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Analysis of the non-Markov parameter in continuous-time signal processing
J J Varghese1, P A Bellette1, K J Weegink1
1University of Queensland, Brisbane, Australia.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 30, 2014
Summary
This study simplifies the non-Markov parameter (NMP) from statistical mechanics, revealing a closed-form expression dependent on power spectrum properties. This offers a new signal processing approach for analyzing complex systems without complex theoretical frameworks.
Area of Science:
- Statistical mechanics
- Signal processing
- Complex systems analysis
Background:
- Statistical complexity metrics aid in analyzing complex systems with unknown dynamics.
- The Mori-Zwanzig framework is foundational for the generalized non-Markov parameter (NMP).
- NMP has proven effective in analyzing diverse complex system signals.
Purpose of the Study:
- To derive a simplified, closed-form expression for the first non-Markov parameter (NMP).
- To establish a modular method for constructing higher-order NMPs.
- To offer a signal processing perspective on NMP analysis, independent of Mori-Zwanzig equations.
Main Methods:
- Derivation of a closed-form expression for the first NMP based on power spectrum characteristics (spread and amplitude envelope).
- Modular construction of higher-order NMPs from lower-order ones.
- Analysis of parametric sensitivity using three model systems: band-limited white noise, an all-pole filter, and a driven harmonic oscillator.
Main Results:
- The first NMP simplifies to a function of the power spectrum's second moment and amplitude envelope for C(1) smooth autocorrelation functions.
- Higher-order NMPs can be built modularly from lower-order NMPs.
- The zero-frequency value of the first NMP is primarily sensitive to the power spectrum's tail decay rate.
Conclusions:
- A simplified, signal processing-based method for calculating NMPs is presented.
- This approach bypasses the need for complex Mori-Zwanzig generating equations.
- The findings provide a new perspective on analyzing and discriminating states in complex systems using spectral properties.
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