Adaptive Approximation of Signals

Abstract

A lot of works devoted to the problems of approximation both continuous and discrete signals. But, in spite of this, important practical problems arise, especially in the field of Informatics and applied mathematics, which require development and testing of new approaches of experimental data approximation. First of all it is connected with the fact that data processing is conducted in the majority in real time. Besides, strict conditions are laid down on the developed algorithms: they must be constructive in programming for optimal performance and real-time problem solving. Approaches to the approximation of the continuous processes are proposed, but on their basis it is easy to derive discrete counterparts. As a rule, in applied tasks signals into discrete moments are measured. Thats why differencing schemes can prove to be more effective for use. When using the proposed algorithms the questions of analysis of convergence of the following iterative procedures arise. It can be done on the basis of Lyapunov methods and special criteria of stability. Adaptive signals approximation models in structural-parametric classes of functions are considered. Approximation is made by using an iterative procedure in the form of an ordinary differential equations system. In order to confirm the effectiveness of the proposed approach, software for simulated examples and real problems testing was developed. Conditions for the convergence of the iterative scheme for approximating signals, which are based on Lyapunov stability theory, are given. Suggested methods can be effectively applied for the detection of chemical and biological analysis of the spectral data. To demonstrate the effectiveness model examples for the approximation of the continuous signals are given.