Realization of input-output maps using generalized orthogonal basis functions

This paper derives a new formula for the state-space realization for the Hambo transform corresponding to a generalized orthonormal basis. The inner function associated to the basis decides the input-output equivalent system, which is called the lifted system. Since the lifted and original systems have the same state, the derived system also share the common state. This allows one to treat multi-input multi-output systems the same way as single-input single-output systems.