  After introducing the concept of commutativity for continuous-time linear
time-varying systems, the related literature and the results obtained so far
are presented. For a simple introduction of the commutativity of discrete-time
linear time-varying systems, the problem is formulated for first-order systems.
Finally, explicit necessary and sufficient conditions for the commutativity of
first-order discrete-time linear time-varying systems are derived, and their
advantageous use in digital system design is illustrated; which are the main
objectives of the paper. The results are verified by examples which include an
application in amplitude modulation for digital telecommunication.
