Over-Determined Estimation of Pulse Transfer Function Model by Least-Squares Method

Abstract Asymptotic properties oi least-squares estimators of over-determined pulse transfer function models are discussed. The locations of poles and zeros of the models can be obtained by the explicit form of biases of least-squares estimators. The relation between the biases of the numerator and denominator of over-determined model is also provided. Using these results, it is proved that the over-determined model closes to the true when the order of models is enough high or the noise level is very low because the extra poles and zeros cancel each other out.