  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.
