Reconstruction of the Fourier transform from its parts

[jtn2009]

I am using ROOT to calculate the Fourier transform of a digital signal. I can extract the individual parts of the transform, the magnitude and phase in the form of a 1D histogram. I am attempting to reconstruct the transforms from the phase and magnitude but cannot seem to figure it out. Any help would be great. I think it is just a general question on how to reconstruct the transform from its individual parts.

 

[olivermsun]

First, can you write down what the Fourier transform means in terms of the phase and magnitude?

Given that, what have you tried so far?