$2.$Discrete Cosine Transform$($test images: fig$1.$jpg$)$

$($a$)$ Perform the DCT on whole image and each $\backslash (8*8\backslash )$ block of the image respectively.

$($b$)$ Change the number of preserved harmonics$($variable f$),$ make the value the AC components to zero and assign a part of DC components to zero.

$($c$)$ Apply Inverse$-$DCT to restore the image. Observe how well an image can be approximated with different number of DCT coefficients.

$($d$)$ Think about the difference when applying DCT over the whole image and the image in $\backslash (8*8\backslash )$ block.

Please Note:

$(1)$ All the intrinsic functions of MATLAB or OpenCV $($e$.$g$.$ histeq in MATLAB$)$ are not allowed to be used during implementation. Those functions can be only used for result comparison.

$(2)$ The experiment results should contain: the original image and the image after compression, runnable code and description. Your answer about why do not we simply apply DCT to the entire image instead?