Research on Weak Signal Amplification Principle Based on Parabola Map

Abstract

In this paper, a new nonlinear amplification principle based on chaotic theory is proposed. Firstly, according to the basic properties of chaotic systems, such as the sensitivity of the initial conditions and the one-to-one correspondence between chaotic orbit and the initial value, we established the nonlinear enlarge model based on the parabola map. Then, after we studied the nonlinear amplification of the parabola map, and the binary relationship between input and output, we achieved the simulation of the nonlinear amplification with common signals. Thirdly, we compared the result of linear amplification with nonlinear amplification; and discussed the advantages and disadvantages of nonlinear amplification under real situation. Finally, we get the conclusion that the weak signal amplification principle which is based on parabola map has superiority. It can reduce the noise while enlarging the useful signal. In other words, it can improve the signal to noise ratio.