Amplitude of FFT is not correct

Vollmers asked: 2021-09-29 fft , amplitude , scaling , windowing

Learn why your FFT amplitude might be incorrect in MATLAB and discover the scaling factors needed for accurate spectral analysis. Get the right amplitude now!

Expert Answer

John Michell answered . 2025-07-30 15:17:58

You are multiplying your signal times a window, which reduces the signal amplitude. That has to have a significant effect on the fft. The code below shows the effect, which for the (misnamed) hanning window drops the fundamental by a factor of 2.

For an oscillation at one frequency, the peak amplitude in the frequency domain is reduced by a factor equal to the average value of the window function. Since the Hann window is a cos^2 function, and since the average value of cos^2 is 1/2, the frequency domain peak is reduced by that amount.

N = 1000;          % signal length
t = (0:N-1)/N;
f0 = 40;
y =  cos(2*pi*f0*t)/N;
yH = (cos(2*pi*f0*t)/N).*hanning(N)';
f = (0:N-1);
yf = fft(y);
yfH = fft(yH);
ind = 1:N/2;
figure(1)
stem(f(ind),2*abs(yf(ind)))
grid on
figure(2)
stem(f(ind),2*abs(yfH(ind)))
grid on

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