Discrete cosine transform of a chess board

consider a chess board ..that is an 8x8 matrix with alternate white & black boxes(pixels).
what would be the output matrix if we take discrete cosine transform.
how many non zero values will be there in that resultant matrix.

Re: interesting on DCT..

You can do it in MatLab by yourself. Try it.

I would like only give one comment. The best compression for this image will be given by Walsh-Hadamard transform. (Or similar ones)

Re: interesting on DCT..

HI,
I can try to give some insights. Since this is the maximum variation that can occur it would have peaks at x[0][8] and x[8][0] (if x is the DCT matrix).
Further if the value of white and black are some thing like (+1 and -1) then the DC would be zero. (x[0][0] = 0).
Regarding the other coefficients they would have a sinc variation with the peak at x[0][8] and x[8][0]. This is just a guess using the basis corelation (DCT) with the input signal.
But usually people say that this give the maximum number of coefficient ( all 64 coefficients) and it not good for compression. And it is a usual assumption that natural images would not have such a characteristics and would always have a gradual variation and that is the reason DCT works good.

Regards,
KJN