TY - JOUR
T1 - 1∕ f β noise for scale-invariant processes
T2 - how long you wait matters
AU - Leibovich, Nava
AU - Barkai, Eli
N1 - Publisher Copyright:
© 2017, EDP Sciences, SIF, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2017/11/1
Y1 - 2017/11/1
N2 - 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 [tw, tw + tm], namely the observation started after a waiting time tw, and tm is the measurement duration. We introduce a generalized aging Wiener–Khinchin theorem which relates between the spectrum and the time- and ensemble-averaged correlation functions for arbitrary tm and tw. Furthermore we provide a general relation between the non-analytical behavior of the scale-invariant correlation function and the aging 1∕fβ noise. We illustrate our general results with two-state renewal models with sojourn times’ distributions having a broad tail.
AB - 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 [tw, tw + tm], namely the observation started after a waiting time tw, and tm is the measurement duration. We introduce a generalized aging Wiener–Khinchin theorem which relates between the spectrum and the time- and ensemble-averaged correlation functions for arbitrary tm and tw. Furthermore we provide a general relation between the non-analytical behavior of the scale-invariant correlation function and the aging 1∕fβ noise. We illustrate our general results with two-state renewal models with sojourn times’ distributions having a broad tail.
UR - http://www.scopus.com/inward/record.url?scp=85036633133&partnerID=8YFLogxK
U2 - 10.1140/epjb/e2017-80398-6
DO - 10.1140/epjb/e2017-80398-6
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
SN - 1434-6028
VL - 90
JO - European Physical Journal B
JF - European Physical Journal B
IS - 11
M1 - 229
ER -