Procedure of Nonparametric Characterization of Nonlinear Devices Based on Expansion of Multidimensional Transfer Functions on Simple Functions

Abstract

The decomposition for functions of many variables on simple functions is developed in following: decomposition is introduced for arbitrary points, algorithm is given for defining simple functions; and, finally, the decomposition for functions of many variables on the shorten set of simple functions is possible to consider as new kind of approximation. That is theoretical and algorithmic basis of presented measurement procedure, which is reduced to estimating of multidimensional transfer functions (MTF) - kernels of Volterra-Wiener polynoms. The MTF are defined with help measured data of response, when the input is excited by different type of sinusoidal signals. Main steps of procedure consist of following: 1) measurement and estimating a set of the MTF narrowings; 2) definition of the set of simple functions, which correspond to the set of the MTF narrowings; 3) synthesis of MTF's as sum of simple functions. As a result we can produce the state, quasi-state, and quasi-stationary nonparametric characterizations and complete nonparametric characterization. All characterizations are approximations for complete nonparametric characterization.