A $55$ input image $f[m,n]$ is given below.

a$.$ Find the discrete$-$space Fourier transform of $f[m,n].$

b$.$ The image $f[m,n]$ is applied to an LSI system whose transfer function $H(e^{j{}_m},e^{j{}_n})=$

$2cos{}_m+2cos{}_n.$ Find the output image such that

$g[m,n]=F^{-1}\{F(e^{j{}_m},e^{j{}_n})H(e^{j{}_m},e^{j{}_n})\}$

Note: For this problem, the use of computers is not allowed.