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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, $H(1)=\frac{5}{4}$. The poles of $H(z)$ are $p_{k}=\frac{1}{\sqrt{2}} \text{exp}(j\frac{(2k-1)\pi}{4})$ 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.)
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