Elements of information theory
Elements of information theory
On the use of stochastic resonance in sine detection
Signal Processing
Stochastic resonance for an optimal detector with phase noise
Signal Processing
Stochastic resonance in sequential detectors
IEEE Transactions on Signal Processing
Optimal noise benefits in Neyman-Pearson and inequality-constrained statistical signal detection
IEEE Transactions on Signal Processing
Noise enhanced nonparametric detection
IEEE Transactions on Information Theory
Stochastic resonance and improvement by noise in optimal detection strategies
Digital Signal Processing
Noise enhanced hypothesis-testing in the restricted Bayesian framework
IEEE Transactions on Signal Processing
Stochastic resonance in locally optimal detectors
IEEE Transactions on Signal Processing
Noise-enhanced performance for an optimal Bayesian estimator
IEEE Transactions on Signal Processing
Stochastic resonance in discrete time nonlinear AR(1) models
IEEE Transactions on Signal Processing
Theory of the Stochastic Resonance Effect in Signal Detection: Part I—Fixed Detectors
IEEE Transactions on Signal Processing - Part I
Noise Benefits in Quantizer-Array Correlation Detection and Watermark Decoding
IEEE Transactions on Signal Processing
Generalized Entropy Power Inequalities and Monotonicity Properties of Information
IEEE Transactions on Information Theory
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For processing a weak periodic signal in additive white noise, a locally optimal processor (LOP) achieves the maximal output signal-to-noise ratio (SNR). In general, such a LOP is precisely determined by the noise probability density and also by the noise level. It is shown that the output-input SNR gain of a LOP is given by the Fisher information of a standardized noise distribution. Based on this connection, we find that an arbitrarily large SNR gain, for a LOP, can be achieved ranging from the minimal value of unity upwards. For stochastic resonance, when considering adding extra noise to the original signal, we here demonstrate via the appropriate Fisher information inequality that the updated LOP fully matched to the new noise, is unable to improve the output SNR above its original value with no extra noise. This result generalizes a proof that existed previously only for Gaussian noise. Furthermore, in the situation of non-adjustable processors, for instance when the structure of the LOP as prescribed by the noise probability density is not fully adaptable to the noise level, we show general conditions where stochastic resonance can be recovered, manifested by the possibility of adding extra noise to enhance the output SNR.