Elementary linear filtering tasks using CNNs with minimum-size templates

In this paper we investigate the linear filtering capabilities of the standard cellular neural network in the general case of non-symmetric templates. We approached here systematically the CNNs with minimum-size templates (1x3), analyzing in detail their filtering capabilities in the one-dimensional case. Starting from a general form of the spatial transfer function, we emphasize some useful filtering functions that can be obtained. For each filter type, we derive the relations which give the template parameter values, in order to design a given CNN filter with specified characteristics-like central frequency, bandwidth, selectivity etc. Filters with symmetric templates are treated as a particular case. For each type of filtering the characteristics are shown and simulation results are presented as well. Some of these results are then extended to 2-D CNNs and several simulations of useful filtering tasks are presented on real images