Linear Filtering Based on a Pulsed Neuron Model with an Orthogonal Filter Bank

Abstract

This paper deals with the model and learning rules of a pulsed neuron, which provide the linear filtering of signals represented by pulse trains. To reduce the number of training parameters of a pulsed neuron we propose using a bank of orthogonal filters as a model of synaptic connections. For this model of pulsed neuron, we derive a supervised learning rule in a general form that can include various orthogonal basis functions. The rules minimize the mean square error between the desired and the actual output signal of a linear filter realized on the base of the pulsed neuron model. We derive two special learning rules: with set of exponential complex orthogonal functions and set of block-pulse orthogonal functions. For both set of these functions, we demonstrate rule’s properties by computer simulation of linear filters that implement high-pass filtering and double integration of the input signal transformed to pulse train. We show the impulse and frequency responses of the filters as well as the dependencies of the normalized mean square error on the number of training iterations.