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You are hired by a signal processing firm and you are

Question: You are hired by a signal processing firm and you are hoping to impress them with the skills that you have acquired in this course. The firm asks you to design an LTID system that has the property that if the input is given by

x[k] = (1/3)^ku[k] - (1/4)^{k -1}u[k]

yje output is given by

y[k] = (1/4)^ku[k]

(i) Determine the z-transfer function of the LTID system.

(ii) Determine the impulse response of the LTID system.

(iii) Determine the difference-equation representation of the LTID system.

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