The Hambo Transform: A Signal and System Transform Induced by Generalized Orthonormal Basis Functions

Abstract

A signal and system transformation is analyzed that is induced by a recently introduced generalized orthonormal basis for H2-systems and l2-signals. This basis is very flexible and generalizes the pulse, Laguerre and Kautz bases. The corresponding system and signal transformations generalize the Fourier and z-transforms; interesting properties of the representations in the transform domain are shown. The transformations are indispensable in the asymptotic analysis of related system identification algorithms, and provide powerful results in system approximation.