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General measures for signal-noise separation in nonlinear dynamical systems
J W Robinson1, J Rung, A R Bulsara
1Defence Research Establishment, SE 172 90 Stockholm, Sweden. john@sto.foa.se
Summary
Straight phi divergences offer a superior method for separating signal from noise in stochastic nonlinear dynamical systems (SNDS). These divergences provide a more informative and universally applicable alternative to traditional signal-to-noise ratio (SNR) measures.
Area of Science:
- Statistics and Information Theory
- Nonlinear Dynamical Systems
Background:
- Traditional signal-to-noise ratio (SNR) has limitations in characterizing signal-noise separation in complex systems.
- Stochastic resonance (SR) curves, while useful, can represent suboptimal detection performance.
Purpose of the Study:
- Introduce straight phi divergences as novel separation indices for stochastic nonlinear dynamical systems (SNDS).
- Provide a more informative and broadly applicable alternative to SNR.
- Reinterpret classical stochastic resonance (SR) within an information-theoretic framework.
Main Methods:
- Utilized properties of straight phi divergences from statistics and information theory.
- Analyzed a prototype double-well system with Gaussian noise and embedded signals.
- Investigated SNDS driven by wide- and narrow-band signals.
Main Results:
- Straight phi divergences offer a more informative measure of signal-noise separation than SNR.
- The classical SR curve can be explained as the performance of a mismatched detector.
- Information loss in SNDS can be attributed to suboptimal detection criteria.
Conclusions:
- Straight phi divergences are a powerful tool for analyzing signal-noise separation in SNDS.
- The choice of performance criterion significantly impacts the universality of SNDS analysis.
- Results are applicable to a wide range of signals and stochastic systems.