Measurement of frequency response functions in the presence of correlated input/output errors

The frequency response function (FRF) of a system is often measured by taking the ratio of the output to the input Fourier coefficients of the steady state response of the system to a periodic excitation. Generator noise, common disturbances picked up by the acquisition channels of the measurement device, and an external feedback loop, cause a correlation between the input/output errors of such an FRF measurement. This paper quantifies the bias error and the variance of the FRF measurement due to correlated input/output errors.