Частотно-часовий аналіз сигналів на основі функцій поведінки і арифметичних рядів. Частина 1. Аналіз підходів, опис методу.

Abstract

The material carrier of information about the state of objects is signals, the classification of which is sufficiently fully considered. As a rule, today, on the basis of the reading theorem, signals are represented in a discrete form. In this case, an ordered sequence of signal measurement results recorded at successive points in time is usually called a time series.In solving practical problems, both space-time and frequency signal processing tools are used. As practice has shown, any space-time signal can be described by a set of basic functions.Most often, to obtain a spectrum, orthogonal function decomposition is used. The most widely used classical approach based on the direct and inverse Fourier transform. These transformations are a good tool for studying stationary processes. The Fourier transform provides a map to the point of information about the periodicity of the function in the process of transition from the time domain to the frequency domain.Fourier transform provides efficient analysis of stationary time series in the frequency domain. However, the results of applying the known criteria to real time series, which allow checking the statistical hypothesis of a series being stationary, show that most of them, turn out to be non-stationary.Recently, approaches to the analysis of time series based on wavelet transforms have become widespread. Despite the fairly high efficiency of wavelet analysis of non-stationary time series, as practice has shown, there are a number of difficulties in their use. In particular, in the case of using wavelet transforms it is necessary to take into account a number of distortions.The purpose of the article is to highlight an alternative approach to the analysis of time series, which, to a certain extent, is free from the key weaknesses of Fourier analysis, has advantages over the wavelet transform, but is simpler in their implementation and takes into account the non-stationary behavior of the system.The proposed approach as a whole allows solving the problem of frequency-time analysis of non-stationary discrete signals, which are represented by time series. The simplicity of the calculations, which do not require the use of integration functions, greatly simplifies the determination of frequency spectra.