A study on stochastic system transformation using generalized orthonormal basis functions

Generalized orthonormal basis functions induce system transformation called Hambo transform, which maps continuous-time deterministic models to discrete-time deterministic models with the property that it preserves inputoutput norms. This paper shows that generalized orthonormal basis functions also induce stochastic system transformation, and studies its properties. It is shown that under suitable definitions the equivalence between continuous-time stochastic systems and transformed discrete-time stochastic systems exists. The results are of fundamental importance to continuous-time system identification.