A new adaptive architecture: analogue synthesiser of orthogonal functions

Abstract

A new adaptive nonlinear (neural-like) architecture, an analogue synthesiser of orthogonal functions which is able to produce a plurality of mutually orthogonal signals as functions of time such as Legendre, Chebyshev and Hermite polynomials, cosine basis of functions, smoothed cosine basis, etc., is proposed. A proof-of-concept breadboard version of the analogue synthesiser is described. The device is characterised by a very fast (approximately 100 iterations) and stable process of signal synthesis. The proposed new device could find applications e.g. in analogue systems of function approximation, in particular as a main unit in an analogue implementation of so-called Chebyshev polynomial-based (CPB) neural networks, as a unit in a fast adaptive alternative to Volterra polynomial neural networks, and also as a preprocessing element (performing some transforms, filtration, etc.) in analogue neural network-based systems of information processing.