Vector Space Framework for Unification of One- and Multidimensional Filter Bank Theory

IEEE Transactions on Signal Processing

Volumn 42, Issue 8, 1994, Pages 2006-2021

  Chen, Tsuhan ^a   Vaidyanathan, P P ^b  

^a LUCENT TECHNOLOGIES   (United States)

^b CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CIRCUIT THEORY; DIGITAL FILTERS; ELECTRIC NETWORK ANALYSIS; ELECTRIC NETWORK SYNTHESIS; IMAGE RECONSTRUCTION; MATHEMATICAL TRANSFORMATIONS; MATRIX ALGEBRA; SIGNAL ENCODING; THEOREM PROVING; VECTORS;

DISCRETE WAVELET TRANSFORM; FILTER BANK THEORY; GENERALIZED PARSEVAL'S RELATION; PERFECT RECONSTRUCTION PROPERTY; VECTOR SPACE FRAMEWORK; WAVELET CONVOLUTION THEOREM;

SIGNAL FILTERING AND PREDICTION;

EID: 0028484513     PISSN: 1053587X     EISSN: 19410476     Source Type: Journal    
DOI: 10.1109/78.301839     Document Type: Article

References (38)

1. P. P. Vaidyanathan, “Theory and design of M-channel maximally decimated quadrature mirror filters with arbitrary M, having the perfectreconstruction property,” IEEE Trans. Acoust., Speech, Signal Processing, vol. 35, no. 4, 476–492, Apr. 1987.
2. M. Vetterli, “Filter banks allowing for perfect reconstruction,” Signal Processing, vol. 10, pp. 219–244, Apr. 1986.
3. M. J. T. Smith and T. P. Barnwell III, “A new filter-bank theory for time-frequency representation,” IEEE Trans. Acoust., Speech, Signal Processing, vol. 35, pp. 314–327, Mar. 1987.
4. P.Q. Hoang and P. P. Vaidyanathan, “Non-uniform multirate filter banks: Theory and design,” in Proc. IEEE Int. Symp. Circuits, Systems (Portland), 1989.
5. K. Nayebi, T. P. Barnwell III, and M. J. T. Smith, “The design of perfect reconstruction nonuniform band filter banks,” in Proc. IEEE Int. Conf. Acoust., Speech, Signal Processing, (Canada), 1991, pp. 1781–1784
6. J. KovaCevic and M. Vetterli, “Perfect reconstruction filter banks with rational sampling rate changes,” in Proc. IEEE Int. Conf. Acoust., Speech, Signal Processing (Canada), 1991, pp. 1785–1788.
7. R. A. Gopinath and C. S. Burrus, “On upsampling, downsampling and rational sampling rate filter banks,” IEEE Trans. Signal Processing, Apr. 1994.
8. B. Paillard, J. Soumagne, P. Mabilleau, and S. Morissette, “Filters for subband coding, analytical approach,” in Proc. IEEE Int. Conf. Acoustics, Speech, Signal Processing (Dallas, TX), Apr. 1987, pp. 50.2.1-50.2.5.
9. E. H. Adelson, E. P. Simoncelli, and R. Hingorani, “Orthogonal pyramid transforms for image coding,” in Proc. SPIE Visual Commun., Image Processing, 1987, pp. 50–58.
10. M. Vetterli and D. Le Gall, “Perfect reconstruction FIR filter banks: Some properties and factorization,” IEEE Trans. Acoust., Speech, Signal Processing, vol. 37, no. 7, pp. 1057–1071, July 1989.
11. K. Nayebi, T. P. Barnwell III, and M. J. T. Smith, “Time domain conditions for exact reconstruction in analysis/synthesis systems based on maximally decimated filter banks,” Proc. Southeastern Symp. Syst. Theory, Mar. 1987.
12. A. N. Akansu and R. A. Haddad, Multiresolution Signal Decomposition: Transforms, Subbands, and Wavelets. New York: Academic, 1992.
13. H. S. Malvar, Signal Processing with Lapped Transforms. Norwood, MA: Artech, 1992.
14. V. Nuri and R. H. Bamberger, “A theoretical framework for the analysis and design of size-limited multirate filter banks,” in Proc. IEEE-SP Int. Symp. Time-Frequency, Time-Scale Anal., 1992.
15. C. K. Chui, An Introduction to Wavelets. New York: Academic, 1992.
16. M. Vetterli and C. Herley, “Wavelets and filter banks: theory and design,” IEEE Trans. Signal Processing, vol. 40, no. 9, pp. 2209–2232, Sept. 1992.
17. IEEE Trans. Commun., Special Issue on Transmultiplexers, vol. 30, no. 7, July 1982.
18. M. Vetterli, “Perfect transmultiplexers,” in Proc. IEEE Int. Conf. Acoust., Speech, Signal Processing (Tokyo, Japan), Apr. 1986, pp. 2567–2570.
19. R. D. Koilpillai, T. Q. Nguyen, and P. P. Vaidyanathan, “Some results in the theory of crosstalk-free transmultiplexers,” IEEE Trans. Signal Processing, vol. 39, no. 10, pp. 2174-2183, Oct. 1991.
20. P. P. Vaidyanathan, “Orthonormal and biorthonormal filter-banks as convolvers, and convolutional coding gain,” IEEE Trans. Signal Processing, vol. 41, no. 6, pp. 2110–2130, June 1993.
21. I. Daubechies, Ten Lectures on Wavelets, SIAM, CBMS series, Apr. 1992.
22. P. P. Vaidyanathan, Multirate Systems and Filter Banks. Englewood Cliffs, NJ: Prentice-Hall, 1993.
23. D. E. Dudgeon and R. M. Mersereau, Multidimensional Digital Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 1984.
24. R. Ansari and C.L. Lau, “Two-dimensional IIR filters for exact reconstruction in tree structured subband decomposition,” Electron. Lett., vol. 23, pp. 633–634, June 1987.
25. E. Viscito and J. P. Allebach, “Design of perfect reconstruction multidimensional filter banks using cascaded Smith form matrices,” in Proc. IEEE Int. Symp. Circuits, Systems (Espoo, Finland), June 1988, pp. 831–834.
26. G. Karlsson and M. Vetterli, “Theory of two-dimensional multirate filter banks,” IEEE Trans. Acoust., Speech, Signal Processing, vol. 38, no. 6, pp. 925–937, June 1990.
27. P. P. Vaidyanathan, “Fundamentals of multidimensional multirate digital signal processing,” Sadhana, vol. 15, pp. 157–176, Nov. 1990.
28. E. Viscito and J. P. Allebach, “The analysis and design of multidimensional FIR perfect reconstruction filter banks for arbitrary sampling lattices,” IEEE Trans. Circuits, Syst., vol. 38, no. 1, pp. 29–41, Jan. 1991.
29. J. W. Woods, Subband Image Coding. Norwood, MA: Kluwer, 1991.
30. D. G. Luenberger, Optimization by Vector Space Methods. New York: Wiley, 1969.
31. C. C. MacDuffee, The Theory of Matrices. New York: Chelsea, 1946.
32. T. Kailath, Linear Systems. Englewood Cliffs, NJ: Prentice-Hall, 1980.
33. M. Vidyasagar, Control System Synthesis: A Factorization Approach. Cambridge, MA: The M.I.T. Press, 1985.
34. T. Chen and P. P. Vaidyanathan, “The role of integer matrices in multidimensional multirate systems,” IEEE Trans. Signal Processing, vol. 41, no. 3, 1035–1047, Mar. 1993.
35. N. S. Jayant and P. Noll, Digital Coding of Waveforms. Englewood Cliffs, NJ: Prentice-Hall, 1984.
36. V. Sathe and P. P. Vaidyanathan, “Effects of multirate systems on the statistical properties of random inputs,” IEEE Trans. Signal Processing, vol. 41, no. 1, pp. 131–146, Jan. 1993.
37. A. K. Soman and P. P. Vaidyanathan, “Coding gain in paraunitary analysis/synthesis systems,” IEEE Trans. Signal Processing, vol. 41, no. 5, pp. 1824–1835, May 1993.
38. A. K. Soman and P. P. Vaidyanathan, “Paraunitary filter banks and wavelet packets,” in Proc. IEEE Int. Conf. Acoust, Speech, Signal Processing (San Francisco, CA), vol. 4, Mar. 1992, pp. 397–400.