The identification of cycles in periodic signals is a ubiquitous problem in time series analysis. Many real-world datasets only record a signal as a series of discrete events or symbols. In some cases, only a sequence of (non-equidistant) times can be assessed. Many of these signals are furthermore corrupted by noise and offer a limited number of samples, e.g., cardiac signals, astronomical light curves, stock market data, or extreme weather events. We propose a novel method that provides a power spectral estimate for discrete data. The edit distance is a distance measure that allows us to quantify similarities between non-equidistant event sequences of unequal lengths. However, its potential to quantify the frequency content of discrete signals has so far remained unexplored. We define a measure of serial dependence based on the edit distance, which can be transformed into a power spectral estimate (EDSPEC), analogous to the Wiener–Khinchin theorem for continuous signals. The proposed method is applied to a variety of discrete paradigmatic signals representing random, correlated, chaotic, and periodic occurrences of events. It is effective at detecting periodic cycles even in the presence of noise and for short event series. Finally, we apply the EDSPEC method to a novel catalog of European atmospheric rivers (ARs). ARs are narrow filaments of extensive water vapor transport in the lower troposphere and can cause hazardous extreme precipitation events. Using the EDSPEC method, we conduct the first spectral analysis of European ARs, uncovering seasonal and multi-annual cycles along different spatial domains. The proposed method opens new research avenues in studying of periodic discrete signals in complex real-world systems.
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Power spectral estimate for discrete data
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Research Article|
May 25 2023
Power spectral estimate for discrete data
Special Collection:
Ordinal Methods: Concepts, Applications, New Developments and Challenges
Norbert Marwan
;
Norbert Marwan
a)
(Conceptualization, Data curation, Formal analysis, Funding acquisition, Investigation, Methodology, Project administration, Resources, Software, Supervision, Validation, Visualization, Writing – original draft, Writing – review & editing)
1
Potsdam Institute for Climate Impact Research (PIK), Member of the Leibniz Association
, Telegrafenberg A31, 14473 Potsdam, Germany
2
University of Potsdam, Institute of Geoscience
, Karl-Liebknecht-Straße 32, 14476 Potsdam, Germany
a)Author to whom correspondence should be addressed: marwan@pik-potsdam.de
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Tobias Braun
Tobias Braun
(Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Resources, Software, Validation, Visualization, Writing – original draft, Writing – review & editing)
1
Potsdam Institute for Climate Impact Research (PIK), Member of the Leibniz Association
, Telegrafenberg A31, 14473 Potsdam, Germany
Search for other works by this author on:
a)Author to whom correspondence should be addressed: marwan@pik-potsdam.de
Note: This paper is part of the Focus Issue on Ordinal Methods: Concepts, Applications, New Developments and Challenges.
Chaos 33, 053118 (2023)
Article history
Received:
January 20 2023
Accepted:
April 03 2023
Citation
Norbert Marwan, Tobias Braun; Power spectral estimate for discrete data. Chaos 1 May 2023; 33 (5): 053118. https://doi.org/10.1063/5.0143224
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