Consider a discrete-time system with input x[n] and output y[n]. When the input is...

Consider a discrete-time system with input x[n] and output y[n]. When the input is

the output is

Determine which of the following statements is correct:

• The system must be LTI.

• The system could be LTI.

• The system cannot be LTI.

If your answer is that the system must or could be LTI, give a possible impulse response. If your answer is that the system could not be LTI, explain clearly why not.