State whether the system T defined as satisfies each one of

State whether the system T defined as

satisfies each one of the following properties.

Prove your answer or give a counterexample.

(a) memoryless, (b) causal, (c) linear, (d) time-invariant, (e) stable, (f) invertible.

Solution

(a) System is not memoryless as the output of the system depends on present input as well as past input.

(b) System is casual because the output of the system does not depend on future input.

(c) System is linear because all the input terms are linear (exponent is 1)

(d) System is not time invariant, as with increased n, the output of the system will consistently increase or decrease depending on the nature of input. But it won\'t be periodic in nature, therefore, not time invariant.

(e) System is not stable because the output of the system is unbounded.

(f) System is not invertible.