obtain the fourier trasnform doing the fft. Do I need to normalize??

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SYML2nd 2019-6-24

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编辑： Matt J 2019-6-25

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Hi,

I have a signal in time domain, actually, specific kinetic energy was calculated in time domain and its medium value is 10 m2/s2 (with some peak at 60 m2/s2). I wanted to obtain the Fourier transform of this signal in time domain. Then I did an FFT on the signal and converted to frequency domain; but the amplitude of this kinetic energy in frequency domain is at the magnitude order of 10e6. Why this difference? Should I normalize this FFT in some way to obtain the Fourier trasform? If I do the fft the unit lenght is m2/s2, while if I do the Fourier trasform the unit lenght should be m2/s, so I thought that my problem could be due to a normalization

This is the code (the tket.txt contain the signal, which can be read at the 34th column) can you help me?

tket1=readtable('tket.txt');
tket=table2array(tket1);
Tinc=0.001;
% Tinc is the time step
Fs=1/Tinc;
L=length(tket);
f = Fs*(0:(L/2))/L;
tkef1= fft(tket(:,34:34),L);
fl=length(f);
tkef=tkef1(1:fl,:);

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SYML2nd 2019-6-24

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Ok. Thank you very much for your detailed answer. I tried to solve the fact that is a complex quantity by doing

y=abs(tkef)

Do you think it is a proper way to do that??

dpb 2019-6-24

As Matt J says, "it all depends" on what you're actually trying to compute.

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Matt J 2019-6-24

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编辑：Matt J 2019-6-24

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To approximate a continuous Fourier transform integral, you need to multiply by the time step,

tkef1= fft(tket(:,34:34),L) * Tinc;

Depending on whether you are an engineer or a physicist, you may also need to multiply by 1/sqrt(2*pi), as different professions define the Fourier Transform scaling differently.

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SYML2nd 2019-6-25

Ok, I tried to study and this solution of multiplying by Tinc seems to me have sense.

Indeed using this method is verified the fact that, if take the frequency 0 of the fourier trasform I should obtain the integral of the time history, as stated below:

But I am still confused about the fact that here https://it.mathworks.com/help/matlab/ref/fft.html it is recommended to divide by L. Can you explain me why?