Consider the following difference equation and excitation:y[n] – 0.75y[n – 1] + 0.125y[n –...

Consider the following difference equation and excitation:

y[n] – 0.75y[n – 1] + 0.125y[n – 2] = x[n];

(a) Find y[n], using the z-transform.

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(b) Check the partial-fraction expansions in Part (a) using MATLAB.

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(c) Verify the results of Part (a) for n = 0, 1, 2, 3, and 4, by solving the difference equation by iteration.

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(d) Use MATLAB to check the results in Part (c).

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(e) Verify the value of y[0] in Part (a), using the initial-value property.

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(f) 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.