How do I normalize the fft output for a signal?

Question

Tom 2011-2-1

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https://ww2.mathworks.cn/matlabcentral/answers/661-how-do-i-normalize-the-fft-output-for-a-signal

I've got data taken at 1000hz (1millisecond per sample), and am trying to convert it into the frequency domain. My code is so far

resolution = size(footfall,2);
tempfftvar = abs(fft2(detrend(footfall(:)'),1,2^nextpow2(size(footfall,2))));
fftvar = tempfftvar(1:(size(tempfftvar,2)/2))/resolution;

where footfall is my data. This gives my a graph that looks right, but the frequency scale is incorrect. I read somewhere that MATLAB FFT function doesn't normalise automatically, so above I tried to divide by N, num of samples. This still does not give me the scale I want.

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Vieniava 2011-2-1

Why do you use 2D FFT? Do you have image for processing?

Resolution is derived in a wrong way.

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Answer 1

Vieniava 2011-2-1

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https://ww2.mathworks.cn/matlabcentral/answers/661-how-do-i-normalize-the-fft-output-for-a-signal#answer_980

在 MATLAB Online 中打开

Try this:

   Fs=1000;            % Hz
   NFFT=2^nextpow2(size(footfall,2));
   resolution=Fs/NFFT; % Hz/bin
   faxe=(1:(NFFT/2) - 1)*resolution;  % half of spectrum. DC component is taken into account via "-1"