Realization of input-output maps using generalized orthonormal basis functions

This paper studies the input-output equivalent transformation (or Hambo transform) of linear time-invariant systems induced by generalized orthonormal basis functions. Transformation formulae of the system matrices are derived using the fact that the lifted system associated with the inner function which defines a generalized orthonormal basis is an abstract form of the Hambo transform. The new formulae are supplements to the results in the literature, and they are equally applicable to continuous-time and discrete-time systems and MIMO and SISO systems.