In this paper, model sets for continuous--time linear time invariant systems that are spanned by fixed pole orthonormal bases are investigated. These bases generalise the well known Laguerre and two--parameter Kautz cases. It is shown that the obtained model sets are norm dense in the Hardy space $H_1(Pi)$ under the same condition as previously derived by the authors for the norm denseness in the ($Pi$ is the open right half plane) Hardy spaces $H_p(Pi)$, $1 < p <infty$. As a further extension, the paper shows how orthonormal model sets, that are norm dense in $H_p(Pi)$, $1<p<infty$ and which have a prescribed asymptotic order may be constructed. Finally, it is established that the Fourier series formed by orthonormal basis functions converge in all spaces $H_p(Pi)$, $1<p<infty$. The results in this paper have application in system identification, model reduction and control system synthesis.