Unbiased expression of FRF with exponential window function in impact hammer testing

The exponential window function is widely used in impact hammer testing to reduce leakage errors as well as to get a nice S/N ratio. The larger the exponential decay rate of the window is, the more effectively the leakage errors are reduced. But if the decay rate of the exponential window function is too large, the frequency response function (FRF) is distorted by its side effects. The modal parameters of the system cannot be exactly identified from the distorted FRF even though modal analysis technique is used. Therefore, it is a difficult problem to determine a proper exponential decay rate in an impact hammer testing. s paper, the amount of the FRF distortion caused by the exponential window function is theoretically uncovered, and an unbiased expression of the exponential-windowed FRF is represented. A new circle fitting method is also proposed so that the modal parameters are directly extracted from the impulse response spectrum distorted by the exponential window function. The results identified by the conventional and proposed circle fitting method are compared through numerical examples.