Order assumption and singularity of information matrix for pulse transfer function models

In this correspondence we discuss the relation between singularity of information matrix and assumed order of pulse transfer function for estimating the parameters of transfer function under Gaussian excitation. By considering simple examples, it is shown that over assuming the order does not always lead to singularity, and that the matrix can in some cases become singular with the order assumed being correct. A generalization of the result is conjectured.