The Accuracy of Transfer Function Estimation with Stationary Stochastic Excitation

Abstract

Errors of missing initial conditions are sources of inaccuracy in relating a finite segment of an output signal via an estimated transfer function to the corresponding part of ‘ an uninterrupted stationary stochastic input signal. The effect of the transient remainder terms is usually characterized with error bounds on the fourier transform of the output signal. This note shows that the uncertainty in an estimated transfer function can be quantified more precisely in terms of bias and variance. The accuracy of three estimators is compared. The variance of the Experimental Transfer Function Estimate is shown to be infinite for stationary stochastic input signals.