Commutativity of first-order discrete-time linear time-varying systems

Abstract

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.