Question about DFT math

[mathenthusiast]

Hello to everyone.

My question is this: When I compute the inverse DFT, I get the complex coefficients Ck. How to derive the real cos/sin coefficients Ak and Bk from them in order to construct an approximation of the original time-domain signal ? How does it happen that the imaginary unit "i" disappears ? What are the conditions and necessary steps to perform computations in such a way that the imaginary "i" doesn't spoil the computation and remains neutral ?

Thank you.

[jsolar]

When you perform an inverse DFT you actually get the Ak and Bk. Your tool may present the answer to you in amplitude and phase instead of the indiidual real and imaginary components. So if you have Ck you should also have the angle associated with each amplitude. You can convert from amplitude and phase into real and imaginary by built in routines or by doing the math yourself. i.e. Ak = Ck * cos( phase k ) and Bk = Ck * sin( phase k ) or something like that.
If the data in the IDFT domain is actually real valued only, which will be the case if the original data was real and you ignore any numerical error terms that have a non zero imaginay component then your Ak = Ck and Bk = 0; So you actually do have the answer you want!