Perfect Reconstruction FIR Filter Banks: Some Properties and Factorizations

IEEE Transactions on Acoustics, Speech, and Signal Processing

Volumn 37, Issue 7, 1989, Pages 1057-1071

  Vetterli, Martin ^a   Le Gall, Didier ^b  

^a Och Spine at New York Presbyterian Hospitals   (United States)

^b TELCORDIA TECHNOLOGIES   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

MATHEMATICAL TECHNIQUES--TIME DOMAIN ANALYSIS; MATHEMATICAL TRANSFORMATIONS--Z TRANSFORMS; SIGNAL FILTERING AND PREDICTION;

PERFECT RECONSTRUCTION FIR FILTER BANKS; POLYPHASE FILTER MATRICES; WINDOWED MODULATED FILTER BANKS;

ELECTRIC FILTERS, DIGITAL;

EID: 0024699807     PISSN: 00963518     EISSN: None     Source Type: Journal    
DOI: 10.1109/29.32283     Document Type: Article

References (50)

1. V. Beleviteh, Classical Network Synthesis. San Francisco, CA: Holden-Day, 1968.
2. R.E. Blahut, Fast Algorithms for Digital Signal Processing. Reading, MA: Addison-Wesley, 1984.
3. M.G. Bellanger and J.L. Daguet, “TDM-FDM transmultiplexer: Digital polyphase and FFT,” IEEE Trans. Commun., vol. COM-22, pp. 1199–1204, Sept. 1974.
4. P. Cassereau, “A new class of optimal unitary transforms for image processing,” S.M. thesis, Dep. Elec. Eng. Comput. Sci., Massachusetts Inst. Technol., Cambridge, May 1985.
5. P.L. Chu, “Quadrature mirror filter design for an arbitrary number of equal bandwidth channels,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-33, pp. 203–218, Feb. 1985.
6. R.V. Cox. “The design of uniformly and nonuniformly spaced pseudoquadrature mirror filters,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-34, pp. 1090–1096, Oct. 1986.
7. R.E. Crochiere and L.R. Rabiner, Multirate Digital Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 1983.
8. A. Croisier, D. Esteban, and C. Galand, “Perfect channel splitting by use of interpolation, decimation, tree decomposition techniques,” in Proc. Int. Conf. Inform. Sci./Syst., Patras, Greece, Aug. 1976, pp. 443–446.
9. P.J. Davis, Circulant Matrices. New York: Wiley Interscience, 1979.
10. Z. Doganata and P.P. Vaidyanathan, “On one-multiplier implementation of FIR lattice structures,” IEEE Trans. Circuits Syst., vol. CAS-34, pp. 1608–1609, Dec. 1987.
11. C.R. Galand and H.J. Nussbaumer, “Quadrature mirror filters with perfect reconstruction and reduced computational complexity.” in Proc. 1985 Int. IEEE Conf. Acoust., Speech, Signal Processing, Tampa, FL, Mar. 1985, pp. 525–529.
12. T. Kailath, Linear Systems. Englewood Cliffs, NJ: Prentice-Hall, 1980.
13. D.J. LeGall, “Subband coding of images with low computational complexity,” presented at the Picture Coding Symp., Stockholm, Sweden, June 1987.
14. H.S. Malvar, “Optimal pre- and post-filtering in noisy sampled data systems,” Ph.D. dissertation, Dep. Elec. Eng. Comput. Sci., Massachusetts Inst. Technol., Cambridge, Aug. 1986.
15. J. Masson and Z. Picel, “Flexible design of computationally efficient nearly perfect QMF filter banks,” in Proc. 1985 IEEE Conf. Acoust., Speech, Signal Processing, Tampa. FL, Mar. 1985.
16. F. Mintzer. “Filters for distortion-free two-band multirate filter banks.” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-33, pp. 626–630, June 1985.
17. F.D. Murnaghan, The Unitary and Rotation Groups. Washington, DC: Spartan, 1962.
18. M.J. Narasimha and A.M. Peterson, “Design of a 24-channel transmultiplexer,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-27, pp. 752–762, Dec. 1979.
19. M.J. Narasimha and A.M. Peterson, “On the computation of the discrete cosine transform,” IEEE Trans. Commun., vol. COM-26, pp. 934–936, June 1978.
20. K. Nayebi, T.P. Barnwell, and M.J.T. Smith, “Time domain conditions for exact reconstruction in analysis/synthesis systems based on maximally decimated filter banks,” in Proc. Southeast. Symp. Syst. Theory, Mar. 1987, pp. 498–503.
21. T.Q. Nguyen and P.P. Vaidyanathan, “Perfect reconstruction QMF structures which yield linear phase FIR analysis filters,” in Proc. Int. Symp. Circuits Syst., Helsinki. Finland, June 1988, pp. 297–300.
22. H.J. Nussbaumer, “Pseudo-QMF filter bank,” IBM Tech. Disclosure Bull., 1981.
23. H.J. Nussbaumer, Fast Fourier Transform and Convolution Algorithms. Berlin: Springer, 1982.
24. H.J. Nussbaumer and M. Vetterli, “Computationally efficient QMF filter banks,” in Proc. 1984 Int. IEEE Conf. Acoust., Speech, Signal Processing, San Diego, CA, Mar. 1984.
25. J. Princen and A. Bradley, “Analysis/synthesis filter bank design based on time domain aliasing cancellation,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-34, pp. 1153–1161, Oct. 1986.
26. J. Princen, A. Johnson, and A. Bradley, “Subband/transform coding using filter bank designs based on time domain aliasing cancellation,” in Proc. ICASSP′87, Dallas, TX, Apr. 1987, pp. 2161–2164.
27. T.A. Ramstad, “Analysis/synthesis filter banks with critical sampling,” in Proc. Int. Conf. Digital Signal Processing, Florence, Italy, Sept. 1984, pp. 130-134.
28. J.H. Rothweiler, “Polyphase quadrature filters—A new subband coding technique.” in Proc. 1983 Int. IEEE Conf. Acoust., Speech, Signal Processing, Boston, MA, Mar. 1983, pp. 1280–1283.
29. M.J.T. Smith and T.P. Barnwell, “A procedure for designing exact reconstruction filter banks for tree structured subband coders,” in Proc. IEEE ICASSP′84, San Diego, CA, Mar. 1984.
30. M.J.T. Smith and T.P. Barnwell, “Exact reconstruction for tree-structured subband coders,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-34, pp. 434–441, June 1986.
31. M.J.T. Smith and T.P. Barnwell, “A unifying framework for analysis/synthesis systems based on maximally decimated filter banks,” in Proc. ICASSP′85, Tampa, FL, Mar. 1985, pp. 521–524.
32. M.J.T. Smith and T.P. Barnwell, “A new filter bank theory for time-frequency representation,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-35, pp. 314–327, Mar. 1987.
33. P.P. Vaidyanathan and S.K. Mitra, “A general family of multivariable digital lattice filters,” IEEE Trans. Circuits Syst., vol. CAS-32, pp. 1234–1245, Dec. 1985.
34. P.P. Vaidyanathan, “Theory and design of M-channel maximally decimated quadrature mirror filters with arbitrary M, having perfect reconstruction property,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-35, pp. 476–492, Apr. 1987.
35. P.P. Vaidyanathan and P.-Q. Hoang, “The perfect reconstruction QMF bank: New architectures, solutions, and optimization strategies,” in Proc. IEEE Int. Conf. Acoust., Speech, Signal Processing, Dallas, TX, Apr. 1987, pp. 2169–2172.
36. P.P. Vaidyanathan, Z. Doganata, and T.Q. Nguyen, “More results on the perfect reconstruction problem in M-band parallel QMF banks,” in Proc. IEEE Int. Symp. Circuits Syst., Philadelphia, PA, May 1987, pp. 847–850.
37. P.P. Vaidyanathan, “Quadrature mirror filter banks, M-band extensions and perfect-reconstruction technique,” IEEE ASSP Mag., vol. 4, pp. 4–20, July 1987.
38. P.P. Vaidyanathan, Z. Doganata, and T.Q. Nguyen, “General synthesis procedures for FIR lossless transfer matrices, for perfect-reconstruction multirate filter bank applications,” Dep. Elec. Eng., California Inst. Technol., Pasadena, Tech. Rep., Aug. 1987. See also IEEE Trans. Acoust., Speech, Signal Processing, vol. 36, pp. 1561–1574, Oct. 1988.
39. P.P. Vaidyanathan and P.-Q. Hoang, “Lattice structures for optimal design and robust implementation of two-band perfect reconstruction QMF banks,” IEEE Trans. Acoust., Speech, Signal Processing, vol. 36, pp. 81–94, Jan. 1988.
40. P.P. Vaidyanathan and S.K. Mitra, “Polyphase networks, block digital filtering, LPTV systems, and alias-free QMF banks: A unified approach based on pseudocirculants,” IEEE Trans. Acoust., Speech, Signal Processing, vol. 36, pp. 381–391, Mar. 1988.
41. P.P. Vaidyanathan and Z. Doganata, “The role of lossless systems in modern digital signal processing: A tutorial,” IEEE Trans. Educ., to appear, Aug. 1989.
42. P.P. Vaidyanathan, private communication, June 1988.
43. M. Vetterli, “Multidimensional subband coding: Some theory and algorithms,” Signal Processing, vol. 6, pp. 97–112, Feb. 1984.
44. M. Vetterli and H.J. Nussbaumer, “Simple FFT and DCT algorithms with reduced number of operations,” Signal Processing, vol. 6, pp. 267–278, Aug. 1984.
45. M. Vetterli, “Splitting a signal into subsampled channels allowing perfect reconstruction,” in Proc. IASTED Conf. Appl. Signal Processing Digital Filtering, Paris, France, June 1985.
46. M. Vetterli, “Filter banks allowing perfect reconstruction,” Signal Processing, vol. 10, pp. 219–244, Apr. 1986.
47. M. Vetterli, “A theory of multirate filter banks,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-35, pp. 356–372, Mar. 1987.
48. M. Vetterli and D. Le Gall, “Perfect reconstruction FIR filter banks: Lapped transforms, pseudo-QMF's and paraunitary matrices,” in Proc. Int. Symp. Circuits Syst., Helsinki, Finland, June 1988, pp. 2249–2253.
49. M. Vetterli and D. Le Gall, “Analysis and design of perfect reconstruction filter banks satisfying symmetry constraints,” in Proc. Princeton Conf. Inform. Sci. Syst., Mar. 1988, pp. 670–675.
50. E. Viscito and J. Allebach, “The design of tree-structured M-channel filter banks using perfect reconstruction filter blocks,” in Proc. ICASSP′88, New York, NY, Apr. 1988, pp. 1475–1478.