GATE Electronics and Communications (EC) 2019 Solved Paper

Let $\mathit{h}\left[\mathit{n}\right]$ be a length-7 discrete-time finite impulse response filter, given by and $\mathit{h}\left[\mathit{n}\right]$ is zero for $\left[\mathit{n}\right]\ge 4$. A length-3 finite impulse response approximation $\mathit{g}\left[\mathit{n}\right]$ of $\mathit{h}\left[\mathit{n}\right]$ has to be obtained such that
$\mathit{E}\left(\mathit{h},\mathit{g}\right)=\underset{-\mathit{\pi }}{\overset{\mathit{\pi }}{\int }}{\left|\mathit{H}\left({\mathit{e}}^{\mathit{j}\mathit{\omega }}\right)-\mathit{G}\left({\mathit{e}}^{\mathit{j}\mathit{m}}\right)\right|}^2\mathit{d}\mathit{\omega }$
is minimized, where $\mathit{H}\left({\mathit{e}}^{\mathit{j}\mathit{\omega }}\right)$ and $\left({\mathit{e}}^{\mathit{j}\mathit{\omega }}\right)$ are the discrete-time Fourier transforms of $\mathit{h}\left[\mathit{n}\right]$ and $\mathit{g}\left[\mathit{n}\right]$, respectively. For the filter that minimizes $\mathit{E}\left(\mathit{h},\mathit{g}\right)$, the value of $10\mathit{g}\left[-1\right]+\mathit{g}\left[1\right]$, rounded off to 2 decimal places, is ___________.