Effects of Overlapping and Windowing on the Estimates of Frequency Response Functions of Linear Systems with Random Input Signals

The use of block overlapping and time windowing in the estimation of frequency response functions of linear systems is considered. The systems are subjected to stationary white random excitation and there is no external noise. The sources of errors for the bias and variance of the frequency response are identified to be due to the Fourier transforms of the transient terms or end effects that arise due to non-periodic signals. Using a pure time delay as an example for the system, it is shown that there is a limit to the improvement achievable in reducing the variance as the block overlap is increased.