Analysis and design of cellular neural networks, through a space-time spectral approach

It is known that a cellular neural network (CNN) can be analyzed as a system that depends on one or two discrete space and one continuous time coordinates. In this paper the state of the network is represented as a linear combination of a suitable space mode basis. The nonlinear differential equations, that originally describe the CNN, are transformed into an equivalent set of equations that involve the space mode coefficients. Such a system of equations is able to describe the network in the whole state space and not only in the CNN linear region. It is shown that the study of the time evolution of the most significant space modes allows one to understand the behavior of a CNN as a nonlinear space filter and to develop useful design strategies