A linear time-invariant system is characterized by the system function 3 42-1 H(2) = 1-...

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A linear time-invariant system is characterized by the system function 3 – 42-1 H(2) = 1- 3.5z-1 +1.5z-2 (a) What are the zeros and poles of H(2)? Give a pole-zero plot. Ak (b) Find the partial fraction decomposition of H(2), i.e., rewrite H(2) as H(2) = Ek (c) Specify the ROC of H(z) and determine h; [n] (i = 1, 2) in the following two cases: (i) hi [n]: the system is stable (ii) h2 [n]: the system is anticausal (d) For which of the sequences above can you compute the DTFT? Justify. Hint: Do not compute DTFT, just state whether DTFT exists or not. A linear time-invariant system is characterized by the system function 3 – 42-1 H(2) = 1- 3.5z-1 +1.5z-2 (a) What are the zeros and poles of H(2)? Give a pole-zero plot. Ak (b) Find the partial fraction decomposition of H(2), i.e., rewrite H(2) as H(2) = Ek (c) Specify the ROC of H(z) and determine h; [n] (i = 1, 2) in the following two cases: (i) hi [n]: the system is stable (ii) h2 [n]: the system is anticausal (d) For which of the sequences above can you compute the DTFT? Justify. Hint: Do not compute DTFT, just state whether DTFT exists or not.