$1.$ Given that an image is $1280$ x $768,$ calculate the size of its image printout using $200$ ppi resolution.

$2.$ For a one dimensional image of $8$ pixels, having the gray color values $[0,128,200,255,240,180,50,0],$ using the Discrete Cosine Transform DCT equation,

a$.$ Compute and plot the basis functions or frequency components $1,3$ & $7$

b$.$ Calculate the coefficients $($weights$)$ F$($u$)$ of the pixels' frequency components $1,3$ & $7.$

c$.$ 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$)$

d$.$ 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. $($suggest C$++$ language$)$

$3.$ Given that a color pixel's RGB hex value is $($AB$,$CD$,$EF$)$hex$,$ compute its gray scale value. $($convert the hex to decimal first$)$

$4.$ Compute the YIQ color model's Y$,$ I, Q color components' values for the same color pixel in Q$4$ above.

$5.$ Insert a pixel with RGB hex values of AB CD EF into an Octree. Draw the Octree.

$6.$ Huffman Encoding

Color Frequency

a $5$

b $11$

c $2$

d $2$

e $1$

f $3$

g $9$

h $4$

i $2$

j $1$

k $1$

l $6$