Suppose that the difference equation model shown below describes an LTI system:y[n] –.75y[...

Suppose that the difference equation model shown below describes an LTI system:

y[n] –.75y[n – 1] + 0.125y[n – 2] = x[n];

(a) Find the system transfer function H(z).

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(b) Find the unit-step response, y[n], of the system of (a).

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(c) Use MATLAB to plot the unit-step response of the system.

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(d) Verify the value of y[0] in Part (b), using the initial-value property. Does this agree with the plotted value from Part (c)?

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(e) Will the final-value property give the correct value of y[ ∞ ]? If your answer is yes, find the final value. Otherwise, state why the final-value property is not applicable.