Generalized Fourier and Toeplitz results for rational orthonormal bases

This paper provides a generalization of certain classical Fourier convergen ce and asymptotic Toeplitz matrix properties to the case where the underlyi ng orthonormal basis is not the conventional trigonometric one but rather a rational generalization which encompasses the trigonometric one as a speci al case. These generalized Fourier and Toeplitz results have particular app lication in dynamic system estimation theory. Specifically, the results all ow a unified treatment of the accuracy of least-squares system estimation u sing a range of model structures, including those that allow the inclusion of prior knowledge of system dynamics via the specification of fixed pole o r zero locations.