Algebraic Polynomial Dependence of Change of the Spectral Characteristics of Aggregate Signal of Control Systems On Its Compression or Stretching in Time

Abstract

The article reveals and describes the existing regularity in the form of algebraic polynomial transformations between the time changes of the signal of the control object of varying degrees of complexity and the change of its spectral characteristics - decomposition coefficients obtained using an adaptive orthonormal basis. It is shown that if the signal can be represented in the form of a trigonometric polynomial, then the change in spectral characteristics can be described by algebraic polynomials of various degrees depending on the order of the model which describes the control object. The change of the signals in time is understood their compression or stretching. This regularity is manifested when using the spectral characteristics of the signal calculated according to the adaptive orthonormal basis proposed by the author. It is shown that this regularity is universal and it is valid for any time-finite signals. This property has a general theoretical value, it can be interpreted as the dependence of the spectral characteristics of a signal from its change of time: acceleration or deceleration. This property can be practically used when identifying control objects, modeling and recognizing spatio-temporal changes of aggregate signals in control systems, in monitoring, in diagnostics, in non-destructive testing and other digital signal processing systems.