Approximation splin models to improve telecommunication system efficiency indicators

DOI: 10.31673/2412-9070.2019.053539

Abstract

On the basis of the scientific literature analysis, it has been determined that there are properties of signals, without which the setting of many tasks of signal processing itself makes no sense. Such properties of information signals are their properties of smoothness, which characterize the behavior of the signal in some neighborhood of an arbitrary point, which belongs to the interval of the signal. These properties contain information about the existence of a certain number of continuous derivatives of the investigated signal, as well as information on some of the analytical properties of these derivatives. On the basis of this theory, a mathematical model of information signals based on fundamental trigonometric splines is developed and substantiated, which allows taking into account the differential properties of information signals. In the study of various kind of errors in linear units in the theory of information-measuring systems, such as linear amplifiers and filters, it is advisable to use periodic models of information signals. This necessity is explained by the fact that the trigonometric functions used in the construction of periodic models are the eigenfunctions of linear operators, as such they do not change with the accuracy to the constant under the action of linear operators on them. Thus, it is proved that in the role of mathematical models of information signals it is efficient to use trigonometric splines, and for the restoration of signals as components of filters, it is efficient to apply fundamental approximation trigonometric splines. The importance of such an approach is due to the fact that when linear methods are used, processing can be applied only to fundamental functions. This fact allows us to carry out the necessary calculations for the processing of experimental data in two stages. In the first stage, calculations related to the processing of fundamental functions are carried out (these calculations can be carried out in advance), in the second stage, calculations that take into account the value of the reproduced functions are performed.

Keywords: signals; transformations of Fourier; approximate models, fundamental trigonometric splines.

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