Singular-spectrum analysis and the normalized range method as a method for differentiation noisy experimental curves
Bakhmutsky M. L.1
1Scientific Research Institute for System Analysis of the National Research Centre «Kurchatov Institute», Moscow, Russia
Email: mbakhmut@mail.ru
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.
- R. Vautard, P. Yiou, M. Ghil, Physica D, 58, 95 (1992). DOI: 10.1016/0167-2789(92)90103-T
- N.E. Golyandina, Metod Gusenitsa"-SSA: analiz vremennykh ryadov (Izd. VVM, SPb., 2004) (in Russian)
- J. Feder, Fractals (Plenum Press, 1988)
- J.W. Demmel, Applied numerical linear algebra (SIAM, 1997)
- R.N. Horne, Modern well test analysis. A computer-aided approach (Petroway, 2002)
- A.N. Tikhonov, V.Ya. Arsenin. Metody resheniya nekorrektnykh zadach (URSS, M., 2022).