Behavior of discrete-time linear systems of infinite order

In this paper the behavior of BIBO-stable (bounded input-bounded output) discrete-time LTI-systems (linear and time-invariant) is investigated. It is shown that for a certain class of LTI-systems the input output map is not given by the convolution sum. We use Sandberg's representation theorem for a complete characterization of all BIBO-stable LTI-systems of convolution type.