Let $h[n]$ be a length – $7$ discrete-time finite impulse response filter, given by
$$h[0]=4, \quad h[1]=3,\quad h[2]=2,\quad h[3]=1,$$
$$\quad h[-1]=-3, \quad h[-2]=-2, \quad h[-3]=-1,$$
and $h[n]$ is zero for $|n|\geq4.$ A length – $3$ finite impulse response approximation $g[n]$ of $h[n]$ has to be obtained such that
$$E(h,g)=\int_{-\pi}^{\pi} \mid H(e^{j\omega})-G(e^{j\omega}) \mid^{2}d\omega$$
in minimized where $H(e^{j\omega})$ and $G(e^{j\omega})$ are the discrete-time Fourier transforms of $h[n]$ and $g[n],$ respectively. For the filter that minimizes $E(h,g),$ the value of $10g[-1]+g[1],$ rounded off to $2$ decimal places, is __________.
