Suppose I take a grayscale image and break it into 8x8 pixel blocks, then take the DCT of those blocks. What is the DC coefficient of the block in relation to the whole image?
To simplify I'm thinking of this in 1D. I have a row of 64 pixels and I break it into length 8 vectors. I pick one of these 8-vectors and take its DCT. The average of the 8-vector is not the DC term of the entire 64-row. Now suppose I took the DCT of the entire 64-row. What coefficient in the 64-pixel-DCT would the DC term of the 8-pixel-DCT be projected onto?
EDIT: Thank you for the replies so far. The context of this question is I'm trying to assign a cyles/pixel value to the DC coefficient of the 8-pixel sub-block, but in the context of the whole 64-block. Its clear to me now that the DC coefficient of the 64-block is the average of the DC coefficients of each of the 8-blocks. But while the 8-block is a sample of the 64-block it doesn't make sense to me to say that the 8-block DC coefficient is actually 0 cycles/pixel. For example, one could represent nonzero frequencies using only these 8-block DC coefficients.