College of Automation Engineering, Qingdao University, Qingdao, People's Republic of China.
PLoS One. 2012;7(4):e34282. doi: 10.1371/journal.pone.0034282. Epub 2012 Apr 6.
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.
Fisher 信息量的起源在于其作为参数估计性能度量的应用。我们对其进行了扩展，并证明了 Fisher 信息量可以刻画几种其他重要的信号处理操作的性能。对于在加性白噪声中处理弱信号，我们证明了 Fisher 信息量决定了（i）周期性信号的最大输出信噪比；（ii）信号检测的最优渐近功效；（iii）信号传输的最佳互相关系数；以及（iv）无偏估计器的最小均方误差。通过 Fisher 信息量的不等式，这种统一的图景被用于建立通过随机共振来改善噪声是否可行的条件。
