Consider a causal and stable LTI system with rational transfer function H(z), whose corresponding impulse response begins at n = 0. Furthermore, H (1) = \frac{5}{4}. The poles of H(z) are p_{k} = {1}/{\sqrt{2}}\exp ⁡ (j\frac{ (2k−1) }{4}\pi ) for k = 1, 2, 3, 4. The zeros of H(z) are all at z = 0. Let g[n] = j n h[n]. The value of g[8] equals __________. (Give the answer up to three decimal places.)

GATE Electrical Engineering (EE) 2017 Shift 1 Solved Paper

Question : 61 of 65

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Consider a causal and stable LTI system with rational transfer function H(z), whose corresponding impulse response begins at n = 0. Furthermore,

H (1) = \;{5}/{4}

. The poles of H(z) are

p_{k} = \;{1}/{{√{2}}}\exp ⁡ (j\;{\;(2k−1)\;}/{4}π )

for k = 1, 2, 3, 4. The zeros of H(z) are all at z = 0. Let g[n] = jⁿh[n]. The value of g[8] equals __________. (Give the answer up to three decimal places.)

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