Some results in the theory modulated filter banks and modulated wavelet tight frames

Applied and Computational Harmonic Analysis

Volumn 2, Issue 4, 1995, Pages 303-326

  Gopinath, R A ^a   Burrus, C S ^a  

^a RICE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0012695752     PISSN: 10635203     EISSN: 1096603X     Source Type: Journal    
DOI: 10.1006/acha.1995.1023     Document Type: Article

References (29)

1. I. Daubechies, Orthonormal bases of compactly supported wavelets, Comm. Pure Applied Math.41 (Nov. 1988), 909-996.
2. Z. Doganata, P. P. Vaidyanathan, and T. Q. Nguyen, General synthesis procedures for FIR lossless transfer matrices, for perfect-reconstruction multirate filter bank applications, IEEE Trans. ASSP36 No. 10(Oct. 1988), 1561-1574.
3. R. A. Gopinath, “Wavelet and Filter Banks New Results and Applications,” Ph.D. thesis, Rice University, Houston, TX 77251, August 1992.
4. R. A. Gopinath and C. S. Burrus, Wavelets and filter banks, in“Wavelets: A Tutorial in Theory and Applications” (C. K. Chui, Ed.), p. 603-654. Academic Press, San Diego, 1992. Also Tech. Report CMLTR91-20, September 1991.
5. R. A. Gopinath, J. E. Odegard, and C. S. Burrus, On the optimal and robust wavelet representation of signals and the wavelet samplingtheorem, IEEE Trans. CAS II41 No. 4 (April 1994). Also Tech. Report CML TR92-05.
6. R. D. Koilpillai and P. P. Vaidyanathan, Cosine-modulated FIR filter banks satisfying perfect reconstruction, IEEE Trans. SP, 40 No. 4(Apr. 1992), 770-783.
7. W. M. Lawton, Tight frames of compactly supported affine wavelets, J. Math. Phys.31 No. 8 (Aug. 1990), 1898-1901. Also, Aware, Inc.Tech. Report AD891012.
8. H. Malvar, “Signal Processing and Lapped Transforms,” Artech House, Norwood, MA, 1992.
9. H. S. Malvar, Modulated QMF filter banks with perfect reconstruction, Electr. Lett. 26(Jun. 1990), 906-907.
10. J. Mau, Perfect reconstruction modulated filter banks, in“Proc. Int.Conf. Acoust., Speech, Signal Processing,” Vol. 4, p. 273, IEEE, SanFrancisco, 1992.
11. K. Nayebi, T. P. Barnwell III, and M. J. T. Smith, The time domainanalysis and design of exactly reconstructing FIR analysis/synthesisfilter banks, IEEE Trans. ASSP1991.
12. K. Nayebi, T. P. Barnwell III, and M. J. T. Smith, Time-domain filter bank analysis: A new design theory, IEEE Trans. SP40 No. 6 (Jun.1992), 1412-1429.
13. T. Q. Nguyen, A class of generalized cosine-modulated filter banks, in“Proceedings of ISC AS, San Diego, CA, pp. 943-946. IEEE, 1992.
14. T. Q. Nguyen and R. D. Koilpillai, The design of arbitrary lengthcosine-modulated filter banks and wavelets satisfying perfect reconstruction, in“Proceedings of IEEE-SP Symposium on Time-Frequency and Time-Scale Methods’92, Victoria, BC, pp. 299-302, IEEE, 1992.
15. T. Q. Nguyen and P. P. Vaidyanathan, Maximally decimated perfect-reconstruction FIR filter banks with pairwise mirror-image analysis and synthesis frequency responses, IEEE Trans. ASSP, 36 No. 5 (1988), 693-706.
16. J. E. Odegard, R. A. Gopinath, and C. S. Burrus, Optimal waveletsfor signal decomposition and the existence of scale limited signals, in“Proc. Int. Conf. Acoust., Speech, Signal Processing,” Vol. 4, pp.597-600, San Francisco, CA, March 1992. IEEE. Also Tech. ReportCML TR91-07.
17. L. Rabiner and D. Crochière, “Multirate Digital Signal Processing,”Prentice-Hall, New York, 1983.
18. T. A. Ramstad and J. P. Tanem, Cosine-modulated analysis-synthesis filterbanks with critical sampling and perfect reconstruction, in“Proc. Int. Conf. Acoust., Speech, Signal Processing,” pp. 1789-1792, Toronto, May 1991, IEEE.
19. K. R. Rao and P. Yip, “Discrete Cosine Transform—Algorithms, Advantages and Applications, Academic Press, San Diego, 1990.
20. M. J. Smith and T. P. Barnwell III, Exact reconstruction techniquesfor tree-structured subband coders, IEEE Trans. ASSP34 (1986), 434-441.
21. P. Steffen, P. Heller, R. A. Gopinath, and C. S. Burrus, Theory of regularM-band wavelet bases, IEEE Trans. SP41 No. 12 (Dec. 1993).
22. Special Transaction issue on wavelets, Rice contribution also in Tech.Report No. CML TR-91-22, November 1991.
23. P. P. Vaidyanathan, Theory and design ofM-channel maximally decimated quadrature mirror filters with arbitraryM, having perfect reconstruction properties, IEEE Trans. ASSP35 No. 4 (Apr. 1987), 476-492.
24. P. P. Vaidyanathan, “Multirate Systems and Filter Banks," Prentice Hall, Englewood Cliffs, NJ, 1992.
25. P. P. Vaidyanathan and Phuong-Quan Hoang, Lattice structures for optimal design and robust implementation of two-channel perfectreconstruction QMF banks, IEEE Trans. ASSP36 No. 1 (Jan. 1988), 81-93.
26. P. P. Vaidyanathan, T. Q. Nguyen, Z. Doganata, and T. Saramaki, Improved technique for design of perfect reconstruction FIR QMFbanks with lossless polyphase matrices, IEEE Trans. ASSP37 No. 7(Jul. 1989), 1042-1056.
27. M. Vetterli, A theory of multirate filter banks, IEEE Trans. ASSP35 No. 3 (Mar. 1987), 356-372.
28. M. Vetterli and D. Le Gall, Perfect reconstruction FIR filter banks: Some properties and factorizations, IEEE Trans. ASSP37 No. 7 (Jul.1989), 1057-1071.
29. H. Zou and A. H. Tewfik, Discrete orthogonal Af-band wavelet decompositions, in“Proc. Int. Conf. Acoust., Speech, Signal Processing,” Vol. 4, pp. 605-608, IEEE, San Francisco.