How to find the Fourier transfer function of a Laplacian operation?
The answer is trivial:

$$H(x,y)=4\delta(x,y)-\delta(x+1,y)-\delta(x-1,y)-\delta(x,y+1)-\delta(x,y-1)$$

Or in a coefficient representation:

$$H_{xy}=\begin{bmatrix}
0 &amp; -1 &amp; 0\\ 
-1 &amp; 4 &amp; -1\\ 
0 &amp; -1 &amp; 0
\end{bmatrix}$$

This is a representation of the 2D derivative operator, which is known to have a "high filtering" shape both in $x$ and $y$ axis