Consider an LTI system whose system function is the product of five terms(a) Write the dif...

Consider an LTI system whose system function is the product of five terms

(a) Write the difference equation that gives the relation between the input x[n] and the output y[n].

Hint: Multiply out the factors of H(z).

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(b) Plot the poles and zeros of H(z) in the complex z-plane.

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(c) If the input is of the form , for what values of  will y[n] = 0?