3. Let a = 2e-1fit and 3 = e-12f2t where f = 0.1 and f2 =...

 

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3. Let a = 2e-1²fit and 3 = e-12f2t where f₁ = 0.1 and f2 = 0.3. Consider the transfer function 1 H (₂) = z−² − (a + B)z-¹ + aß. 2 - (a) (5 points) What are the poles and zeros of this transfer function H? (b) (5 points) What is the impulse response of this system? Make sure it is clear what part of the impulse response corresponds to time zero. (You may write your answer in terms of a and 3 if convenient.) (c) (5 points) Is this system causal? Justify your answer; no marks without justification. (d) (5 points) Is this system BIBO stable? Justify your answer carefully; no marks without justification. (BIBO = bounded-input bounded-output) 3. Let a = 2e-1²fit and 3 = e-12f2t where f₁ = 0.1 and f2 = 0.3. Consider the transfer function 1 H (₂) = z−² − (a + B)z-¹ + aß. 2 - (a) (5 points) What are the poles and zeros of this transfer function H? (b) (5 points) What is the impulse response of this system? Make sure it is clear what part of the impulse response corresponds to time zero. (You may write your answer in terms of a and 3 if convenient.) (c) (5 points) Is this system causal? Justify your answer; no marks without justification. (d) (5 points) Is this system BIBO stable? Justify your answer carefully; no marks without justification. (BIBO = bounded-input bounded-output)