Spectral analysis and system identification algorithm are used to analyze a set of acceleration response records obtained from a shaking table test. The method is based on the linear discrete time systems theory, and the soil-pile system can be represented as a linear filter of a finite order with time-varying coefficients. The recorded ground motion at the pile tip is the input, and the motion at the different level along the pile and the structure is the output of the filter. Knowing the input and output, the time varying parameters of the filter can be determined by using the system identification method. Once the filter parameters are known, the transfer function, and the kinematic interaction between the soil-pile-structure can be determined
