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The spectrum of impulse response signal from an impulse hammer testing is widely used to obtain frequency response function(FRF) of the structure. However the FRFs obtained from impact hammer testing have not only leakage errors but also finite record length errors when the record length for the signal processing is not sufficiently long. The errors cannot be removed with the conventional signal analyzer which treats the signals as if they are always steady and periodic. Since the response signals generated by the impact hammer are transient and have damping, they are undoubtedly non-periodic. It is inevitable that the signals be acquired for limited recording time, which causes the finite record length error and the leakage error. In this paper, the errors in the frequency response function of multi degree of freedom system are formulated theoretically. And the method to remove these errors is also suggested. This method is based on the optimization technique. A numerical example of 3-dof model shows the validity of the proposed method.