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

Nava Leibovich () and Eli Barkai
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Nava Leibovich: Institute of Nanotechnology and Advanced Materials, Bar-Ilan University
Eli Barkai: Institute of Nanotechnology and Advanced Materials, Bar-Ilan University

The European Physical Journal B: Condensed Matter and Complex Systems, 2017, vol. 90, issue 11, 1-8

Abstract: 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 functions 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 β noise. We illustrate our general results with two-state renewal models with sojourn times’ distributions having a broad tail.

Date: 2017
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Citations: View citations in EconPapers (2)

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DOI: 10.1140/epjb/e2017-80398-6

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