Making a Fourier Transformation by hand for Infrared Spectroscopy

Hello

I want to make a Fourier Transformation by Hand for Infrared Spectroscopy. I decided to use the method of real DTF because it is a good starting point. My Problem:

How I understand it so far:

To record FT-IR spectra a time dependent signal is recorded. I ignore the time at all, and take the magnitudes. In that way I have a 1 x N Matrix, which is my "Time Domain"

Now I make real DFT with it and obtain two 1 x (N/2+1) matrices the Real and the Imaginary.

My Problem is: real DFT is over now, but I haven't got a new spectrum now, with the time Domain converted to frequency Domain.

My Idea is to convert the rectangular notation into polar notation. This will make two 1 x (N/2+1) matrices Magnitude and Phase. After that I want to draw the Magnitude in function of the Wave number (which is calculated from the Phase)

My question: Is this the right way? Is it possible to calculate the wave number out of the phase without knowing the place, time and Angular frequency? What I have to do with my two spectrums to obtain an IR-Spectrum?