Theoretical Elements in Fourier Analysis of q-Gaussian Functions

• Autorzy: Rodrigues P S. S. , Giraldi G. A.

Identyfikatory

DOI

10.20904/272016

• Języki publikacji: EN

Abstrakty

EN

There 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 a 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 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. In the computational experiments, we analyze the q-Gaussian kernel in the space and Fourier domains using the concepts of space window, cut-o frequency, and the Heisenberg inequality.

Słowa kluczowe

EN

q-Gaussian kernel; signal processing

• Wydawca: Instytut Informatyki Teoretycznej i Stosowanej Polskiej Akademii Nauk
• Czasopismo: Theoretical and Applied Informatics
• Rocznik: 2015
• Tom: Vol. 27, No. 2
• Strony: 16--44
• Opis fizyczny: Bibliogr. 31 poz., rys.

Twórcy

autor

Rodrigues P S. S.

autor

Giraldi G. A.

Bibliografia

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Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.