Analysis of Discrete Signals with Stochastic Components using Flicker Noise Spectroscopy

TL;DR

This paper explores extracting information from discrete stochastic signals using flicker-noise spectroscopy, highlighting differences in spectral analysis at various sampling frequencies and proposing the sampling interval as a key parameter.

Contribution

It extends flicker-noise spectroscopy to discrete signals, demonstrating the interpretation of mathematical functions as stochastic components and analyzing EEG data at different sampling rates.

Findings

Power spectrum and difference moment contain different information for discrete signals.

Sampling interval should be included as a parameter in signal analysis.

Formal proof of differences between continuous and discrete signal analysis.

Abstract

The problem of information extraction from discrete stochastic time series, produced with some finite sampling frequency, using flicker-noise spectroscopy, a general framework for information extraction based on the analysis of the correlation links between signal irregularities and formulated for continuous signals, is discussed. It is shown that the mathematical notions of Dirac and Heaviside functions used in the analysis of continuous signals may be interpreted as high-frequency and low-frequency stochastic components, respectively, in the case of discrete series. The analysis of electroencephalogram measurements for a teenager with schizophrenic symptoms at two different sampling frequencies demonstrates that the "power spectrum" and difference moment contain different information in the case of discrete signals, which was formally proven for continuous signals. The sampling interval itself is suggested as an additional parameter that should be included in general parameterization procedures for real signals.