@ARTICLE{Rodrigues_Paulo_S._Theoretical_2015,
 author={Rodrigues, Paulo S. and Giraldi, Gilson A.},
 volume={vol. 27},
 number={No 2},
 journal={Theoretical and Applied Informatics},
 pages={16-44},
 howpublished={online},
 year={2015},
 publisher={Committee of Informatics of Polish Academy of Science},
 publisher={Institute of Theoretical and Applied Informatics of Polish Academy of Science},
 abstract={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.},
 type={Article},
 title={Theoretical Elements in Fourier Analysis of q-Gaussian Functions},
 URL={http://journals.pan.pl/Content/118530/PDF-MASTER/rodrigues_theoretical%20elements.pdf},
 keywords={sq-Gaussian kernel, signal processing},
}