. Diminution-rapide-de-la-frquence-de-la-composante-fondamentale, La ddcomposition de Malvar met en vidence cette diminution de la frrquence, mais, encore une fois, avec une trop grande imprrcision dans les coordonnnes temporelles Du fait du ddcoupage frrquentiel global du signal, la transformme de Meyer n'est pas trrs sensible cette volution Seule la prrsence d''nergie dans des zones plus basses frrquences la signale. Notons qu'en augmentant le nombre d''chelles de ddcomposition, la transformme de Meyer peut mettre en vidence cette caracttristique (en ayant une prrcision temporelle trrs moyenne, mais dans ce cas elle ddcoupe d'avantage les zones homoggnes (1) et (2) (cf gure 5.7c). Du fait du ddcoupage adaptatif la fois en temps et en frrquence, l'algorithme DT met en vidence avec une prrcision temporelle suusante cette volution

. De-la-rponse, Rapparition La ddcomposition de Malvar ddtecte trrs bien cette caracttristique car elle est dddnie sur un large intervalle temporel. En revanche le ddcoupage des paquets d'ondelettes est trop grossier, avec une bande frrquentielle trop large. Comme pour le point (3), ceci peut tre ammliorr avec un nombre d''chelles plus important mais provoquant dans d'autres zones un phhnommne de sur-segmentation. L'algorithme DT fait apparaatre correctement cette zone trrs localisse frrquentiellement et s

. Colonnee-d-''nergie-sur-la-bande-frquentielle-15-de-la-rponse, Avec le systtme de Malvar, cette colonne n'est pas du tout apparente du fait d'une trrs mauvaise rrsolution temporelle et d'un ddcoupage trop important de l'axe frrquentiel. La ddcomposition de Meyer ddtecte cette zone en sslectionnant de grandes fenntres frrquentielles , mais le rrsultat est moins prrcis que l'algorithme DT qui

A. Partir-de-cet-exemple, nous ddduisons quelques conclusions permettant de faire un bilan sur les diiirentes techniques TF tudiies dans les trois derniers chapitres : La ddcomposition de Malvar s'adapte trrs bien des composantes localisses ou trrs localisses BIBLIOGRAPHIE Bibliographie 1] S. Adak. Time-dependent spectral analysis of nonstationary time series, 1995.

E. Ademovic, G. Charbonneau, and J. C. Pesquet, Wheezing lung sounds analysis with adaptive local trigonometric transform, First CORSA WP III Symposium on Signal Processing in Lung Sound Analysis, Helsinki University of Technology (FI), 1995.

E. Ademovic, P. Helisto, and J. C. Pesquet, Segmentation of infant respiratory sounds with Malvar's wavelets, Proceedings of 16th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, 1994.
DOI : 10.1109/IEMBS.1994.412131

M. Antonini, M. Barlaud, I. Daubechies, and P. Mathieu, Image coding using vector quantization in the wavelet transform domain, International Conference on Acoustics, Speech, and Signal Processing, 1990.
DOI : 10.1109/ICASSP.1990.116036

P. Auscher, G. Weiss, and V. Wickerhauser, Local Sine and Cosine Bases of Coifman and Meyer and the Construction of Smooth Wavelets, Wavelets: A Tutorial in Theory and Applications, p.2377256, 1992.
DOI : 10.1016/B978-0-12-174590-5.50014-9

A. Witkin, Scale space ltering, 1983.

M. Basseville, Distances en traitement du signal et reconnaissance des formes, 1988.

A. Bijaoui, J. Starck, and F. Murtagh, Restauration des images multi-echelles par l'algorithme a trous, Traitement du Signal, vol.11, p.2322243, 1994.

P. Burt and E. Adelson, The laplacien pyramid as a compact image code, IEEE Trans. Comm, vol.31, p.4822550, 1983.

J. Canny, A computational approach to edge detection, IEEE Trans. on PAMI, vol.8, issue.6, p.6799698, 1986.

R. Carmona, W. Hwang, and R. Frostig, Wavelet analysis for brain-function imaging, IEEE Transactions on Medical Imaging, vol.14, issue.3, p.556564, 1995.
DOI : 10.1109/42.414621

R. A. Carmona, Extrema Reconstructions and Spline Smoothing: Variations on an Algorithm of Mallat & Zhong, Wavelets and Statistics, p.83394, 1995.
DOI : 10.1007/978-1-4612-2544-7_6

P. Carrr, DDbruitage par transformme en ondelettes : applications aux images irmf, 1996.

P. Carrr and C. Fernandez, DDbruitage d'une image par reprrsentation en bords multiichelles : utilisation de l'information angle, 166me colloque GRESTI, 1997.

P. Carrr and C. Fernandez, A nonuniform, shift-invariant, and optimal algorithm for malvar's wavelet decomposition, International Symposium on Time-Frequency and Time-Scale Analysis, 1998.

P. Carrr and C. Fernandez, Research of stationary partitions in nonstationary processes by measurement of spectral distance with the help of nondyadic malvar's decomposition, International Symposium on Time-Frequency and Time-Scale Analysis, 1998.

P. Carrr and C. Fernandez, The construction of a meyer's wavelets packets decomposition: an algorithm for the extraction of signal components, 1999.

P. Carrr and C. Fernandez, Paquets d'ondelettes de meyer pour le traitement d'images, 177me colloque GRESTI, 1999.

P. Carrr and C. Fernandez, Use of the angle information in the wavelet transform maxima for image denoising, 1999.

P. Carrr and C. Fernandez, DDbruitage de multiples copies d'un signal ou d'une image par transformme en ondelettes non-ddcimme, RFIA, 2000.

P. Carrr, H. Leman, C. Marque, and C. Fernandez, Denoising the EHG signal with an undecimated wavelet transform, IEEE Trans. on Biomedical Engineering, issue.8, p.45110441113, 1998.

P. Carrr, N. Richard, C. Fernandez, and J. Paquereau, Non-dyadic decomposition algorithm with meyer's wavelet packets: an application to eeg signal, Wavelet Applications in Signal and Image Processing, 1999.

S. Chang, Image interpolation using wavelet-based edge enhancement and texture analysis, 1995.

S. G. Chang, Z. Cvetkovic, and M. Vetterli, Resolution enhancement of images using wavelet transform extrema extrapolation, 1995 International Conference on Acoustics, Speech, and Signal Processing, p.237992382, 1995.
DOI : 10.1109/ICASSP.1995.479971

J. P. Cocquerez and S. Phillip, Analyse d'images : Filtrage et segmentation, 1995.
URL : https://hal.archives-ouvertes.fr/hal-00706168

A. Cohen, Ondelettes et Traitement nummrique du Signal, 1992.

A. Cohen, W. Dahmen, and R. Devore, Multiscale decomposition on bounded domains, 1996.

I. Cohen, S. Raz, and D. Malah, Orthonormal shift-invariant adaptative local trigonometric decomposition, Signal Processing, vol.57, issue.1, 1997.
DOI : 10.1016/s0165-1684(96)00185-5
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.20.4561

R. Coifman and S. Donoho, Translation-Invariant De-Noising, Wavelets and Statistics, p.1255150, 1995.
DOI : 10.1007/978-1-4612-2544-7_9

R. Coifman and F. Majid, Adapted waveform analysis and denoising, Progress in Wavelet Analysis and Applications (Proceedings of the International Conference Wavelets and Applicationss, p.63376, 1992.

R. Coifman and Y. Meyer, Remarque sur l'analyse de fourier fenntres, Comptes Rendus de l'Acaddmie des Sciences, p.2599261, 1991.

R. Coifman and M. Wickerhauser, Entropy-based algorithms for best basis selection, IEEE Transactions on Information Theory, vol.38, issue.2, p.719746, 1992.
DOI : 10.1109/18.119732

R. Coifman and M. Wickerhauser, Wavelets and adapted waveform analysis. A toolkit for signal processing and numerical analysis, 1993.
DOI : 10.1090/psapm/047/1268000

R. Coifman and M. Wickerhauser, Adapted waveform denoising for medical signals and images, IEEE Engineering in Medecine and Biology, vol.14, issue.5, p.5788586, 1995.

D. Donoho, Wavelet shrinkage and w.v.d.: A 10-minute tour, 1992.

D. Donoho, De-noising by soft-thresholding, IEEE Transactions on Information Theory, vol.41, issue.3, pp.613-627, 1995.
DOI : 10.1109/18.382009
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.161.9704

D. Donoho and I. Johnstone, Adapting to Unknown Smoothness via Wavelet Shrinkage, Journal of the American Statistical Association, vol.31, issue.432, 1994.
DOI : 10.1080/01621459.1979.10481038

D. Donoho and I. Johnstone, Ideal spatial adaptation by wavelet shrinkage, Biometrika, vol.81, issue.3, p.425455, 1994.
DOI : 10.1093/biomet/81.3.425
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.124.5288

D. Donoho, S. Mallat, and R. V. Sachs, Estimating covariances of locally stationary processes: consistency of best basis methods, Proceedings of Third International Symposium on Time-Frequency and Time-Scale Analysis (TFTS-96), 1996.
DOI : 10.1109/TFSA.1996.547482

D. Donoho, S. Mallat, and R. V. Sachs, Estimating covariances of locally stationary processes: Rates of convergence of best basis methods, 1997.

B. Dubuisson, Diagnostic et reconnaissances des formes, Hermes, 1990.

P. Duhamel and M. Vetterli, Fast Fourier Transforms, Signal Processing, vol.19, p.2599299, 1990.
DOI : 10.1201/9781420046076-c7

P. Flandrin, Temps-frequence, Hermes, 1993.
URL : https://hal.archives-ouvertes.fr/jpa-00230468

D. Gabor, Theory of communication, Journal of the Institution of Electrical Engineers - Part I: General, vol.94, issue.73, p.93431, 1946.
DOI : 10.1049/ji-1.1947.0015

H. Gao, Choice of thresholds for wavelet shrinkage estimate of the spectrum, Journal of Time Series Analysis, vol.18, issue.3, 1994.
DOI : 10.1111/1467-9892.00048

H. Gao and A. Bruce, Waveshrink with semisoft shrinkage, 1995.

P. Gregson, Using angular dispersion of gradient direction for detecting edge ribbons, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.15, issue.7, p.6822695, 1993.
DOI : 10.1109/34.221169

C. Herley, Boundary lters for nite-length signals and time-varying lter banks, IEEE Trans. on Circuits and Systems II, 1994.

C. Herley, J. Kovacevic, K. Ramchandran, and M. Vetterli, Tillings of the time-frequency plane: Construction of arbitrary orthogonal bases and fast tilling algorithms, IEEE Trans. on Signal Processing, issue.12, p.41334113359, 1993.

C. Herley and M. Vetterli, Orthogonal time-varying lter banks and wavelet packets, IEEE Transactions on Signal Processing, vol.42, p.265002663, 1994.
DOI : 10.1109/78.324731
URL : http://infoscience.epfl.ch/record/33887

M. Hilton, T. Ogden, D. Hattery, G. Eden, and B. Jawerth, Wavelet denoising of functional mri data, Wavelet Applications in Biology and Medecine, 1996.

M. Holschneider, R. Kronland-martinet, J. Morlet, and P. Tchamitchian, A real-time algorithm for signal analysis with the help of the wavelet transform, Wavelet, Time-Frequency Methods and Phase Space, p.2899297, 1989.

W. Hwang and S. Mallat, Characterization of Self-Similar Multifractals with Wavelet Maxima, Applied and Computational Harmonic Analysis, vol.1, issue.4, 1993.
DOI : 10.1006/acha.1994.1018

B. Jawerth, Y. Liu, and W. Sweldens, Signal compression with smooth local trigonometric bases, Optical Engineering, vol.33, issue.7, p.21252135, 1994.
DOI : 10.1117/12.172253

I. Johnstone and B. Silverman, Wavelet Threshold Estimators for Data with Correlated Noise, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.59, issue.2, p.319351, 1997.
DOI : 10.1111/1467-9868.00071

E. Kolaczyk, Wavelet Methods for the Inversion of Certain Homogeneous Linear Operators in the Presence of Noisy Data, 1994.

A. Laine and J. Fan, An adaptive approach for texture segmentation by multi-channel wavelet frames, 1993.

A. Laine and J. Fan, Texture classiication by wavelet packet signatures, IEEE Trans. on PAMI, vol.15, issue.11, p.11861191, 1993.
DOI : 10.1109/34.244679
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.203.6022

M. Lang, H. Guo, C. Burrus, and R. Wells, Nonlinear processing of a shift invariant dwt for noise reduction, Mathematical Imaging: Wavelet Applications for Dual Use, 1995.

M. Lang, H. Guo, J. Odegard, C. Burrus, and R. Wells, Noise reduction using an undecimated discrete wavelet transform, IEEE Signal Processing Letters, vol.3, issue.1, p.10012, 1996.
DOI : 10.1109/97.475823
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.24.4098

C. Lee, Mobile cellular telecommunications systems. Mc Gray-Hill international editions, 1990.
DOI : 10.1016/b978-075067291-7/50048-0

W. Lee, Mobile Communications Design Fundamentals, 1993.
DOI : 10.1002/9780470930427

J. Lu, Signal Recovery and Noise Reduction with Wavelets, 1993.

J. Lu, On consistent signal reconstruction from wavelet extrema represention, Wavelet Applications in Signal and Image Pocessing, 1997.

J. Lu, J. Weaver, D. Healy, and Y. Xu, Noise reduction with a multiscale edge representation and perceptual criteria, [1992] Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis, 1992.
DOI : 10.1109/TFTSA.1992.274118

S. Mallat, A theory for multiresolution signal decomposition: the wavelet transform, IEEE Trans. on PAMI, vol.11, issue.7, p.6744693, 1989.

S. Mallat, A wavelet Tour of Signal Processing, 1998.

S. Mallat and W. Hwang, Singularity detection and processing with wavelets, IEEE Transactions on Information Theory, vol.38, issue.2, p.617643, 1992.
DOI : 10.1109/18.119727

S. Mallat and S. Zhong, Characterization of signals from multiscale edges, IEEE Trans. on PAMI, vol.14, issue.7, p.710732, 1992.

H. Malvar, Lapped transform for eecient transform/subband coding, IEEE Trans. Acoustic Speech Signal Processing, vol.38, issue.6, p.9699978, 1990.

Y. Meyer, Ondelettes et opprateurs, volume I, 1990.

Y. Meyer, Ondelettes et algorithmes concurrents, Hermann, 1992.

Y. Meyer, Les ondelettes : algorithmes et applications, 1994.

P. Moulin, Wavelet thresholding techniques for power spectrum estimation, IEEE Transactions on Signal Processing, vol.42, issue.11, p.312663136, 1994.
DOI : 10.1109/78.330372

G. Nason, Wavelet shrinkage using cross-validation, J. Roy. Statist. Soc. B, vol.58, p.4633479, 1996.

G. Nason and B. Silverman, The Stationary Wavelet Transform and some Statistical Applications, Wavelets and Statistics, p.2811299, 1995.
DOI : 10.1007/978-1-4612-2544-7_17

A. Papoulis, Probability, random variables, and stochastic process, 1984.

D. Pastor and R. Gay, Decomposition d'un processus stationnaire du second ordre, Traitement du Signal, vol.11, issue.5, p.39333136, 1995.

J. Pesquet, H. Krim, and H. Carfantan, Time-invariant orthonormal wavelet representations, IEEE Transactions on Signal Processing, vol.44, issue.8, p.196441970, 1996.
DOI : 10.1109/78.533717
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.45.2234

Y. Pousset, Optimisations pour la prediction des zones de couverture radioelectrique, 1998.

Y. Pousset, P. Carrr, and R. Vauzelle, Comparaison of two wavelet analysis for a radiomobile signal processing, Progress in Electromagnetics Research Symposium, 1998.

Y. Pousset, P. Carrr, and R. Vauzelle, Optimization in computation time of the coverage zone by wavelet maxima, URSI, 1999.

U. Ruttimann, N. Ramsey, D. Hommer, and P. Thhvenaz, Analysis of functional magnetic resonnace images by wavelet decomposition, Int. Conf. on Image Processing, p.6333636, 1995.

M. Shensa, Wedding the trous and mallat algorithms, IEEE Trans. Signal Processing, vol.40, issue.10, p.24642482, 1992.

M. Shensa, An inverse dwt for nonorthogonal wavelets, NCCOSC, 1993.

J. Starck and F. Murtagh, Image restoration with noise suppression using the wavelet transform, Astronomy and Astrophysics, 1994.

J. L. Starck, F. Murtagh, and A. Bijaoui, Multiresolution support applied to image ltering and restoration, Comp. Vision, Graphics and Image Proc, vol.57, issue.5, p.420431, 1995.

M. Unser, P. Thhvenaz, C. Lee, and U. Ruttimann, Registration and statistical analysis of PET images using the wavelet transform, IEEE Engineering in Medicine and Biology Magazine, vol.14, issue.5, p.6033611, 1995.
DOI : 10.1109/51.464777

R. Vauzelle, Methode d'optimisation des outils de prediction de la couverture radio en milieu urbain In 3 journee d'etude de la propagation electromagnetique dans l'atmosphere du decimetrique a l'angstrom, 1997.

R. Vauzelle, Wavelet and propagation prediction for mobile radio communications, PIERS, 1998.

M. Vetterli and J. Kovaaevii, Wavelets and Subband Coding, 1995.

E. Wesfreid and M. V. Wickerhauser, Adapted local trigonometric transforms and speech processing, IEEE Transactions on Signal Processing, vol.41, issue.12, p.41359663600, 1993.
DOI : 10.1109/78.258104
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.55.3503

M. Wickerhauser, Adapted Wavelet Analysis from Theory to Software, 1994.

M. V. Wickerhauser, Lectures on wavelet packet algorithms, 1991.

Z. Xiong, Representation and coding of images using wavelets, 1996.

D. Youla and H. Webb, Image restoration by the method of convex projections, IEEE Trans. on Medical Imaging, issue.1, p.811101, 1982.

H. Youlal, M. Janati-idrissi, and M. Najim, Modelisation parametrique en traitement d'images, 1994.

S. Zhong, Edge Representation from Wavelet Transform Maxima, 1990.

. De-la-mmme-faaon, nous avons : E(r y ) = s x; y + h 1 ] ? s x, p.235