Singular-spectrum analysis and the normalized range method as a method for differentiation noisy experimental curves

M. L. Bakhmutsky

Scientific Research Institute for System Analysis of the National Research Centre "Kurchatov Institute", Moscow

Abstract: It is proposed to differentiate the experimental curve by finite differences in physical space. In this case, the amplitude of the noise increases sharply, but this does not change the random nature of the noise. Using the singular- spectrum analysis, the derivative is presented as a sum of additive components. The fractal dimension (Hurst index) of these components is estimated by the normalized range method. When synthesizing the derivative, the components are summed until the Hurst index of the derivative begins to decrease.

Keywords: differentiation, singular- spectrum analysis, Hurst index.

Received: 28.07.2025
Revised: 19.08.2025
Accepted: 25.09.2025

DOI: 10.61011/PJTF.2026.03.62176.20454

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