A comparison between transfer-function and state-space approaches to signal modeling

There exist well known algorithms for estimating either a transfer function or a state-space description corresponding to a given noise-free impulse response. When the data consists of impulse response plus noise, the algorithms have to be modified in order to give good performance. In both the transfer function and state-space approaches, the key modification involves the use of the singular value decomposition (SVD). However, there are fundamental differences in the way in which the SVD is used to improve performances in the noisy data case. IN this paper, the differences between the two approaches are studied, as well as the corresponding performance of each method.