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 input-output 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.