Finding Accurate Amplitude Using FFT

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Emmett - 2021-01-11T10:07:31+00:00
Question: Finding Accurate Amplitude Using FFT

I have been working on code to use the FFT to find the amplitude of a signal. However, despite my best efforts to window I seem to get incorrect amplitudes. When I manually find Amplitude by inspecting the signal I get A = 63.7. When I use the following code I get A = 54.8. This is causing significant errors in my Bode plot.   I tried using a flat top window to maximize amplitude accuracy. My signal does not seem significantly noisy. I expected an amplitude much closer to the true value.   function Amplitude = Gaindb(x) if size(x, 2) > 1 x = x'; end x = x - mean(x); N = length(x); win = flattopwin(N); x = fft(x.*flattopwin(N)); Amplitude = 2*max(abs(x))/N; end

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    • Expert Answer

    Profile picture of Kshitij Singh Kshitij Singh answered . 2025-11-20

    When I run your code I get 14.5 for the answer, so I am not sure how you are getting 54.8. But the 14.5 is consistent with the Matlab definition of the flattop window. From the documentation, the flattop is a sum of cosines with certain coefficients, along with a constant coefficient a0 = .216. a0, the area of the window, is basically the amplitude reduction factor for the signal.
    Without any windowing of x, the fft comes up with a signal amplitude of 67.1, and 67.1 x .216 = 14.5 which is consistent.
    The Matlab window peaks out at a value of 1.
    Wikipedia has an example a flattop window from SRS that multiplies all the coefficients by 4.639, so the window peaks out at that value and a0 = 1. For a continuous sinusoidal  signal such as yours the resulting amplitude will be basically unchanged.


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