Question: Consider a discrete-time system with input x[n] and output y[n]. When the input is x[n] = (1/4) n u[n], the output is y[n] = (1/2)

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

x[n] = (1/4)ⁿ u[n],

the output is

y[n] = (1/2)ⁿ for all n.

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.

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