$(3)$ Frequency$-$domain filtering: Filter an image in the frequency domain using a frequency$-$selective operation

$H$ defined as follows:

$H(u,v$;$D_0)=\{\begin{array}{ccc}1,& D(u,& v)D_0\\ 0,& D(u,& v)>D_0\end{array}$

where $D_0$ is a positive constant referred to as the cut$-$off frequency and $D(u,v)$ is the distance between a point

$(u,v)$ in the frequency domain and the coordinates of the center $(\frac{P}{2},\frac{Q}{2})$ defined as follows:

$D(u,v)=\sqrt[\phantom{2}]{(u-\frac{P}{2}{)}^2+(v-\frac{Q}{2}{)}^2}$

where $P$ and $Q$ are the number of rows and columns in the image, respectively. Assume even number of rows

and columns. What artefacts do you observe in the image obtained by computing the inverse DFT of the filtered

image?

Note: The filter given above is centered in the frequency domain. To use such a centered filter, you will either

need to shift the origin of the filter to $(0,0)($by using fftshift in MATLAB or the corresponding function

in Python$)$ or center the $2-$D DFT of the image.