Approximation and realization using generalized orthonormal bases

This paper considers the approximation of linear systems by means of orthonormal basis functions, which are generated by stable all-pass functions. These basis functions induce the so called Hambo transform, which transforms scalar systems into square systems of i/o dimension equal to the order of the all-pass function considered. We will consider the construction of the Markov parameters of the system representation in the transform domain and show how these can be used to realize minimal state space representations for the exact and partial knowledge case. Additionally a projection mechanism is presented to allow inverse transformation of any sequence of Markov parameters in the transform domain. This mechanism is illustrated with an example.