Nonlinear Enhancement of Weak Signals Using Optimization Theory

摘要

Stochastic Resonance (SR) is a phenomenon that performance of the nonlinear system can be improved with the addition of optimal amount of noise. Stochastic resonance has been increasingly used for signal processing. The output of the nonlinear bistable dynamic system can be used to restore the weak input signal corrupted by white Gaussian noise, if the similarity between the input signal and the output can be maximized. This paper will first use the optimization theory to show that the normalized power norm (CI) describing the similarity will reach a larger maximum when tuning both the system parameters and noise intensity, compared with that of only adjusting noise intensity (classical stochastic resonance) of only adjusting system parameters (parameter- tuning stochastic resonance). Then, a practical fast-converging optimization algorithm is mentioned to search the optimal system parameters and noise intensity. Finally, computer simulations are performed to verify this proposal and demonstrate its application in signal processing.