The FFT Algorithm Normalization

[cacsphysics]

• I have been looking at the FFT today and I decided to check the FFT of y(t) = sin(2np.pit). When I use the spectrum_wwind.py script it produces large power for the peak.
• I proceeded to recreate the FFT script, copy & paste, but I included a particular normalization, one that incorporates the windowing function, "hemming". The notes on this can be found here chapter 8-9.
• For a given time range the spectrum_wwind.py script appears to apply a specific factor to all signals. This is okay if we are comparing signals with the same time range. Now if we were to compare the noise portion, [-10, 0us], of the Bdot signals to the bdot signal within [50,150us] the spectrum_wwind script would apply different factors to the power spectrum.
• The application of windowing normalization fixes the issues. I created a plot showing the difference in power outputs from both algorithms, the function I used is y(t) = sin(2np.pit).