$2.$ For a one dimensional image of $8$ pixels, having the gray color values $[0,128,200,255,240,180,50,0],$ Write a small program, using the programming language of your choice, to compute the coefficients $($weights$)$ F$($u$)$ for all of the pixels' frequency components $($for u $=07).$ Show the commented program source code and results. $($suggest C$++$ language$)$

Write a small program using the programming language of your choice to compute the pixel color values f$($r$),$ given the values generated in part c above.