The normal form derived by Mansour [I] for single-input / single-output, time-invariant, linear discrete systems will be extended to the multivariable case. An algorithm will be used to achieve simple computation of this form starting with the Luenberger first canonical form. The construction of this form will be illustrated by examples applied to model reduction of multivariable discrete-time ...

However, these powers are often hard to calculate in a nice closed form. For this reason we shall consider their Fourier transforms in some suitable context. The idea being that intricate computation of products in the group algebra are replaced by simple point wise products. More precisely, we shall derive new extended versions of a formula of Garsia (see (1) below) and of similar formulas obt...