Decomposing an image into two frequency components using DCT?

Question

I am a beginner in digital image processing field, recently I am working on a project where I have to decompose an image into two frequency components namely (low and high) usin

Answer 1

An easy example:

I2 = dct_img;
I2(8:end,8:end) = 0;
I3 = idct2(I2);
imagesc(I3)

I3 can be seen as the image after low pass filter (the low frequency components), then idct2(dct_img - I2) can be viewed as high frequency.