Mathematica Extracting frequency from DFT set in Mathematica

AI Thread Summary
The discussion centers on the challenges of extracting frequency distribution from a sampled Gaussian pulse after applying the discrete Fourier transform (DFT). While the amplitude distribution is easily obtained by calculating the absolute values of the complex numbers resulting from the DFT, the extraction of frequency distribution poses difficulties. The phase information from the Fourier set is not yielding the expected Gaussian frequency distribution. It is emphasized that the DFT inherently represents the frequency distribution of the data set, suggesting that the issue may lie in the interpretation or application of the phase data. Further insights or methods to resolve this extraction problem are sought from the community.
MaratasS
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Maybe someone else had this problem.
Lets say we have a sampled Gaussian pulse in time domain and transform it into frequency domain. For that I use the discrete Fourier transform. Now the resulting set of transformed values is made up of complex numbers. I want to extract two things from that set: Amplitude distribution and frequency distribution.
The first one is straight forward - I just take the absolute value of the complex numbers an the resulting set of values has a Gaussian shape.
However I have problems getting the frequencies. I don't know how to extract them by having the phase of the Fourier set. And no matter what I do I can't get the Gaussian frequency distribution.
All ideas will be greatly appreciated.
 
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The DFT is the frequencies. The distribution of the DFT of a set of data is the distribution of the frequencies of that set of data, by defintion.
 

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