A comparison of transfer function estimators

The response of a linear time invariant process on a stochastic input signal is characterized by the impulse response function or by the transfer function. Unknown past inputs and future outputs are sources of inaccuracy in relating a finite segment of an output signal via an estimated transfer function to the corresponding input segment. The end effects are usually characterized with error bounds on the Fourier transform of the output signal. This notes shows that the inaccuracy 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. It is also shown that the variance due to additive noise depends on whether the input is a stochastic or a deterministic signal