Paper Info
Title
Fourier Analysis and q-Gaussian Functions: Analytical and Numerical Results.
Abstract
It 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.
Year
Venue
Field
2016
arXiv: Computer Vision and Pattern Recognition
Applied mathematics,Fourier analysis,Computer science,Mathematical analysis,Fourier inversion theorem,Short-time Fourier transform,Fourier transform,Artificial intelligence,Discrete-time Fourier transform,Gaussian filter,Pattern recognition,Discrete Fourier transform,Fractional Fourier transform
DocType
Volume
Citations 
Journal
abs/1605.00452
0
PageRank 
References 
Authors
0.34
0
2
Name
Order
Citations
PageRank
Paulo S. Rodrigues1467.12
Gilson Antonio Giraldi21477.93