Noise-to-signal ratio of single-trajectory spectral densities in centered Gaussian processes

Autor:	Squarcini, Alessio, Marinari, Enzo, Oshanin, Gleb, Peliti, Luca, Rondoni, Lamberto
Rok vydání:	2022
Předmět:	Condensed Matter - Statistical Mechanics Physics - Data Analysis Statistics and Probability
Druh dokumentu:	Working Paper
DOI:	10.1088/1751-8121/ac8cc0
Popis:	We discuss the statistical properties of a single-trajectory power spectral density $S(\omega,\mathcal{T})$ of an arbitrary real-valued centered Gaussian process $X(t)$, where $\omega$ is the angular frequency and $\mathcal{T}$ the observation time. We derive a double-sided inequality for its noise-to-signal ratio and obtain the full probability density function of $S(\omega,\mathcal{T})$. Our findings imply that the fluctuations of $S(\omega,\mathcal{T})$ exceed its average value $\mu(\omega,\mathcal{T})$. This implies that using $\mu(\omega,\mathcal{T})$ to describe the behavior of these processes can be problematic. We finally evaluate the typical behavior of $S(\omega,\mathcal{T})$ and find that it deviates markedly from the average $\mu(\omega,\mathcal{T})$ in most cases. Comment: 10 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2205.12055 Zobrazit plný text záznamu View this record from Arxiv