Hello,

How exactly is constructed the cosine transform from the fft?
I tried to make the development with the symetry in the way:

abcd dcba

but I don't get the cosine formula.

Thank you.

fft_programmer,
This is all explained in Section 12.3 of the Numerical Recipes books. Look at the routines cosft1 and cosft2, and be sure to read the explanations before each routine. Both routines call realft1 (real FFT routine), which in turn calls four1 (the FFT routine).
Cheers,
Bill P.