Theory and design of optimum FIR compaction filters

IEEE Transactions on Signal Processing

Volumn 46, Issue 4, 1998, Pages 903-919

  Kiraç, Ahmet ^b   Vaidyanathan, P P ^a,b  

^a IEEE

^b California Institute of Technology   (United States)

Author keywords

Energy compaction; Nyquist filters; Orthonormal filter banks; Subband coding; Wavelets

Indexed keywords

EID: 0001164856     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/78.668545     Document Type: Article

References (45)

1. K. C. Aas and C. T. Mullis, "Minimum mean-squared error transform coding and subband coding," IEEE Trans. Inform. Theory, vol. 42, pp. 1179-1192, July 1996.
2. S. O. Aase and T. A. Ramstad, "On the optimality of nonunitary filter banks in subband coders," IEEE Trans. Image Processing, vol. 4, pp. 1585-1591, Dec. 1995.
3. A. N. Akansu and Y. Liu, "On signal decomposition techniques," Opt. Eng., vol. 30, pp. 912-920, July 1991.
4. 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.
5. J. Katto and Y. Yasuda, "Performance evaluation of subband coding and optimization of its filter coefficients," in Proc. SPIE, Visual Commun. Image Process.: Visual Commun., 1991, vol. 1605, pp. 95-106.
6. 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.
7. M. Unser, "An extension of the Karhunen-Loeve transform for wavelets and perfect reconstruction filterbanks," in Proc. SPIE Math. Imaging, 1993, vol. 2034, pp. 45-56.
8. -, "On the optimality of ideal filters for pyramid and wavelet signal approximation," IEEE Trans. Signal Processing, vol. 41, pp. 3591-3596, Dec. 1993.
9. P. P. Vaidyanathan, "Theory of optimal orthonormal filter banks," in Proc. IEEEICASSP, May 1996, Atlanta, GA, vol. 3, pp. 1487-1490.
10. _, Multirate Systems and Filter Banks. Englewood Cliffs, NJ: Prentice-Hall, 1993.
11. N. S. Jayant and P. Noll, Digital Coding of Waveforms. Englewood Cliffs, NJ: Prentice-Hall, 1984.
12. A. Tirakis, A. Delopoulos, and S. Kollias, "Two-dimensional filter bank design for optimal reconstruction using limited subband information," IEEE Trans. Image Processing, vol. 4, pp. 1160-1165, Aug. 1995.
13. B. Xuan and R. H. Bamberger, "2D factorizable FIR principal compo-nent filter banks," in Proc. IEEE ICASSP, May 1996, Atlanta, GA, pp. 1538-1541.
14. _, "Complete FIR principal component filter banks," in Proc. IEEE ISCAS, May 1996, Atlanta, GA, pp. 417-420.
15. _, "Multi-dimensional paraunitary principal component filter banks," in Proc. IEEEICASSP, May 1995, Detroit, MI, pp. 1488-1491.
16. R. A. Horn and C. R. Johnson, Matrix Analysis. Cambridge, U.K.: Cambridge Univ. Press, 1985.
17. A. Kirac and P. P. Vaidyanathan, "Optimality of orthonormal transforms for subband coding," in Proc. IEEE DSP Workshop, Snowbird, UT, 1998.
18. _, "Optimal nonuniform orthonormal filter banks for subband coding and signal representation," submitted for publication.
19. -, "On existence of FIR principal component filter banks," in Proc. IEEE ICASSP, Seattle, WA, 1998.
20. P. Moulin, M. Anitescu, K. Kortanek, and F. Potra, "Design of signaladapted FIR paraunitary filter banks," in Proc. IEEEICASSP, May 1996, Atlanta, GA, vol. 3, pp. 1519-1522.
21. 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.
22. D. Taubman and A. Zakhor, "A multi-start algorithm for signal adaptive subband systems," in Proc. IEEE ICASSP, Mar. 1992, San Francisco, CA, vol. 3, pp. 213-216.
23. Q. Jin, T. Luo, and K. M. Wong, "Optimum filter banks for signal decomposition and its application in adaptive echo cancellation," IEEE Trans. Signal Processing, vol. 44, pp. 1669-1680, July 1996.
24. M. K. Tsatsanis and G. B. Giannakis, "Time-varying system iden-tification and model validation using wavelets," IEEE Trans. Signal Processing, vol. 41, pp. 3512-3523, Dec. 1993.
25. 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.
26. K. C. Aas, K. A. Duell, and C. T. Mullis, "Synthesis of extremal wavelet-generating filters using Gaussian quadrature," IEEE Trans. Signal Processing, vol. 43, pp. 1045-1057, May 1995.
27. R. A. Roberts and C. T. Mullis, Digital Signal Processing. Reading, MA, Addison-Wesley, 1987.
28. http://www.systems.caltech.edu/kirac/
29. H. Caglar, Y. Liu, and A. N. Akansu, "Statistically optimized PRQMF design," in Proc. SPIE, Visual Commun. Image Process.: Visual Commun., 1991, vol. 1605, pp. 86-94.
30. L. Vandendorpe, "CQF filter banks matched to signal statistics," Signal Process., vol. 29, pp. 237-249, 1992.
31. P. Moulin, "A new look at signal-adapted QMF bank design," in Proc. IEEE ICASSP, May 1995, Detroit, MI, vol. 5, pp. 1312-1315.
32. P. Moulin, M. Anitescu, K. Kortanek, and F. 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.
33. B. E. Usevitch and M. T. Orchard, "Smooth wavelets, transform coding, and markov-1 processes," IEEE Trans. Signal Processing, vol. 43, pp. 2561-2569, Nov. 1995.
34. V. Silva and L. de Sa, "Analytical optimization of CQF filter banks," IEEE Trans. Signal Processing, vol. 44, pp. 1564-1568, June 1996.
35. J. Tuqan and P. P. Vaidyanathan, "A state space approach for the design of optimum FIR energy compaction filters," in preparation.
36. A. Kirac and P. P. Vaidyanathan, "Efficient design methods of optimal FIR compaction filters for M-channel FIR subband coders," in Proc. 30th Asilomar Conf. Signals, Syst., Comput., 1996.
37. -, "Analytical method for 2-channel optimum FIR orthonormal filter banks," in Proc. IEEE ISCAS, June 1997, Hong Kong.
38. _, "Fir compaction filters: New design methods and properties," in Proc. IEEE 1CASSP, May 1997, Munich, Germany, pp. 2229-2232.
39. V. F. Pisarenko, "The retrieval of harmonics from a covariance function," Geophys. J. Roy. Astron. Soc., vol. 33, pp. 347-366, 1973.
40. N. I. Ahiezer and M. Krein, Some Questions in the Theory of Moments. Translations of Mathematical Monographs, Vol. 2. Providence, RI: Amer. Math. Soc., 1962.
41. P. J. Davis, Interpolation and Approximation. New York: Dover, 1975.
42. F. L. Bauer, "A direct iterative process for the Hurwitz-decomposition of a polynomial," Arch. Elekt. Ubertr., vol. 9, pp. 285-290, June 1955;
43. IRE Trans. Circuit Theory, vol. CT-2, pp. 370-371, Dec. 1955.
44. T. Q. Nguyen, "A novel spectral factorization method and its application in the design of filter banks and wavelets," in Proc. IEEE-SP Int. Symp. Time-Freq. Time-Scale Anal, Oct. 1992, pp. 303-306.
45. A. K. Jain, Fundamentals of Digital Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 1989.