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.
Highlights
Fisher information is foremost a measure of the minimum error in estimating an unknown parameter of a probability distribution, and its importance is related to the Cramer-Rao inequality for unbiased estimators [1,2]
With sufficiently large observed data and using the central limit theorem, it is demonstrated that the locally optimal detector is asymptotically optimum and the Fisher information of the noise distribution is the upper bound of the asymptotic efficacy [2,3,4,5,6,7]
To extend the heuristic studies of [1,2,3,4,5,6,7], in this paper, we will theoretically demonstrate that, for a weak signal buried in additive white noise, the performance for locally optimal processing can be generally measured by the Fisher information of the noise distribution
Summary
Fisher information is foremost a measure of the minimum error in estimating an unknown parameter of a probability distribution, and its importance is related to the Cramer-Rao inequality for unbiased estimators [1,2]. To extend the heuristic studies of [1,2,3,4,5,6,7], in this paper, we will theoretically demonstrate that, for a weak signal buried in additive white noise, the performance for locally optimal processing can be generally measured by the Fisher information of the noise distribution We show this for the following signal processing case studies: (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. The applications of SR to nonlinear signal processing are of practical interest
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