Frequency domain identification with generalized orthonormal basis functions

A method is considered for the identification of linear parametric models based on a least squares identification criterion that is formulated in the frequency domain, To this end, use is made of the empirical transfer function estimate (ETFE), identified from time-domain data. As a parametric model structure use is made of a finite expansion sequence in terms of recently introduced generalized basis functions, being generalizations of the classical pulse and Laguerre and Kautz types of bases. An asymptotic analysis of the estimated models is provided and conditions for consistency are formulated. Explicit and transparent bias and variance expressions are established, the latter ones also valid in a situation of undermodeling.