Probability density function for frequency response function measurements using periodic signals

Frequency response function (FRF) measurements are often used to characterize linear dynamic systems. Today, uncertainty bounds on FRF measurements still are based on linear approximations, which are valid for sufficiently large input signal-to-noise-ratios (SNR) only. In this paper, exact uncertainty bounds are calculated, which are valid for any input SNR. These bounds are obtained via an analytic expression of the probability density function (pdf) of the FRF measurements. The results are valid for open- and closed-loop measurements, and the theory is illustrated on a real measurement example.