Linear boundary extensions for finite length signals and paraunitary two-channel filterbanks

IEEE Transactions on Signal Processing

Volumn 52, Issue 11, 2004, Pages 3213-3226

  Jiménez, María Elena Domínguez ^a   Prelcic, Nuria González ^b  

^a UNIVERSIDAD POLITÉCNICA DE MADRID   (Spain)

^b UNIVERSITY OF VIGO   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; FIR FILTERS; MATHEMATICAL TRANSFORMATIONS; MATRIX ALGEBRA; SIGNAL RECONSTRUCTION;

BORDER EFFECTS; BOUNDARY EXTENSIONS; ORTHOGONAL TRANSFORMS; SMOOTH ORTHOGONAL EXTENSIONS; TWO CHANNEL FILTERBANKS;

SIGNAL FILTERING AND PREDICTION;

EID: 7544241230     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2004.836526     Document Type: Article

References (44)

1. P. P. Vaidyanathan, "Multirate digital filters, filterbanks, polyphase networks, and applications: A tutorial," Proc. IEEE, vol. 78, pp. 56-93, Jan. 1990.
2. A. N. Akansu and R. A. Haddad, Multiresolution Signal Decomposition. San Diego, CA: Academic, 1992.
3. C. Herley and M. Vetterli, "Wavelets and filterbanks: Theory and design," IEEE Trans. Signal Processing, vol. 40, pp. 2207-2232, Sept. 1992.
4. A. K. Soman and P. P. Vaidyanathan, "On orthonormal wavelets and paraunitary filterbanks," IEEE Trans. Signal Processing, vol. 41. pp. 1170-1183, Mar. 1993.
5. P. P. Vaidyanathan, Multirate Systems and filterbanks. Englewood Cliffs, NJ: Prentice-Hall. 1993.
6. S. G. Mallat, "A theory for multiresolution signal decomposition: The wavelet representation" IEEE Trans. Pattern Anal. Machine Intell., vol. 11, pp. 674-693, July 1989.
7. I. Daubechies, Ten Lectures on Wavelets. Philadelphia, PA: SIAM, 1992.
8. C. Herley, J. Kovacevic, K. Ramchandran, and M. Vetterli, "Tilings of the time-frequency plane: Construction of arbitrary orthogonal bases and fast tiling algorithms," IEEE Trans. Signal Processing, vol. 41, pp. 3341-3359, Dec. 1993.
9. M. V. Wickerhauser, Adapted Wavelet Analysis From Theory to Software. Wellesley, MA: AK Peters, 1994.
10. M. Vetterli and J. Kovacevic, Wavelets and Subband Coding. Englewood Cliffs. NJ: Prentice-Hall, 1995.
11. G. Strang and T. Q. Nguyen, Wavelets and Filterbanks. Wellesley, MA: Wellesley-Cambridge, 1996.
12. A. N. Akansu and M. J. T. Smith. Subband and Wavelet Transforms: Design and Applications. Boston, MA: Kluwer Academic, 1996.
13. C. S. Burrus, R. A. Gopinath, and H. Guo, Wavelets and Wavelet Transforms. Upper Saddle River, NJ: Prentice-Hall, 1997.
14. A. R. Lindsey, "Wavelet packet modulation for orthogonally multiplexed communication," IEEE Trans. Signal Processing, vol. 45. pp. 1336-1339, May 1997.
15. A. N. Akansu, P. Duhamel, X. Lin, and M. de Courville. "Orthogonal transmultiplexers in communication: A review," IEEE Trans. Signal Processing, vol. 46, pp. 979-995, Apr. 1998.
16. L. Vandendorpe et al., "Fractionally spaced linear and decision-feedback detectors for transmultiplexers," IEEE Trans. Signal Processing, vol. 46, pp. 996-1011, Apr. 1998.
17. Y. Shiyou et al., "Wavelet-Galerkin method for computations of electromagnetic fields," IEEE Trans. Magn., vol. 34, pp. 2493-2496, Sept. 1998.
18. G. B. Giannakis, "Highlights of signal processing for communications," IEEE Signal Processing Mag., vol. 16, pp. 14-50, Mar. 1999.
19. A. Scaglione, G. B. Giannakis, and S. Barbarossa, "Redundant filterbank precoders and equalizers - Part I: Unification and optimal designs," IEEE Trans. Signal Processing, vol. 47, pp. 1988-2006, July 1999.
20. T. Painter and A. Spanias, "Perceptual coding of digital audio," Proc. IEEE, vol. 88, pp. 451-515, Apr. 2000.
21. D. S. Taubman and M. W. Marcellin, Jpeg2000: Image Compression Fundamentals, Standards, and Practice. Boston, MA: Kluwer, 2001.
22. N. G. Prelcic, F. P. González, and M. E. D. Jiménez, " Wavelet-packet-based subband adaptive equalization," Signal Process., vol. 81. pp. 1641-1662, Aug. 2001.
23. P. P. Vaidyanathan, Y. Lin, S. Akkarakaran, and S. Phoong, "Discrete multitone modulation with principal component filterbanks," IEEE Trans. Circuits Syst. I, vol. 49, pp. 1397-1412, Oct. 2002.
24. W. E. Hutchcraft and R. K. Gordon, "Two-dimensional higher order wavelet-like basis functions in the finite element method," in Proc. 34th Southeastern Symp. System Theory, Huntsville, AL, Mar. 2002. pp. 147-151.
25. G. Karlsson and M. Vetterli, "Extension of finite length signals for sub-band coding," Signal Process., vol. 17, pp. 161-168, June 1989.
26. R. L. de Queiroz, "Subband processing of finite-length signals without border distortions," in Proc. IEEE ICASSP, vol. 4, San Francisco, CA, Mar. 1992, pp. 613-616.
27. R. H. Bamberger, S. L. Eddins, and V. Nuri, "Generalized symmetric extension for size-limited multirate filterbanks," IEEE Trans. Image Processing, vol. 3, pp. 82-87, Jan. 1994.
28. J. N. Bradley and V. Faber, "Perfect reconstruction with citically sampled filterbanks and linear boundary conditions," IEEE Trans. Signal Processing, vol. 43, pp. 994-997, Apr. 1995.
29. R. L. de Queiroz and K. R. Rao, "On reconstruction methods for processing finite-length signals with paraunitary filterbanks," IEEE Trans. Signal Processing, vol. 43. pp. 2407-2410, Oct. 1995.
30. A. Cohen, I. Daubechies, and P. Vial, "Wavelets on the interval and fast wavelet transforms," Applied Comput. Harmon. Anal., vol. 1, pp. 54-81, Jan. 1993.
31. C. Herley and M. Vetterli, "Orthogonal time-varying filterbanks and wavelet packets," IEEE Trans. Signal Processing, vol. 42. pp. 2650-2663, Oct. 1994.
32. C. Herley, "Boundary filters for finite-length signals and time-varying filterbanks," IEEE Trans. Circuits Syst. II, vol. 42. pp. 102-114, Feb. 1995.
33. R. L. de Queiroz, "Further results on reconstruction methods for processing finite-length signals with perfect reconstruction filterbanks," IEEE Trans. Signal Processing, vol. 48, pp. 1814-1816, June 2000.
34. V. Silva and L. de Sá, "General method for perfect reconstruction sub-band processing of finite length signals using linear extensions," IEEE Trans. Signal Processing, vol. 47, pp. 2572-2575, Oct. 1999.
35. M. E. Dominguez Jiménez and N. G. Prelcic, "Processing finite length signals via filterbanks without border distortions: A nonexpansionist solution," in Proc. IEEE ICASSP, vol. 3, Phoenix, AZ, Mar. 1999, pp. 1481-1484.
36. A. Mertins, "Boundary filter optimization for segmentation-based sub-band coding," IEEE Trans. Signal Processing, vol. 49, pp. 1718-1727, Aug. 2001.
37. M. E. Dominguez Jiménez and N. G. Prelcic, "Polynomial extension method for size-limited paraunitary filterbanks," in Proc. Eur. Signal Process. Conf., vol. 2, Toulouse, France, Sept. 2002, pp. 545-548.
38. M. E. Dominguez Jiménez, "Diseno de Extensiones Para Procesamiento de Senales Finitas Mediante Wavelets," Ph.D. dissertation, Univ. Politécnica Madrid, Madrid, Spain, 2001.
39. J. Williams and K. Amaratunga, "A discrete wavelet transform without edge effects using wavelet extrapolation," J. Fourier Anal. Applicat., vol. 3, no. 4, pp. 435-449, 1997.
40. M. E. Dominguez Jiménez and N. G. Prelcic, "Design of nonexpansionist and orthogonal extension methods for tree-structured filterbanks," in Proc. IEEE ICASSP, vol. 1, Istanbul, Turkey, June 2000, pp. 532-535.
41. M. E. Dominguez Jiménez, "New orthogonal extension methods for tree-structured filterbanks," in Proc. Eur. Signal Process. Conf., vol. 2, Tampere, Finland, Sept. 2000, pp. 1073-1076.
42. M. E. Dominguez Jiménez, "Orthogonal extensions of AR processes without artificial discontinuities for size-limited filterbanks," in Proc. IEEE Workshop Statistical Signal Process., Singapore, Aug. 2001, pp. 579-582.
43. M. E. Dominguez Jiménez and N. G. Prelcic, "Smooth orthogonal signal extensions for paraunitary tree-structured filterbanks," in Proc. IEEE ICASSP, vol. 2, Orlando, FL, May 2002, pp. 1233-1236.
44. G. H. Golub and C. F. Van Loan, Matrix Computations, Third ed. Baltimore, MD: Johns Hopkins Univ. Press, 1996.