Issues with Direct Fourier Transform in Mathematica

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SUMMARY

The discussion focuses on issues encountered when using the Discrete Fourier Transform (DFT) in Mathematica to analyze a sampled Gaussian pulse. The user successfully extracts the amplitude distribution by calculating the absolute values of the complex numbers resulting from the DFT, which yields a Gaussian shape. However, they face challenges in obtaining the frequency distribution from the phase information of the Fourier-transformed data. The user seeks solutions to accurately derive the Gaussian frequency distribution from the phase data.

PREREQUISITES
  • Understanding of Discrete Fourier Transform (DFT)
  • Familiarity with complex numbers and their properties
  • Knowledge of Mathematica software and its functions
  • Basic principles of signal processing, particularly Gaussian pulses
NEXT STEPS
  • Research methods to extract frequency information from phase data in Fourier transforms
  • Explore Mathematica's built-in functions for frequency analysis
  • Learn about the Fast Fourier Transform (FFT) and its applications in signal processing
  • Investigate techniques for visualizing frequency distributions from DFT results
USEFUL FOR

This discussion is beneficial for signal processing engineers, Mathematica users, and researchers analyzing frequency distributions of signals, particularly those dealing with Gaussian pulses and Fourier analysis.

MaratasS
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Issues with Discrete Fourier Transform in Mathematica

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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