On bias in transfer functions estimated with stochastic excitation

In stationary stochastic processes, the input signal will already be present before the measurement interval starts and the response will continue after that interval. The unknown past inputs and the end effects cause inaccuracies in estimating a transfer function from the simultaneous frames of the input and output signals. The effect of the transient remainder terms is usually characterized with error bounds on the Fourier transform of the output signal. This paper presents a bias and a variance expression to describe the uncertainty in an estimated transfer function. The theoretical expressions are applied to different algorithms for transfer function estimation and their accuracy has been established in simulation experiments