Chebyshev Spectra Resistance to Trend of Random Noise

Abstract

Spectral analysis of random noise in the space of discrete Chebyshev polynomials is an alternative to spectral Fourier analysis. The importance of Chebyshev spectral approach is associated with the fact that the discrete Chebyshev transformation of the [Formula: see text]-th order eliminates automatically the polynomial trend of the ([Formula: see text]−1) order. Using the method of artificial trend, it was found that, under the real experimental conditions, the intensity of Chebyshev spectral lines with numbers higher than 1 is resistant to a strong trend of random process. This effect is observed when we use both the arithmetic averaging and the median. The Chebyshev spectral approach is a powerful tool for spectral analysis of random time series with a strong trend.