Aiming at the fact that the output signal is difficult to recover in the strong noise background

to solve this problem

power function recovery system is proposed to realize the signal restoration in this paper.The influence of different parameters and noise intensity as well as signal amplitude on the recovery performance are studied by using the mutual correlation coefficient as the measurement index.Power function recovery system achieves single-frequency sinusoidal signal and multi-frequency sinusoidal signal as well as single pulse signal recovery in the case of fewer sampling points and optimize parameters are opted with the particle swarm algorithm.Simulation results show that the theoretical analysis results are consistent with the simulations

which proves the proposed method is feasible and effective

and the achieved recovery effect is ideal.