Effects of Overlapping and Windowing on Frequency Response Function Estimates of Systems With Random Inputs

The use of block overlapping and time windowing in the estimation of the frequency response functions (FRFs) 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 nonperiodic 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.