MATLAB: Amplitude of (signal) after FFT operation

fftMATLAB

I have this code, I am suppose sin of amplitude 10 with frequency 200hz and sampling frequency 20000 hz and do FFT on this signal,
why the Amplitude after FFT is 1000?? where the amplitude must be stay 10
 Fs = 20000;
t = 0:1/Fs:0.01;
fc1=200;
 x = 10*sin(pi*fc1*t)
  x=x';
 xFFT = abs(fft(x));
 xDFT_psd = abs(fft(x).^2);

Best Answer

Mary,
In general, to return a FFT amplitude equal to the amplitude signal which you input to the FFT, you need to normalize FFTs by the number of sample points you're inputting to the FFT.
Fs = 20000;
t = 0:1/Fs:0.01;
fc1=200;
x = 10*sin(pi*fc1*t)
x=x';
 xFFT = abs(fft(x))/length(x);
 xDFT_psd = abs(fft(x).^2);
Note that doing this will divide the power between the positive and negative sides, so if you are only going to look at one side of the FFT, you can multiply the xFFT by 2, and you'll get the magnitude of 10 that you're expecting.
The fft documentation has a pretty good example that illustrates this and some other fft best practices.
http://www.mathworks.com/help/matlab/ref/fft.html
*Edited for clarity, - see Matt J's comment for the original statement.
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