Question of the Day 20-11-2018

Question of the Day
GATE 2017   EE   Question No. 51

Consider a causal and stable LTI system with rational transfer function \$ H(z) \$, whose corresponding impulse response begins at \$ n=0.\$ Furthermore, $H\left(1\right)=\frac{5}{1}$. The poles of \$ H(z) \$ are ${P}_{k}=\frac{1}{\sqrt{2}}exp\left(j\frac{\left(2k-1\right)\mathrm{\pi }}{4}\right)$ for \$ k=1,2,3,4. \$ The zeros of \$ H(z) \$ are all at \$ z=0. \$ Let \$ g(n)=j^n=h\lbrack n\rbrack. \$ The value of \$ g\lbrack8\rbrack \$ equals ___________. (Give the answer up to three decimal places.)

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