On Analog Networks and Mixed-Domain Spatio-Temporal Frequency Response

In this paper, we extend the linear cellular neural network (CNN) paradigm by introducing temporal derivative diffusion connections between neighboring cells. Our proposal results in an analog network topology for implementing general continuous-time discrete-space mixed-domain 3-D rational transfer functions for linear filtering. The network connections correspond one-to-one to the transfer function coefficients. The mixed-domain frequency response is treated as a temporal frequency-dependent spatial function and we show how nonseparable properties of the spatio-temporal magnitude response can be derived from the combination of: 1) sinusoidal functions of spatial frequencies and 2) polynomials of the continuous-time frequency in the 3-D frequency response expression. A generic VLSI-compatible implementation of the network based on continuous-time integrators is also proposed. Based on our proposed CNN extension, the analysis of a spatio-temporal filtering example originated from analytical modeling of receptive fields of the visual cortex is presented and a spatio-temporal cone filter is designed and presented with numerical simulation results.