Article
Version 1
Preserved in Portico This version is not peer-reviewed
Spike Spectra for Recurrences
Version 1
: Received: 31 August 2022 / Approved: 5 September 2022 / Online: 5 September 2022 (08:59:28 CEST)
A peer-reviewed article of this Preprint also exists.
Kraemer, K.H.; Hellmann, F.; Anvari, M.; Kurths, J.; Marwan, N. Spike Spectra for Recurrences. Entropy 2022, 24, 1689. Kraemer, K.H.; Hellmann, F.; Anvari, M.; Kurths, J.; Marwan, N. Spike Spectra for Recurrences. Entropy 2022, 24, 1689.
Abstract
A novel kind of power spectrum is constructed, the inter-spike spectrum, which transforms any signal into its spike-frequency domain. This method clearly shows the apparent cycles in the data and overcomes the problems for spike-train-like signals when using the obvious idea of Fourier-transforming it. We invent this instructive approach with the idea of transforming the τ-recurrence rate of a recurrence plot (RP), which often has a spiky appearance. The τ-recurrence rate is the density of recurrence points along diagonals of the RP, which are parallel to the main diagonal with a distance of τ. In this context the inter-spike spectrum can be interpreted as a nonlinear power spectrum of a potentially high dimensional system which constitutes the RP. The proposed measure is robust to noise and is able to detect and analyze bifurcations.
Keywords
Decomposition; Frequency Analysis; Recurrence Analysis; Bifurcations
Subject
Computer Science and Mathematics, Applied Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Comments (0)
We encourage comments and feedback from a broad range of readers. See criteria for comments and our Diversity statement.
Leave a public commentSend a private comment to the author(s)
* All users must log in before leaving a comment
