp. 1045-1057, May 1995.
10. M. K. Tsatsanis and G. B. Giannakis, "Time-varying system identification and model validation using wavelets," IEEE Trans. Signal Processing, vol. 41, pp. 3512-3523, Dec. 1993.
11. M. Unser, "On the optimality of ideal filters for pyramid and wavelet signal approximation," IEEE Trans. Signal Processing, vol. 41, pp. 3591-3596, Dec. 1993.
12. P. P. Vaidyanathan, "Theory of optimal orthonormal subband coders," IEEE Trans. Signal Processing, vol. 46, pp. 1528-1543, June 1998.
13. M. G. Strintzis, "Optimal biorthogonal wavelet bases for signal decomposition," IEEE Trans. Signal Processing, vol. 44, pp. 1406-1416, June 1996.
14. N. S. Jayant and P. Noll, Digital Coding of Waveforms. Englewood Cliffs, NJ: Prentice-Hall, 1984.
15. M. Unser, "An extension of the Karhunen-Loeve transform for wavelets and perfect reconstruction filter banks," SPIE Math. Imag., vol. 2034, pp. 45-56, 1993.
16. A. W. Marshall and I. Olkin, Inequalities: Theory of Majorization and its Applications. New York:Academic, 1979.
17. A. Kirac and P. P. Vaidyanathan, "On existence of FIR principal component filter banks," Proc. ICASSP, vol. 3, pp. 1329-1332, May 1998.
18. P. Moulin and M. K. Mihcak, "Theory and design of signal adapted FIR paraunitary filter banks," IEEE Trans. Signal Processing, vol. 46, pp. 920-929, Apr. 1998.
19. S. Akkarakaran and P. P. Vaidyanathan, "On optimization of filter banks with denoising applications," Proc. ISCASS, 1999.
20. M. Unser and A. Aldroubi, "A general sampling theory for nonideal acquisition devices," IEEE Trans. Signal Processing, vol. 42, pp. 2915-2925, Nov. 1994.
21. M. G. Strintzis, "Optimal pyramidal and subband decompositions for hierarchical coding of noisy and quantized images," IEEE Trans. Image Processing, vol. 7, pp. 155-166, Feb. 1998.
22. Y. Nesterov and A. Nemirovskii, Interior Point Polynomial Algorithms in Convex Programming. Philadelphia, PA: SIAM, 1994, vol. 13.
23. S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory. Philadelphia,PA: SIAM, 1994, vol. 15.
24. J. Tuqan and P. P. Vaidyanathan, "Globally optimal two-channel FIR orthonormal filter banks adapted to the input signal statistics," Proc. ICASSP, vol. 3, pp. 1353-1356, May 1998.
25. "The role of the discrete-time Kalman-Yakubovich-Popov (KYP) lemma in designing statistically optimum FIR orthonormal filter banks," Proc. ISCAS, vol. 5, June 1998, pp. 122-125.
26. P. P. Vaidyanathan and P. Q. Hoang, "Lattice structures for optimal design and robust implementation of two channel perfect reconstruction QMF banks," IEEE Trans. Acoust., Speech, Signal Processing, vol. 36, pp. 81-94, Jan. 1988.
27. P. Delsarte, B. Macq, and D. T. M. Slock, "Signal-adapted multiresolution transform for image coding," IEEE Trans. Inform. Theory, vol. 38, pp. 897-904, Mar. 1992.
28. D. Taubman and A. Zakhor, "A multi-start algorithm for signal adaptive subband systems," Proc. ICASSP, vol. 3, pp. 213-216, 1992.
29. H. Caglar, Y Liu, and A. N. Akansu, "Statistically optimized PR-QMF design," SPIE, Visual Commun. Image Process., vol. 1605, pp. 86-94, 1991.
30. L. Vandendorpe, "CQF filter banks matched to signal statistics," Signal Process., vol. 29, pp. 237-249, 1992.
31. P. Moulin, M. Anitescu, K. Kortanek, and F. A. Potra, "The role of linear semi-infinite programming in signal dapted QMF bank design," IEEE Trans. Signal Processing, vol. 45, pp. 2160-2174, Sept. 1997.
32. J.-C. Pesquet and P. L. Combettes, "Wavelet synthesis by alternating projections," IEEE Trans. Signal Processing, vol. 44, pp. 728-732, Mar. 1996.
33. A. Kirac and P. P. Vaidyanathan, "Theory and design of optimum FIR compaction filters," IEEE Trans. Signal Processing, vol. 46, pp. 903-919, Apr. 1998.
34. I. Gigberg, Methods in Operator Theory and Signal Processing, I. Schur, Ed. Boston, MA: Birkhauser-Verlag, 1986.
35. B. E. L. Hitz and B. D. O. Anderson, "Discrete positive-real functions and their application to system stability," Proc. Inst. Elect. Eng., pp. 153-155, Jan. 1969.
36. L. Vandenberghe and S. Boyd, "Semidefinite programming," Siam Rev., vol. 38, pp. 49-95, Mar. 1996.
37. S.-P. Wu, S. Boyd, and L. Vandenberghe, "FIR filter design via semidefinite programming and spectral factorization," Proc. IEEE Conf. Decision Contr., 1996.
38. B. D. Anderson and S. Vongpanitlerd, Network Analysis and Synthesis: A Modern System Theory Approach. Englewood Cliffs, NJ: PrenticeHall, 1973.
39. J. C. Willems, "Least squares stationary optimal control and the algebraic Ricatti equation," IEEE Trans. Automat. Contr., vol. 7, pp. 621-634, Dec. 1971.
40. B. D. Anderson, "Algebraic properties of minimal degree spectral factors," Automatica, pp. 491-500, June 1973.
41. L. Vandenberghe andS. Boyd, "SP: Software for semi definite programming, beta version,", Oct. 1994.
42. K. C. Toh, M. J. Todd, and R. H. Tutuncu, "SDPT3-A Matlab software package for semi definite programming," version 2.1, Sept. 1999.
43. R. V Churchill, Complex Variables and Applications. New York:McGraw-Hill, 1990.
44. T.Kailath, Linear Systems. Englewood Cliffs, NJ: Prentice-Hall, 1980.
45. D. Xuan and R. Bamberger, "Complete FIR principal component filter banks," Proc. ISCAS, 19, pp. 417-420.
46. W.-S. Lu and A. Antoniou, "Optimized orthogonal and biorthogonal wavelets using linear parametrization of half band filters," Proc. ISCAS, vol. 5, pp. 102-105, June 1998.
47. J. Tuqan, "On the design of optimal orthogonal finite order transmitter and receiver filters over noisy channels," Proc. 34th Asilomar Conf. Signals, Syst., Comput., Nov. 2000.