Extracting frequency from DFT set in Mathematica

In this case, the DFT of a Gaussian pulse in time domain will have a Gaussian frequency distribution. However, extracting the frequencies from the complex numbers in the DFT can be tricky. The amplitude distribution can be easily obtained by taking the absolute value of the complex numbers, but the frequency distribution requires some additional steps.
  • #1
MaratasS
2
0
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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  • #2
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.
 

1. What is DFT and how is it used in Mathematica?

DFT stands for Discrete Fourier Transform and it is a mathematical technique used to analyze the frequency components of a signal or dataset. In Mathematica, DFT is implemented through the Fourier function, which converts a discrete list of data points into a discrete list of Fourier coefficients.

2. How do I extract frequency information from a DFT set in Mathematica?

To extract frequency information from a DFT set in Mathematica, you can use the FourierParameters option in the Fourier function. Setting the FourierParameters to {1,-1} will return the frequency values in units of cycles per sample. You can also use the FourierDST function, which returns a list of frequencies in units of radians per sample.

3. Can I plot the frequency spectrum of a DFT set in Mathematica?

Yes, you can plot the frequency spectrum of a DFT set in Mathematica using the ListLinePlot function. Simply input the list of Fourier coefficients as the data and use the PlotRange option to specify the frequency range you want to plot.

4. How do I interpret the results of a DFT in Mathematica?

The results of a DFT in Mathematica represent the frequency components present in the original signal or dataset. The amplitude of each frequency component can be seen in the magnitude of the Fourier coefficients, while the phase can be seen in the complex values of the coefficients. The frequency values can be found using the FourierParameters option, as mentioned in question 2.

5. Can I perform a DFT on a non-periodic dataset in Mathematica?

Yes, you can perform a DFT on a non-periodic dataset in Mathematica. However, since the DFT assumes a periodic signal, the results may not be accurate. It is recommended to use a window function, such as HannWindow or BlackmanWindow, to reduce the effects of non-periodicity on the DFT results.

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