DESCRIPTION OF MULTI-PERIODIC SIGNALS GENERATED BY COMPLEX SYSTEMS: NOCFASS-NEW POSSIBILITIES OF THE FOURIER ANALYSIS

Here, we show how to extend the possibilities of the conventional F-analysis and adapt it for quantitative description of multi-periodic signals recorded from different complex systems. The basic idea lies in filtration property of the Dirichlet function that allows finding the leading frequencies (hav-ing the predominant amplitudes) and the shortcut frequency band allows to fit the initial random signal with high accuracy (with the value of the relative error less than 5%). This modification defined as NOCFASS-approach (Non-Orthogonal Combined Fourier Analysis of the Smoothed Signals) can be applied to a wide class of different signals having multi-periodic structure. We want to underline here that the shortcut frequency dispersion has linear dependence Ω_k = c.k+d that differs from the conventional dispersion accepted in the conventional Fourier transformation ω(k) =^2πk. (T is a period of the initial T signal). With the help of integration procedure one can extract a low-frequency trend from trendless sequences that allows to applying the NOCFASS approach for calculation of the desired amplitude-frequency response (AFR) from different noisy random sequences. In order to underline the multi-periodic structure of random signals under analysis we consider two nontrivial examples. (a) The peculiarities of the AFR associated with Weierstrass-Mandelbrot function. (b) The random behavior of the voltammograms (VAGs) background measured for an electrochemical cell with one active electrode. We do suppose that the proposed NOCFASS-approach having new attractive properties as the simplicity of realization, agility to the problem formulated will find a wide propagation in the modern signal processing area.