publication . Preprint . Article . 2017

1 ∕ f β noise for scale-invariant processes: how long you wait matters

Nava Leibovich; Eli Barkai;
Open Access English
  • Published: 05 Jul 2017
Abstract
We study the power spectrum which is estimated from a nonstationary signal. In particular we examine the case when the signal is observed in a measurement time window $[t_w,t_w+t_m]$, namely the observation started after a waiting time $t_w$, and $t_m$ is the measurement duration. We introduce a generalized aging Wiener-Khinchin theorem which relates between the spectrum and the time- and ensemble-averaged correlation function for arbitrary $t_m$ and $t_w$. Furthermore we provide a general relation between the non-analytical behavior of the scale-invariant correlation function and the aging $1/f^{\beta}$ noise. We illustrate our general results with two-state re...
Subjects
free text keywords: Condensed Matter - Statistical Mechanics, Scale invariance, Spectral density, Condensed matter physics, Correlation function, Physics, Complex system, Solid-state physics, Mathematical physics
Related Organizations
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publication . Preprint . Article . 2017

1 ∕ f β noise for scale-invariant processes: how long you wait matters

Nava Leibovich; Eli Barkai;