ANALYSIS OF TIME SERIES USING WAVELET AUTOCOHERENCE AND AUTOCORRELATION

The article is devoted to the development of an effective signal classification algorithm for the detection of Gaussian noise based on wavelet autocorrelation and wavelet autocoherence values. A comparative analysis of autocorrelation methods for the analysis of time series constructed using the base of analytical expressions of model signals and the wavelet-autocoherence method, which is applied to time series of large-scale wavelet coefficients, is carried out. The use of a database of 20 types of model signals (both linear and nonlinear frequency modulation) is provided, which significantly expands the possibilities of applying the algorithm in automatic data recognition systems. The results of the study show that the value of the coefficient of autocoherence remains unchanged in the entire range of changes in noise power, while the value of autocorrelation depends on frequency modulation and has a different character. To obtain a simplified model, the Shapiro–Wilk test (W-test) was used, the signals are classified into two separate groups based on the values of the autocorrelation and wavelet autocoherence coefficients. A noise threshold is determined for signals that correspond to the normal law of data distribution. Keywords: wavelet spectrum, autocoherence, autocorrelation, noise, noise threshold, frequency modulation.