Measurement of frequency response functions in noisy environments

The geometric mean is proposed as an alternative averaging technique for frequency response function (FRF) measurements of a linear system. It is shown that it produces almost unbiased measurements even if the input and output measurements are both disturbed with (normal distributed) noise. The properties of the arithmetic and geometric mean of expression are compared to those of the H₁ and H₂ methods. It is shown that if the S/N ratio on the input and the output measurements is higher than 3 dB, then it is possible to generate measurements without systematic errors