Design of functional observer in transfer function form

In this paper an observer for a discrete-time linear system is designed in the form of transfer function. The exact reconstruction of the state from the input output data over the past finite period, called the reconstructor, is designed in the input and output relation and shown to be same as the finite settling observer if the measurement time is long enough. It is shown that the linear functional observer can be designed in the form of transfer function similar to the reconstructor design