Resolution bias errors in spectral density, frequency response and coherence function measurements, IV: Time delay bias errors

Abstract

The problem of time delay bias errors is treated in this part of the present series of papers as a special case of a general theory of resolution bias errors in spectral estimation presented in a previous part. It is shown that the main effect of an additional time delay between the output and the input of a physical system is to multiply the frequency response and coherence estimators which would be obtained without delay with the normalized autocorrelation function of the window function and its square respectively. Experimental results for the rectangular and Hanning windows are in accord with the theoretical predictions. The theoretical results given in the literature previously are valid for the rectangular window only but not for an arbitrary window function.