Noise-benefit forbidden-interval theorems for threshold signal detectors based on cross correlations
1Department of Electrical and Computer Engineering, Faculty of Engineering Thammasat University, Pathumthani 12120, Thailand.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 11, 2014
Summary
Stochastic resonance benefits threshold detectors with added noise, even when noise levels are within traditional forbidden intervals. This study extends these findings to correlation performance measures for various noise types and signal conditions.
Area of Science:
- Nonlinear Dynamics and Signal Processing
- Information Theory
- Statistical Physics
Background:
- Stochastic resonance (SR) is a phenomenon where adding noise can enhance signal detection.
- Traditional SR forbidden interval theorems apply to specific performance measures like mutual information or error detection probability.
- These theorems define noise ranges where adding noise is detrimental to signal detection.
Purpose of the Study:
- To extend the forbidden interval theorems of stochastic resonance to correlation performance measures.
- To investigate the conditions under which adding noise benefits threshold signal detection across diverse noise and signal types.
- To generalize the concept of forbidden intervals to forbidden bands for broader applicability.
Main Methods:
- Mathematical derivation and analysis of forbidden interval theorems for stochastic resonance.
- Application of correlation performance measures to threshold signal detection.
- Consideration of various noise models, including finite-variance and infinite-variance stable noise, and location-scale families.
- Analysis of arbitrary signals with finite second moments and normal distributions.
Main Results:
- The main forbidden interval theorems of stochastic resonance are shown to hold for correlation performance measures.
- This extension applies to finite-variance noise and all forms of infinite-variance stable noise.
- New theorems establish conditions for local noise benefit in bipolar and general signal systems, introducing forbidden bands of parameters.
Conclusions:
- Correlation performance measures provide a broader framework for understanding stochastic resonance benefits.
- The findings expand the applicability of forbidden interval theorems to a wider range of noise and signal conditions.
- This research offers a more comprehensive understanding of noise-induced signal enhancement in threshold detection systems.
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