Extracting frequency from DFT set in Mathematica

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SUMMARY

The discussion focuses on extracting amplitude and frequency distributions from a discrete Fourier transform (DFT) of a sampled Gaussian pulse using Mathematica. The amplitude distribution is easily obtained by calculating the absolute values of the complex numbers resulting from the DFT, which yields a Gaussian shape. However, the challenge lies in extracting the frequency distribution from the phase of the Fourier set. The participants emphasize that the DFT inherently represents the frequency distribution of the data set.

PREREQUISITES
  • Understanding of discrete Fourier transform (DFT)
  • Familiarity with complex numbers and their properties
  • Knowledge of amplitude and phase in signal processing
  • Experience with Mathematica for data analysis
NEXT STEPS
  • Research methods for extracting frequency information from the phase of a DFT
  • Learn about the Fast Fourier Transform (FFT) implementation in Mathematica
  • Explore techniques for visualizing amplitude and frequency distributions
  • Investigate the relationship between time-domain signals and their frequency-domain representations
USEFUL FOR

Signal processing engineers, data analysts, and researchers working with Fourier transforms and frequency analysis in Mathematica.

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 definition.
 

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