Question: A second-order system is represented by the difference equation y[n] = 0.25y[n 2] + x[n] where x[n] is the input and y[n] the output.

A second-order system is represented by the difference equation y[n] = 0.25y[n − 2] + x[n] where x[n] is the input and y[n] the output.

(a) For the zero-input case, i.e., when x[n] = 0, find the initial conditions y[ − 1] and y[ − 2] so that y[n] = 0.5ⁿ u[n].

(b) Suppose the input is x[n] = u[n], without solving the difference equation can you find the corresponding steady state y_ss[n]? Explain how and give the steady-state output.

(d) If x[n] = δ[n] + 0.5δ[n − 1] is the input to the above difference equation, find the impulse response h[n]of the system.

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a If we let the input be zero the ztransfom of yn is Yz 025z 2 Yz 025y 1z 1 025y 2 where y 1 and y 2 ... View full answer

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