2011/11/24 by Fabing Duan, Duan, Fabing, François Chapeau‐Blondeau +4
Computer Science · Mathematics · Neuroscience · Physics and Astronomy · #Chaos control and synchronization #Data Analysis #FOS: Computer and information sciences #FOS: Physical sciences #Information Theory (cs.IT) #Neural dynamics and brain function #Statistics and Probability (physics.data-an) #cs.IT #math.IT #physics.data-an #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.1111.5679
8 pages, 1 figure
arxiv created 2011/11/24 · openalex publication_date 2011/11/24 · arxiv updated 2011/11/28 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
For a known weak signal in additive white noise, the asymptotic performance of a locally optimum processor (LOP) is shown to be given by the Fisher information (FI) of a standardized even probability density function (PDF) of noise in three cases: (i) the maximum signal-to-noise ratio (SNR) gain for a periodic signal; (ii) the optimal asymptotic relative efficiency (ARE) for signal detection; (iii) the best cross-correlation gain (CG) for signal transmission. The minimal FI is unity, corresponding to a Gaussian PDF, whereas the FI is certainly larger than unity for any non-Gaussian PDFs. In the sense of a realizable LOP, it is found that the dichotomous noise PDF possesses an infinite FI for known weak signals perfectly processed by the corresponding LOP. The significance of FI lies in that it provides a upper bound for the performance of locally optimum processing.