A $44$ gray$-$scale original image passes through three spatial linear shift$-$invariant filters,

resulting in three filtered images

$($a$)$ Compute Filtered Image $1($Use zero$-$padding of the original image$).$

$($b$)$ Compute Filtered Image $3($Use zero$-$padding of the original image$).$

$($c$)$ Based on relationship between Filtered Image $1,$ Filtered Image $2,$ and Filtered Image $3,$

determine the filter coefficients in Shift$-$Invariant Linear Filter $2.$