On the concept of ‘excitation order’ in Laguerre domain identification

In this paper the expansion of discrete time signals in the Laguerre functions is studied in comparison to the expansion in the pulse functions. The order of excitation of the expansion coefficients is investigated and related to the excitation order of the time domain signals. A general definition of the concept of excitation order is presented that provides a convenient tool for determining the excitation properties of, e.g., finite data sets. Examples are included to illustrate the prospects of this new definition. Furthermore, bounds on parameters associated with the regression matrix are given for either basis.