On the statistical decorrelation of the wavelet packet coefficients of a band-limited wide-sense stationary random process

Signal Processing

Volumn 87, Issue 10, 2007, Pages 2320-2335

  Atto, Abdourrahmane M ^a   Pastor, Dominique ^a   Isar, Alexandru ^b  

^a ECOLE DES MINES DE NANTES   (France)

^b UP Timisoara ^*  (Romania)

Author keywords

Autocorrelation function; Battle Lemari filters; Daubechies filters; Mean square integral; Spectral representation of a process; Wavelet packets; Wide sense stationary random process

Indexed keywords

DIGITAL FILTERS; POWER SPECTRAL DENSITY; RANDOM PROCESSES; STATISTICAL METHODS; TREES (MATHEMATICS); WAVELET ANALYSIS;

QUADRATURE MIRROR FILTERS (QMF); SHANNON QMF; WAVELET PACKET;

PACKET NETWORKS;

EID: 34249910092     PISSN: 01651684     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.sigpro.2007.03.014     Document Type: Review

References (34)

1. Tewfik A.H., and Kim M. Correlation structure of the discrete wavelet coefficients of fractional brownian motion. IEEE Trans. Inform Theory 38 2 (March 1992) 904-909
2. Flandrin P. Wavelet analysis and synthesis of fractional brownian motion. IEEE Trans. Inform. Theory 38 2 (March 1992) 910-917
3. Cohen A. Ondelettes et Traitement Numérique du Signal (1992), Masson, Paris
4. Dijkerman R.W., and Mazumdar R.R. On the correlation structure of the wavelet coefficients of fractional brownian motion. IEEE Trans. Inform. Theory 40 5 (September 1994) 1609-1612
5. Walter G.G. Wavelets and Other Orthogonal Systems with Applications (1994), CRC Press, Boca Raton
6. Houdré C. Wavelets, probability, and statistics: some bridges. In: Benedetto J.J., and Frasier M.W. (Eds). Wavelets: Mathematics and Applications (1994), CRC Press, Boca Raton 365-398 (Chapter 9)
7. Craigmile P.F., and Percival D.B. Asymptotic decorrelation of between-scale wavelet coefficients. IEEE Trans. Inform. Theory 51 3 (March 2005) 1039-1048
8. Lemoine C., and Pastor D. Démodulation cohérente par analyse multi-résolution en présence de bruit parasite coloré et gaussien. Traitement du Signal 15 3 (1998) 251-264
9. Zhang J., and Walter G. A wavelet-based KL-like expansion for wide-sense stationary random processes. IEEE Trans. Signal Process. 42 7 (July 1994) 1737-1745
10. Leporini D., and Pesquet J.-C. High-order wavelet packets and cumulant field analysis. IEEE Trans. Inform. Theory 45 3 (April 1999) 863-877
11. Pastor D., and Gay R. Décomposition d'un processus stationnaire du second ordre: propriétés statistiques d'ordre 2 des coefficients d'ondelettes et localisation frequentielle des paquets d'ondelettes. Traitement du Signal 12 5 (1995)
12. Coifman R.R., and Wickerhauser M.V. Entropy-based algorithms for best basis selection. IEEE Trans. Inform. Theory 38 2 (March 1992) 713-718
13. Daubechies I. Ten Lectures on Wavelets (1992), SIAM, Philadelphie, PA
14. Mallat S. A Wavelet Tour of Signal Processing. second ed. (1999), Academic Press, New York
15. Isar A., and Nafornitǎ I. Représentations Temps-Frequence (1998), Ed Politehnica, Timişoara, Roumanie
16. Meyer Y. Wavelets, Algorithms and Applications (1993), SIAM, Philadelphie
17. Wickerhauser M.V. Adapted Wavelet Analysis from Theory to Software (1994), AK Peters
18. Saito N., and Beylkin G. Multiresolution representation using the autocorrelation functions of compactly supported wavelets. IEEE Trans. Signal Process. 41 (December 1993) 3584-3590
19. Shen J., and Strang G. Asymptotic analysis of Daubechies polynomials. Proc. Am. Math. Soc. 124 12 (December 1996) 3819-3833
20. J. Shen, G. Strang, Asymptotics of daubechies filters, scaling functions, and wavelets, Appl. Comput. Harmonic Anal. 5 (HA970234) (1998) 312-331.
21. Aldroubi A., Unser M., and Eden M. Cardinal spline filters: stability and convergence to the ideal sinc interpolator. Signal Process. 28 8 (August 1992) 127-138
22. Cristán A.C., and Walden A.T. Multitaper power spectrum estimation and thresholding: wavelet packets versus wavelets. IEEE Trans. Signal Process. 50 12 (December 2002) 2976-2986
23. Yu J., and Karlsson S. Local spectral analysis using wavelet packets. Circuits Systems Signal Process. 20 5 (2001) 497-528
24. Gabbanini F., Vannucci M., Bartoli G., and Moro A. Wavelet packet methods for the analysis of variance of time series with application to crack widths on the brunelleschi dome. J. Comput. Graph. Stat. 13 3 (2004) 639-658
25. Donoho D.L., and Johnstone I.M. Ideal adaptation by wavelet shrinkage. Biometrica 81 3 (August 1994) 425-455
26. Donoho D.L. De-noising by soft-thresholding. IEEE Trans. Inform. Theory 41 3 (May 1995) 613-627
27. A. Jalobeanu, L. Blanc-Féraud, J. Zerubia, Satellite image deconvolution using wavelet packets, INRIA, Research Report 3955, 2000.
28. Daly D., Heneghan C., Fagan A., and Vetterli M. Optimal wavelet packet modulation under finite complexity constraint. ICASSP 3 (2002) 2789-2792
29. Kjeldsen E., Dill J.C., and Lindsey A.R. Exploiting the synergies of circular simplex turbo block coding and wavelet packet modulation. IEEE MILCOM 2 (2003) 1202-1207
30. You M., and Ilow J. A multi-wavelet packet modulation in wireless communications. CCECE 4 (2004) 2367-2370
31. Ciolino S., Ghavani M., and Aghvami H. On the use of wavelet packets in ultra wideband pulse shape modulation systems. IEICE E88-A (September 2005) 2310-2317
32. Touati S., and Pesquet J.-C. Some results on the wavelet packet decomposition of nonstationary processes. EURASIP J. Appl. Signal Process. 2002 11 (November 2002) 1289-1295
33. Loève M. Probability Theory. fourth ed. (1977), Springer, New York
34. Gikhman I.I., and Skorokhod A.V. Introduction to the Theory of Random Processes (1969), Saunders, London