Model matching and filter design using orthonormal basis functions

Affine model parametrizations using orthonormal basis functions have been widely used in system identification and adaptive signal processing. The main advantage of using orthonormal basis functions in a (generalized) orthonormal Finite Impulse Response (FIR) filter lies in the possibility of incorporating prior knowledge of the system dynamics into the filter design and approximation process. As a result, more accurate and simplified models can be obtained with a limited number of basis functions. In this paper the linear parameter structure of a generalized FIR filter is used to formulate analytic solutions for model matching problems. Several construction methods of orthonormal basis functions are discussed and a case study using the generalized FIR filter to approximate the dynamics of an optimal feed-forward filter is presented.