Filtering affects the calculation of the largest Lyapunov exponent

Peter C. Raffalt, Benjamin Senderling, Nick Stergiou*

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

13 Citations (Scopus)

Abstract

The calculation of the largest Lyapunov exponent (LyE) requires the reconstruction of the time series in an N-dimensional state space. For this, the time delay (Tau) and embedding dimension (EmD) are estimated using the Average Mutual Information and False Nearest Neighbor algorithms. However, the estimation of these variables (LyE, Tau, EmD) could be compromised by prior filtering of the time series evaluated. Therefore, we investigated the effect of filtering kinematic marker data on the calculation of Tau, EmD and LyE using several different computational codes. Kinematic marker data were recorded from 37 subjects during treadmill walking and filtered using a low pass digital filter with a range of cut-off frequencies (23.5–2Hz). Subsequently, the Tau, EmD and LyE were calculated from all cut-off frequencies. Our results demonstrated that the level of filtering affected the outcome of the Tau, EmD and LyE calculations for all computational codes used. However, there was a more consistent outcome for cut-off frequencies above 10 Hz which corresponded to the optimal cut-off frequency that could be used with this data. This suggested that kinematic data should remain unfiltered or filtered conservatively before calculating Tau, EmD and LyE.

Original languageEnglish
Article number103786
JournalComputers in Biology and Medicine
Volume122
ISSN0010-4825
DOIs
Publication statusPublished - 2020
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2020 Elsevier Ltd

Keywords

  • Biomechanics
  • Cut-off frequency
  • Nonlinear analysis
  • Smoothing
  • Walking

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