Stochastic Resonance in a Simple Threshold Sensor System with Alpha Stable Noise

Abstract

We investigate the effect of alpha stable noise on stochastic resonance in a single-threshold sensor system by analytic deduction and stochastic simulation. It is shown that stochastic resonance occurs in the threshold system in alpha stable noise environment, but the resonant effect becomes weakened as the alpha stable index decreases or the skewness parameter of alpha stable distribution increases. In particular, for Cauchy noise a nonlinear relation among the optimal noise deviation parameter, the signal amplitude and the threshold is analytically obtained and illustrated by using the extreme value condition for the output signal-to-noise ratio. The results presented in this communication should have application in signal detection and image restoration in the non-Gaussian noisy environment.

Linearly-coupled sigmoid bistable stochastic resonance for weak signal detection

“…Alpha-stable-distributed noise, also known as Lévy noise, closely resembles natural noise, and its pulse distribution characteristics highly match those of signals used in engineering applications [5]. Thence, the alpha-stable-distributed noise is employed to effectively simulate real signals.…”

“…These signals often exhibit significant spike pulse characteristics [2][3][4], underscoring the inadequacy of Gaussian models for simulating natural noise processes. Consequently, alpha stable distribution [5], a non-Gaussian model which can describe such noise processes more accurately, has received increasing attention. Traditional detection algorithms, which rely on second-order or higher-order statistics, are ineffective for alpha-stable-distributed noise.…”

Fractional stochastic resonance of multi-frequency weak periodic signals in alpha-stable noisy environment

“…The -stable α noise is a limit distribution that can produce mechanism and propagation of a natural noisy process, it is a super-diffusion system of abnormal proliferation [10].…”