Models for processing of information signals based on trigonometric splines

DOI №______

Abstract

Digital technologies are widely used at creation of the modern informative systems. This transformation envisages presentation of weekend of data in a digital form. There is an increase interest of developers of new apparatus in tasks, what presentations of analog signal related to the questions in a digital form and them further treatment. From the mathematical point of view these criteria can be shown as distances in corresponding spaces between the continuous function of certain class (by an analog signal), and function that shows a soba the continuous model of signal. In a role of model of signal in general case examine a function the parameters of that are determined with taking into account of digital values of analog signal. Assume thus, that at high enough quality of presentation of signal is automatically provided high exactness of results of analysis of this signal. Raising of many tasks of treatment of signals does not make sense, if not to take into account property of smoothness of analog informative signals, that characterize behavior of signal in some vicinity of arbitrary point of t0, belong the area specify to the signal. These properties show existence the determined amount of continuous derivatives of the investigated signal, and also information about some analytical properties of these derivatives. In the article the considered models are for treatment of analog signals on the basis of trigonometric splines. The question of consideration of tasks of presentation of analog signal is affected in a digital form and them further treatment Special attention is attracted by properties of smoothness of analog informative signals, that characterize behavior of signal around of arbitrary point, that belong to the interval of signal. The class of signals is set with well-known differential properties. The design of informative signals is examined; thus in a role of models of these signals the classes of trigonometric splines are used. Advantages and lacks of trigonometric splines are shown. On the basis of well-known functions interpolation is conducted by means of trigonometric splines. There is the phenomenon of Gibbs on ends and into the segment of interpolation. Influence of order trigonometric is examined to the spline on the error of interpolation.

Keywords: signals; transformations of Fourier; simple trigonometric splines; treatment of signals; order of trigonometric splines.

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