Time-frequency jigsaw puzzle: Adaptive multiwindow and multilayered Gabor expansions

International Journal of Wavelets, Multiresolution and Information Processing

Volumn 5, Issue 2, 2007, Pages 293-315

  Jaillet, Florent ^a   Torrésani, Bruno ^b  

^a GENESIS   (France)

^b UNIVERSITÉ DE PROVENCE   (France)

Author keywords

Adaptivity; Entropy; Gabor expansion; Multiwindow; Parsimony; Time frequency concentration

Indexed keywords

ACOUSTIC SIGNAL PROCESSING; SIGNAL DETECTION; TRANSIENTS; WAVELET DECOMPOSITION;

DENOISING; GABOR EXPANSION; TRANSIENT DETECTION;

MULTIRESOLUTION ANALYSIS;

EID: 33947535809     PISSN: 02196913     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0219691307001768     Document Type: Article

References (18)

1. R. Carmona, W. L. Hwang and B. Torrésani, Practical Time-Frequency Analysis: Continuous Wavelet and Gabor Transforms, with an Implementation in S, Wavelet Analysis and Its Applications, Vol. 9 (Academic Press, San Diego, 1998).
2. L. Cohen, Time-Frequency Analysis (Prentice Hall, New York, 1994).
3. I. Daubechies, Ten Lectures on Wavelets, CBMS-NFS Regional Series in Applied Mathematics, Vol. 61 (SIAM, 1992).
4. L. Daudet and B. Torrésani, Hybrid representations for audiophonic signal encoding, Signal Process. 82(11) (2002) 1595-1617.
5. M. Dörfler, Gabor analysis for a class of signals called music, PhD thesis, Numerical Harmonic Analysis Group (NuHAG), Mathematics Department, University of Vienna, Austria (2003).
6. M. Dörfler, private communication (August, 2005).
7. H. G. Feichtinger and T. Strohmer, Gabor Analysis and Algorithms, Theory and Applications (Birkhäuser Boston Inc., 1998).
8. P. Flandrin, Time-Frequency/Time-Scale Analysis, Wavelet Analysis and Its Applications, Vol. 10 (Academic Press, San Diego, 1999).
9. R. Gribonval, Approximations non-linéaires pour l'analyse des signaux sonores, PhD thesis, Université de Paris IX Dauphine (1999).
10. F. Jaillet, Représentation et traitement temps-fréquence des signaux audionumériques pour des applications de design sonore, PhD thesis, LATP Marseille (2005).
11. F. Jaillet and B. Torrésani, Remarques sur l'adaptativité des représentations temps-fréquence, in Proceedings of the Symposium GRETSI'03, Paris, France, Vol. I (2003), pp. 145-148.
12. F. Jaillet and B. Torrésani, Adaptive time-frequency representation for sound analysis and processing, in Proceedings of the Joint Congress CFA/DAGA, Strasbourg, France, Vol. 2 (2004), pp. 711-712.
13. S. Mallat and Z. Zhang, Matching pursuits with time-frequency dictionaries, IEEE Trans. Signal Process. 41 (1993) 3397-3415.
14. S. Molla and B. Torrésani, Determining local transientness of audio signals, IEEE Signal Process. Lett. 11(7) (2004) 625-628.
15. S. Molla and B. Torrésani, A hybrid audio scheme using hidden Markov models of waveforms, Appl. Comput. Harmon. Anal. 18 (2005) 137-166.
16. A. Rényi, On measures of entropy and information, in Proc. Fourth Berkeley Symp. Math. Stat. and Probability, University of California, Berkeley, CA, Vol. 1 (1961), pp. 547-561.
17. M. V. Wickerhauser, Adapted Wavelet Analysis from Theory to Software (AK Peters, Boston, MA, USA, 1994).
18. M. Zibulski and Y. Zeevi, Analysis of multiwindow Gabor-type schemes by frame methods, Appl. Comput. Harmon. Anal. 4(2) (1997) 188-212.