Stochastic Resonance Phenomena And Signal-to-noise Ratio Studies In Colored Noise

Within the context of stochastic resonance, the assumption of white noise is ideal. In many practical situations, the idealization of white noise is never exactly realized. Consequently, the effect of colored noise is better than white noise in enhancing the response of the nonlinear system to weak signals under certain conditions.This thesis investigates the signal-to-noise ratio(SNR) of a nonlinear filter in the presence of weak input signals, and gets the relationship between the performance of optimal filter and the Fisher information of noise distributions. Moreover, we deduce the maximum SNR formula, which is not only applicable to white noise but also to colored noise. For mimicking the colored noise, we adopt the first-order moving-average model. According to its weak correlation characteristics, the maximum output SNR expression in arbitrary nonlinear filter is presented. For the scaled or non-scaled noise types, we present the conditions of the occurrence of stochastic resonance phenomenon. This conclusion is verified in a threshold system. In addition we investigate in an array of threshold system; the stochastic resonance phenomenon exists for both non-scaled and scaled noise types. As the noise level increases, the supra-threshold stochastic resonance effect occurs, and the output SNR is enhanced in an array of threshold systems. In a bistable system, we respectively consider the colored noise produced by the two different models. The stochastic resonance phenomenon is also observed. However, it is very difficult to solve the Fokker-Plank equation, and find the matched input signal for the considered colored noise type. Thus, the maximal SNR of the bistable system, as well as the method of optimizing input signal waveform, deserves to be further studied.