On matching correlation sequences by parametric spectral models

The correlation matching property of all-pole models does not extend readily to pole-zero models. We prove that, if the number of poles in a pole-zero model is strictly less than the number of given correlations, a pole-zero model that matches the given correlations may not exist, irrespective of the number of zeroes in the model. We also show that, if we add a set of cepstral constraints, a maximum-entropy pole-zero model that matches the correlation and cepstral constraints may not exist. We conclude that pole-zero modeling based on minimizing some error criterion might be preferable to exact constraint matching.