Issues with Direct Fourier Transform in Mathematica

In summary, the conversation discusses issues with using the discrete Fourier transform in Mathematica. The speaker is trying to extract amplitude and frequency distributions from a set of complex numbers, but is having trouble with the frequency distribution. They are seeking ideas and suggestions to solve this problem.
  • #1
MaratasS
2
0
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.
 
Last edited:
Physics news on Phys.org

Related to Issues with Direct Fourier Transform in Mathematica

1. What is the Direct Fourier Transform in Mathematica?

The Direct Fourier Transform is a mathematical operation in Mathematica that calculates the Fourier transform of a given function or data set. It is used to decompose a function into its individual frequency components.

2. What are some common issues with using the Direct Fourier Transform in Mathematica?

Some common issues with using the Direct Fourier Transform in Mathematica include incorrect input data, choosing the wrong Fourier transform option, and obtaining incorrect results due to the presence of noise or non-periodic data.

3. How can I ensure accurate results when using the Direct Fourier Transform in Mathematica?

To ensure accurate results when using the Direct Fourier Transform in Mathematica, it is important to carefully select the correct Fourier transform option for your data, check for and remove any noise or non-periodic components, and verify the input data is correct.

4. Can the Direct Fourier Transform in Mathematica handle non-periodic data?

No, the Direct Fourier Transform in Mathematica is designed to work with periodic data. If your data is non-periodic, you may need to preprocess it to make it suitable for the Fourier transform, or consider using a different mathematical tool.

5. Are there any alternatives to using the Direct Fourier Transform in Mathematica?

Yes, there are several alternative methods for calculating Fourier transforms in Mathematica, such as the Discrete Fourier Transform, Fast Fourier Transform, and Inverse Fourier Transform. It is important to choose the method that best suits your data and analysis needs.

Similar threads

Mathematica Fourier Transform Help with Mathematica
    • MATLAB, Maple, Mathematica, LaTeX
Replies
2
Views
2K
MATLAB Turning Fourier coefficients into an interpolated freq domain function
    • MATLAB, Maple, Mathematica, LaTeX
Replies
8
Views
1K
I New frequency generation in AM signal
    • Classical Physics
2
Replies
47
Views
2K
MATLAB How to change the frequency values inside a time domain signal phase
    • MATLAB, Maple, Mathematica, LaTeX
Replies
1
Views
801
Fourier Transform - Solutions Error?
    • Calculus and Beyond Homework Help
Replies
5
Views
513
MATLAB MATLAB IFFT doesn't match the analytical one
    • MATLAB, Maple, Mathematica, LaTeX
Replies
10
Views
2K
Mathematica Extracting frequency from DFT set in Mathematica
    • MATLAB, Maple, Mathematica, LaTeX
Replies
1
Views
2K
I Peak of Analytical Fourier Transform
    • Calculus
Replies
4
Views
2K
Using the Fourier Transform on Partitioned Images
    • MATLAB, Maple, Mathematica, LaTeX
Replies
2
Views
2K
I Fourier transform, same frequencies, different amplitudes
    • Calculus
Replies
6
Views
2K

Hot Threads

Recent Insights

Back
Top