In $(1),$ the basis used for computing the k$-$th DCT coefficient Xk$,$ k $=0,...,$ n$1,$is equal tock $=[$cos$($kn $(12)),$ cos$($kn $(1+12)),...,$ cos$($kn $($n $1+12))].$For n $=8,$ plot the n DCT basis functions. Report your observations.$($b$)$ For any n$,$ show that c$0,...,$ cn$1$ form an orthogonal basis for Rn$.($c$)$ In python, you can implement $2$D DCT and inverse DCT using the followingfunctions: