When a transient single-phase fault occurs on shunt reactor compensated transmission lines，there exist components of power frequency and low frequency during voltage recovery stages.This forms the pat frequency phenomenon.Currently， the adaptive reclose criterions based on this have poor performance against disturbances，and cannot be used to identify circuit arc extinguishing time.A new signal processing method—the atomic sparse decomposition method is used to analyze nonlinear fault signals as well as to extract the low frequency components of recovery voltage when the transient single-phase fault occurs.The fault properties can also be identified.Atomic sparse decomposition is more accurate in determining the circuit arc extinguishing time because of its powerful time domain and frequency domain analysis capabilities.The algorithm also has coincidence time setting capability which provides the basis for circuit breaker overlap time setting.The simulation results show that the method proposed can effectively improve the adaptive reclose performance.