@article{Rodrigues_Paulo_S._Theoretical_2015,
 author={Rodrigues, Paulo S. and Giraldi, Gilson A.},
 howpublished={online},
 year={2015},
 abstract={<p>
 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.
 </p>},
 title={Theoretical Elements in Fourier Analysis of q-Gaussian Functions},
 type={Article},
 volume={vol. 27},
 number={No 2},
 journal={Theoretical and Applied Informatics},
 pages={16-44},
 publisher={Committee of Informatics of Polish Academy of Science},
 publisher={Institute of Theoretical and Applied Informatics of Polish Academy of Science},
 keywords={sq-Gaussian kernel, signal processing},
}