Fast training analog approximator on the basis of Legendre polynomials

In a number of applications the approximation or interpolation of certain weakly (when every subsequent term of power series expansion is much less than previous one) nonlinear dependencies d(x), where x an arbitrary signal in time, is demanded. The example is the problem of cancellation of a nonlinear distortion of a signal in high precision analog engineering. In such cases it seems to be reasonable to use polynomial approximation (interpolation) devices. In this paper the neural network based devices, performing the operations of approximation or interpolation, are described. The schemes and working characteristics of a breadboard based on analog radio components are presented. Legendre polynomials were offered as basis functions for significant increasing of the speed of the approximator training. The scheme of analog synthesizer of Legendre polynomials was also suggested.