Consider the discrete system resulting from the association of the systems 1, 2 and 3 indicated in the following figure:

(0.5 points) Write the input-output relationship of the system .

(1.5 points) Study the properties of temporal invariance, causality and stability of the system using the definition of each property and the input-output relationship obtained in part a) (that is, do not use the expression of [] to study the properties of the system).

(0.5 points) Calculate 1[], 2[], 3[] (the responses of each subsystem) and [n],the response to the impulse of the global system.

TS1{x[n]}=x[n+3] TS2{x[n]}=x[n4] TS3{x[n]}=k=nx[k]