$1.(12$ points$)$ System Responses

For each of the following parts, state whether the desired image processing operation can be modeled such that the output is obtained by convolving the input with a filter. If yes, then find the filter. If no$,$ argue why.

$($a$)(6$ points$)$ Full scale contrast stretch

$($b$)(6$ points$)$ Image translation $($i$.$e$.$ if the input image is $\backslash ($ f$($m$,$ n$)\backslash ),$ then the output is given by $\backslash ($ f$($m$-$a$,$ n$-$b$)\backslash )$ where $\backslash (($a$,$ b$)\backslash )$ are given finite integer constants. You can ignore any boundary effects.$)$