Hi Wahab,

if you just have the amplitude but no phase information it won't be possible to recover the original time signal.

Otherwise, i.e. if you have the phase information, you can recover the time signal as it was passed to the FFT (if you just pass a single Gaussian which is an excerpt of a longer signal, than you just recover the single gaussian; if you pass the gaussian together with the remaining signal, than you can recover the Gaussian's original possition in that signal).

Greetings, Sebastian

Thanks Sebastian, Do you have a reference where this type of exercise, where the time scale is generated from the phase information and amplitude is shown? The easiest way, of course, is to plot the ifft wrt the original time, but I was just curious, for a case when the original time information is not given. For example here in this link

http://www.gaussianwaves.com/2015/11/interpreting-fft-results-obtaining-magnitude-and-phase-information/

the time scale t is extracted from the frequency axis as follows:

x_recon = N*ifft(ifftshift(X),N); %reconstructed signal

t = [0:1:length(x_recon)-1]/Fs, where Fs is the sampling frequency and N is the total number of points; this is just the opposite step of what we do to construct the frequency axis.

As Sebastian noted, you would need the phase information in order to reconstruct the signal.

If you want to learn more about implementing the Fourier transform in MATLAB and Python, then you might consider this online course: https://www.udemy.com/fourier-transform-mxc/

Mike