what are the differences between Fourier transform and cosine transform..... i try to find the typical answer the difference ,from where ,the size of input and output form,in time complexity,the domain ,the effect on image itself .
First, you should compare the DCT to the DFT, not the FFT. FFT is just a family of algorithms to approximate the DFT.
[...] In particular, a DCT is a Fourier-related transform similar to the discrete Fourier transform (DFT), but using only real numbers. DCTs are equivalent to DFTs of roughly twice the length, operating on real data with even symmetry (since the Fourier transform of a real and even function is real and even), where in some variants the input and/or output data are shifted by half a sample. There are eight standard DCT variants, of which four are common.