Approximate system identification using system based orthonormal functions

The problem of approximate system identification is addressed. The use of prefilters that are based on a special class of system based orthonormal functions is proposed. It is shown that every linear finite dimensional time invariant discrete time system gives rise to two sets of orthonormal functions and that both can be used as a basis of the space l₂. The derivation of these functions, to be considered as a generalization of the Laguerre polynomials, is based on the properties of discrete time all-pass functions. Transformation of the input/output signals of a linear system in terms of these functions leads to new system descriptions, and new possibilities arise for the construction of approximate identification methods, with favorable properties allowing the use of simple estimation techniques and a systematic choice of prefilters