Relationship Between the Structure Function of Random Time Series and the Discrete Chebyshev Spectrum

The technique of Chebyshev polynomials of discrete variable is used to analyze a random time series. The main result of the work is a new theoretical relationship between the structure function and the discrete Chebyshev spectrum. The relationship is used for the trend-resistant structural analysis of electrochemical noise of corrosion process and for the trend-resistant structural analysis of electronic noise of measuring instrument. Not only the structure function of the analyzed random series, but also the structure function of trend is estimated. The theoretical relationship between the structure function and the discrete Chebyshev spectrum can be used for the trend-resistant structural analysis of random time series of any nature.