Local Optimal Processor Noise Enhancement In The Study

The constructive role of noise in systems has attracted much attention. The established stochastic resonance theories explain many nonlinear phenomena in physics, chemistry, biology, magnetism and electronics. Some scholars argue that the terminology of stochastic resonance usually refers to the possible matching between a characteristic time in dynamics and the characteristic time of the input signal. However, no evident characteristic time exists in the static systems. Thus, in this thesis, the term of noise-enhanced effects is more appropriate for describing the study of stochastic resonance in static systems. In the last two decades, noise-enhanced effects indicate many research directions in signal detection, nonlinear elements, biomedicine and neural dynamics. However, many potential noise-enhanced signal processing methods are not sufficiently explored, and some key problems need to be solved. The applications of noise-enhanced signal processing theories to practical problems should be bounded and studied deeply.Under the weak-signal condition, a simple implemented and near-optimal structure to the Neyman-Pearson processor is the locally optimum processor. In this paper, a novel kind of locally optimum processor is established by the dichotomous noise. It is demonstrated that this locally optimum processor has its maximal output-input SNR gain at a nonzero noise level, this is, the noise-enhanced effect in the locally optimum processor. The possibility of output signal-to-noise ratio exceeding that at the input is demonstrated. We also study the features of generalized correlation detector under the assumptions of weak signals. In this case, the locally optimal detector achieves the maximal efficacy. For the generalized Gaussian noise, the corresponding locally optimal detector does not exist for the uniform noise. Then, we use a three-threshold nonlinearity to detect the weak signal in uniform noise. By adding the dichotomous noise the given data, the infinite efficacy of detection can be attained. This phenomenon is meaningful for the nonlinear signal processing.