Fourier analysis and q-Gaussian functions: analytical and numerical results

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dc.contributor.authorRODRIGUES, Paulo
dc.contributor.authorGIRALDI, G.
dc.date.accessioned2019-08-17T20:00:28Z
dc.date.available2019-08-17T20:00:28Z
dc.date.issued2016
dc.description.abstractalternativeIt is a consensus in signal processing that the Gaussian kernel and its partial derivatives enable the development of robust algorithms for feature detection. Fourier analysis and convolution theory have central role in such development. In this paper we collect theoretical elements to follow this avenue but using the q-Gaussian kernel that is a nonextensive generalization of the Gaussian one. Firstly, we review some theoretical elements behind the one-dimensional q-Gaussian and its Fourier transform. Then, we consider the two-dimensional q-Gaussian and we highlight the issues behind its analytical Fourier transform computation. We analyze the q-Gaussian kernel in the space and Fourier domains using the concepts of space window, cut-off frequency, and the Heisenberg inequality.en
dc.description.firstpage16
dc.description.issuenumber2
dc.description.lastpage44
dc.description.volume27
dc.identifier.citationRODRIGUES, Paulo; GIRALDI, G. Fourier analysis and q-Gaussian functions: analytical and numerical results. Theoretical and Applied Informatics, v. 27, n. 2, p. 16-44, 2016.
dc.identifier.doi10.20904/272016
dc.identifier.issn1896-5334
dc.identifier.urihttps://repositorio.fei.edu.br/handle/FEI/985
dc.identifier.urlhttps://arxiv.org/abs/1605.00452
dc.relation.ispartofTheoretical and Applied Informatics
dc.rightsAcesso Aberto
dc.subject.otherlanguageComputer visionen
dc.subject.otherlanguagePattern recognitionen
dc.titleFourier analysis and q-Gaussian functions: analytical and numerical resultspt_BR
dc.typeArtigopt_BR
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