Browsing by Author "KIMOUCHE, Karima"

Now showing 1 - 4 of 4
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    La méthode d’estimation par seuillage en ondelettes d’un champ aléatoire
    (Faculté des Sciences, 2023) BOUKERFA ,Nedjla; BOUZABIA ,Rayane; KIMOUCHE, Karima
    Ce mémoire est consacré essentiellement à l'étude de l’estimateur de la densité bispectrale dans les champs aléatoires non linéaires, qui est basé sur l'analyse en ondelettes. Nous avons défini les notions de base concernant les processus stochastiques et la densité spectrale, puis nous avons donné un bref sur la transformée en ondelettes (continue et discrète). Ensuite, nous avons étudié les champs aléatoires et l'analyse multirésolution où nous obtenons des expressions explicites pour les covariances de deuxième et troisième ordre entre les ondelettes et le coefficient d'échelle des champs aléatoires discrets. Enfin, nous proposons un estimateur à seuil par ondelettes de la densité bispectrale de champ aléatoire qui est plus performant que les estimateurs linéaires (noyaux).
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    Multidimensional fractional Fourier transform: Properties and applications
    (Faculty of Sciences, 2025) Bouasla ,Yousra; KIMOUCHE, Karima
    This master s thesis focuses on the study of the multidimensional fractional Fourier transform in both its classical and windowed forms as a powerful extension of the con- ventional Fourier transform with enhanced capability for analyzing non-stationary sig- nals. The work presents formal de nitions of both transforms and explores their main mathematical properties, including linearity, time-shift, convolution, scaling, and en- ergy preservation. Special attention is given to the role of window function in improving time-frequency localization in the n-dimensional window fractional Fourier transform framework. A comparative analysis between these transforms is also provided. Finally, selected applications are presented to highlight the relevance of these transforms in various elds
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    The 2D Fourier transform and its generalizations
    (Faculty of sciences , 2024) Sebbagh ,Yousra; KIMOUCHE, Karima
    This graduation note is essentially devoted to the study of 2D Fourier transform and its generalization. In fact, it is a natural generalization of the idea of Fourier transform. This idea makes the 2D Fourier transform very natural in the study. In the …rst part, we de…ned the 2D Fourier transform and we established some properties of this transform. Moreover, some examples and applications across various …elds are illustrated . Then, we gave de…nitions, properties and some applications for 2D windowed Fourier transform. Finally, the de…nition of 2D fractional Fourier transform with some applications are presented
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    Two-dimensional wavelets transform: Basic properties and applications
    (Faculty of Sciences, 2025) Rehaibi ,Sonia; KIMOUCHE, Karima
    Thisgraduationnotefocusesonthetwo-dimensionalcontinuouswavelettransform (2DCWT)byusingtwodi¤erentscaleparameters (a1; a2), weareabletostretchor compressthewaveletindependentlyalongthehorizontalandverticaldirections.This anisotropicscalingo¤ersmore exibilitythanisotropicscaling,whichusesasingle scalefactor.Infact,itisanaturalgeneralizationoftheideaofwavelettransform. Thisideamakesthe2Dwavelettransformverynaturalinthestudy.So,mathematical andappliedresultshavedemonstratedthepowerofthewavelettransforminhandling convolutionoperations,strengtheningitsroleasane¤ectivetoolforaccurateanalysis inmultiple elds.