Given $y[n]=h_1[n]x[n]+h_2[n]x[n-1]+h_3[n]x[n-2]$ is an LTI system with unity gain at $\omega =0$ and zero gain at $\omega =\pi$. $h[n]\neq0$ .Also given that the system has a linear phase. Compute
$h_1[n]$
$h_2[n]$
$h_3[n]$
How do we approach a question like this? Any help is appreciated. I want to confirm my working for $h_1[n]$ and I found other two co-eficients as 1/4