Consider the digital filter shown in Figure.(a) Derive the z-transform of the unit-step re...

Consider the digital filter shown in Figure.

(a) Derive the z-transform of the unit-step response, Y(z).

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(b) Find the steady-state output in response to a unit-step input.

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(c) Find the time-domain unit-step response, y[n].

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(d) Use the result of Part (c) to verify your result from Part (b).

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(e) Use MATLAB to calculate and plot the unit step response of the system.