A comparison of transfer function estimators

The response of a linear time-invariant process on a stochastic input signal is characterized by the transfer function. Unknown past inputs and future output are sources of inaccuracy in relating a finite segment of an output signal via an estimated transfer function to the corresponding input segment. These end effects are usually characterized with error bounds on the Fourier transform of the output signal, but the error in an estimated transfer function can be quantified more precisely in terms of bias and variance. The accuracy of three transfer function estimators is compared, showing an infinite variance for the Experimental Transfer Function Estimate (ETFE) and a better efficiency for the estimators which are based on the cross spectrum. The variance due to additive noise depends on whether the input is a stochastic or a deterministic signal