Errors involved in computing impulse response functions via frequency response functions

This paper discusses the errors that are introduced when calculating the impulse response function from the frequency response function using DFT/FFT analysis technique. The impulse response function is used in many applications of system analysis where a description of the system characteristics is preferred in the time domain rather than in the frequency domain. The case where the system is a single degree of freedom system, with viscous damping, is analysed. It is shown that the estimated impulse response function is not described by a single exponential decaying sinewave but rather as a sum of exponential decaying sinewaves. It is important to apply this slightly more complex model when the measurements are to be used for mathematical modelling of systems containing lightly damped resonances and where measurements free of influence of leakage are performed.