The transfer function in terms of the is given by

 where is a function of the complex variable It is defined on a region of convergence (ROC) on the An analysis similar to that for the continuous-time LTI system can be applied to the discrete-time LTI system. Such an analysis shows that the response of a the linear time-invariant system with impulse response to a deterministic input is

       By taking the DTFT of both sides, we get