Hello,
I have some small periodic data (about 32 points), and I want to fit it in a Fourier transform function.
Actually I use the fast Fourier transform method using the python toolbox (numpy.fft.fft). At first I calculate all Fourier complex coefficients (32 coefficients), however I get a noisy function as shown in the attached figure.
My question, is what is the best method to smooth the results?
Should I reduce the number of points by interpolating other points (e.g. 16 or 8 points) based the 32 points?
Should I apply some filters, like low-pass filter? if yes how can I choose the frequencies threshold to apply this filter?
Should I apply an filter based on the power of the complex Fourier coefficients (power = ||Ci||^2), and keep only frequencies which correspond to high powers? if yes how can I choose the power threshold?
Or are there other methods?
Thanks in advance.
dear Qussama Braydi
You can use some filters like Savitzky-Golay filter on your data before applying Fourier transform to smooth them and then use Fourier transform to find the frequencies of the discrete signal. You can also test interpolation functions like Spline functions instead of Fourier transform to interpolate your data.
Good luck
Dear Oussama Braydi
These links might be an asset, have a look:
1. https://towardsdatascience.com/fast-fourier-transform-937926e591cb
2. https://www.dataq.com/data-acquisition/general-education-tutorials/fft-fast-fourier-transform-waveform-analysis.html
3. https://pubag.nal.usda.gov/download/54750/PDF
4. https://www.sciencedirect.com/topics/computer-science/fast-fourier-transform
5. https://www.nti-audio.com/en/support/know-how/fast-fourier-transform-fft
6. https://www.researchgate.net/post/What-is-Matlab-code-to-smooth-fourier-amplitude-spectrum
Kind Regards
Qamar Ul Islam
If it is possible for you increase the number of points of FFT and adjust your sampling frequency accordingly.
Do You know the repetition period of your sequence? Your sequence looks like interference between the sampling rate and the higher signal repetition rate (Fsignal>=Fsampling/2).
Vladimir Kubov, thanks for your answer, the theoretical repetition period is 2*pi.
Noting that these samples are not the original ones to be treated, there are an example of my original data.
Irfan Majid, Thanks for your answer, indeed adding points,can help to detect the significant frequencies, however I can not increase the number of points.
Qamar Ul Islam, Thanks for your answer, I will see the suggested works.
Saleh Mafi, J. Rafiee
, Thanks for your answers, I will test the suggested methods.
In the midst of the pandemic, a google hit directed me to a free software site, with some consultation on "scientific modeling" from the Math Dept. of a southern Ca school, I think CalTech. FFT's were covered, although I was trying to make sense of acronym I had read in a Lancet article in an Israeli study about the disease.
These things are hard to describe. Primary author Israeli MD, funding Israeli hospital, hundreds of coauthors, worldwide. Title later.
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