Question: Consider a discrete-time LTI system represented by the difference equation with the given initial condition y[n] + 0.5y[n 1] = 2(x[n] x[n

Consider a discrete-time LTI system represented by the difference equation with the given initial condition

y[n] + 0.5y[n − 1] = 2(x[n] − x[n − 1]) n ≥ 0, y[ − 1] = 2

where x[n] is the input and y[n] the output.

Suppose the input of the system is x[n] = (1 + 0.5ⁿ cos(πn)) u[n]. Determine the steady-state response y_ss[n]. If the initial condition is changed, would you get the same steady-state response? Explain.

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