Nonlinear Enhancement of Weak Signals Using Optimization Theory

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 with white Gaussian noise input can be used to restore the weak input signal, if the similarity between the input signal and the output can be maximized. This paper first use the optimization theory to show that the normalized power norm describing the similarity will reach a larger maximum when tuning both system parameters and noise intensity, compared with that of only adjusting noise intensity (classical stochastic resonance) or only adjusting system parameters. Then, computer simulations are performed to verify this proposal and demonstrate its application in signal processing