Parametrization of filters on the basis of orthonormal basis functions have been widely used in system identification and adaptive signal processing. The main advantage of using orthonormal basis functions for a filter parametrization lies in the possibility of incorporating prior knowledge of the system dynamics into the identification process and adaptive signal process. As a result, a more accurate and simplified filter with less parameters can be obtained. In this paper, several construction methods of orthonormal basis function are discussed and analyzed. An application of active noise control based on these orthonormal basis constructions is presented.