A time decoding realization with a CNN

Time encoding is a novel real-time asynchronous mechanism for encoding amplitude information into a time sequence. The analog bandlimited input is fed into a simple nonlinear neuron-like circuit that generates a strictly increasing time sequence based on which the signal can be reconstructed. The heart of the reconstruction is solving a system of ill-conditioned linear equations. The paper shows that the equations can be manipulated so that the reconstruction becomes feasible using a cellular neural network (CNN) with a banded system matrix. In particular, the system is first transformed into a smaller well-conditioned system, and, then, the Lanczos process is used to lay it out into a set of even smaller systems characterized by a set of tridiagonal matrices. Each of these systems can directly be solved by CNNs, whereas the preprocessing (transformation and Lanczos algorithm) and simple postprocessing phases can be partly or fully implemented by using the digital capabilities of the CNN universal machine (CNN-UM). Each step of the proposed formulation is confirmed by numerical (digital) simulations.