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(1)=51. The poles of $ H(z) $ are Pk=12exp(j(2k-1)π4) 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.)