This paper proposes to clarify the mechanism of the impact phenomena of golf clubs and golf balls by both time series analysis and the concept of mechanical impedance in the frequency domain and to investigate the maximum restitution. By using a lumped mass system, the restitution coefficient and the impact transfer efficiency are investigated for the golf clubs and golf balls. Secondly, the optimum combination of golf club and golf ball which gives the maximum restitution coefficient and the maximum impact transfer efficiency is related to the concept of mechanical impedance. That is, the relation between time series analysis and frequency domain analysis is clarified in the problems to obtain the maximum restitution coefficient and the maximum impact transfer efficiency of two bodies. Furthermore, a few experiments on hitting the golf balls with golf clubs are performed, and the results of the experiments are compared with those of the numerical analysis.