Analysis of the non-Markov parameter in continuous-time signal processing

Varghese, J., Bellette, P. A., Weegink, K. J., Bradley, A. P. and Meehan, P. A. (2014) Analysis of the non-Markov parameter in continuous-time signal processing. Physical Review E, 89 2: . doi:10.1103/PhysRevE.89.022109

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Author Varghese, J.
Bellette, P. A.
Weegink, K. J.
Bradley, A. P.
Meehan, P. A.
Title Analysis of the non-Markov parameter in continuous-time signal processing
Journal name Physical Review E   Check publisher's open access policy
ISSN 1539-3755
1550-2376
Publication date 2014-02-10
Year available 2014
Sub-type Article (original research)
DOI 10.1103/PhysRevE.89.022109
Open Access Status File (Publisher version)
Volume 89
Issue 2
Total pages 10
Place of publication College Park, MD, United States
Publisher American Physical Society
Language eng
Formatted abstract
 The use of statistical complexity metrics has yielded a number of successful methodologies to differentiate and identify signals from complex systems where the underlying dynamics cannot be calculated. The Mori-Zwanzig framework from statistical mechanics forms the basis for the generalized non-Markov parameter (NMP). The NMP has been used to successfully analyze signals in a diverse set of complex systems. In this paper we show that the Mori-Zwanzig framework masks an elegantly simple closed form of the first NMP, which, for C1 smooth autocorrelation functions, is solely a function of the second moment (spread) and amplitude envelope of the measured power spectrum. We then show that the higher-order NMPs can be constructed in closed form in a modular fashion from the lower-order NMPs. These results provide an alternative, signal processing-based perspective to analyze the NMP, which does not require an understanding of the Mori-Zwanzig generating equations. We analyze the parametric sensitivity of the zero-frequency value of the first NMP, which has been used as a metric to discriminate between states in complex systems. Specifically, we develop closed-form expressions for three instructive systems: band-limited white noise, the output of white noise input to an idealized all-pole filter,f and a simple harmonic oscillator driven by white noise. Analysis of these systems shows a primary sensitivity to the decay rate of the tail of the power spectrum.

Keyword Physics, Fluids & Plasmas
Physics, Mathematical
Physics
PHYSICS, FLUIDS & PLASMAS
PHYSICS, MATHEMATICAL
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ
Additional Notes Article number 022109.

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mechanical & Mining Engineering Publications
Official 2015 Collection
 
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Created: Wed, 05 Mar 2014, 22:37:25 EST by Alex Fitzgerald on behalf of School of Mechanical and Mining Engineering