Skip to main content

Research Repository

See what's under the surface

Advanced Search

Periodicity in the autocorrelation function as a mechanism for regularly occurring zero crossings or extreme values of a Gaussian process

Wilson, Lorna R. M.; Hopcraft, Keith I.

Authors

Lorna R. M. Wilson

Keith I. Hopcraft



Abstract

The problem of zero crossings is of great historical prevalence and promises extensive application. The challenge is to establish precisely how the autocorrelation function or power spectrum of a one-dimensional continuous random process determines the density function of the intervals between the zero crossings of that process. This paper investigates the case where periodicities are incorporated into the autocorrelation function of a smooth process. Numerical simulations, and statistics about the number of crossings in a fixed interval, reveal that in this case the zero crossings segue between a random and deterministic point process depending on the relative time scales of the periodic and nonperiodic components of the autocorrelation function. By considering the Laplace transform of the density function, we show that incorporating correlation between successive intervals is essential to obtaining accurate results for the interval variance. The same method enables prediction of the density function tail in some regions, and we suggest approaches for extending this to cover all regions. In an ever-more complex world, the potential applications for this scale of regularity in a random process are far reaching and powerful.

Journal Article Type Article
Publication Date Dec 18, 2017
Journal Physical Review E
Print ISSN 2470-0045
Electronic ISSN 1079-7114
Publisher American Physical Society
Peer Reviewed Peer Reviewed
Volume 96
Issue 6
APA6 Citation Wilson, L. R. M., & Hopcraft, K. I. (2017). Periodicity in the autocorrelation function as a mechanism for regularly occurring zero crossings or extreme values of a Gaussian process. Physical Review E, 96(6), doi:10.1103/PhysRevE.96.062129
DOI https://doi.org/10.1103/PhysRevE.96.062129
Publisher URL https://journals.aps.org/pre/abstract/10.1103/PhysRevE.96.062129
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf

Files

pre_2017.pdf (1.1 Mb)
PDF

Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





You might also like



Downloadable Citations

;