In this problem, you will analyze and implement a simple low pass filter given by the $9\backslash$times $9$

point spread function

h$($m$,$ n$)=($

$1/81$ for $|$m$|<=4$ and $|$n$|<=4$

$0$ otherwise $.$

$1.$ Calculate an analytical expression for H$($e

j$,$ ej

u $),$ the DSFT of h$($m$,$ n$),$ and use

Python$$s matplotlib to plot the magnitude of the frequency response $|$H$($e

j$,$ ej

u $)|.$

Make sure to label the axes properly and plot on over the region $[\backslash$pi $,\backslash$pi $]\backslash$times $[\backslash$pi $,\backslash$pi $].$

$2.$ Download the bundle C$-$code.zip containing the C source code for reading and writing

tagged image file format $($TIFF$)$ images. Compile the application Example using an

ANSI C compiler.

$3.$ Run the program Example on the image img$03.$tif by using the command

Example img$03.$tif

This will produce the gray scale image green.tif, which is derived from the green component of img$03.$tif.