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Fisher Information as a Metric of Locally Optimal Processing and Stochastic Resonance

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  • Fabing Duan
  • François Chapeau-Blondeau
  • Derek Abbott

Abstract

The origins of Fisher information are in its use as a performance measure for parametric estimation. We augment this and show that the Fisher information can characterize the performance in several other significant signal processing operations. For processing of a weak signal in additive white noise, we demonstrate that the Fisher information determines (i) the maximum output signal-to-noise ratio for a periodic signal; (ii) the optimum asymptotic efficacy for signal detection; (iii) the best cross-correlation coefficient for signal transmission; and (iv) the minimum mean square error of an unbiased estimator. This unifying picture, via inequalities on the Fisher information, is used to establish conditions where improvement by noise through stochastic resonance is feasible or not.

Suggested Citation

  • Fabing Duan & François Chapeau-Blondeau & Derek Abbott, 2012. "Fisher Information as a Metric of Locally Optimal Processing and Stochastic Resonance," PLOS ONE, Public Library of Science, vol. 7(4), pages 1-6, April.
    • Handle: RePEc:plo:pone00:0034282
    DOI: 10.1371/journal.pone.0034282
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    Cited by:

    1. Ren, Yuhao & Duan, Fabing, 2016. "Theoretical and experimental implementation of vibrational resonance in an array of hard limiters," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 456(C), pages 319-326.
    2. Ren, Yuhao & Pan, Yan & Duan, Fabing, 2022. "SNR gain enhancement in a generalized matched filter using artificial optimal noise," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).

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