Is the window function automatically used when doing the fft function, or do I have to enter code to use the window function?

The fft defaults to a rectangular window that is the length of the signal. That is the only one that is ‘autoomatically’ used. Any others would have to be provided specifically as part of the fft call.

There are several window funcitons available in the Signal Processing Toolbox.

Adding a Hanning window (the hann function) to your code would work like this —

t = (0:0.01:1).'; % Transpose To Column Vector

data = sin(2*pi*t);

plot(t,data)

L = numel(data)

L = 101

fftdata = abs(fft(data.*hann(L))); % Use Hanning Window

% At this time, is the window function automatically used?

f = (0:length(data)-1)*1/length(data);

plot(f,fftdata)

.

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Star Strider 2025-7-2

No correction should be necessary. The purpose of the window function is to correct for the discrete Fourier transform being finite. The symbolic Fourier transform assumes an infinitely-long argument and produces an infinitely long result.

Note that the second half of the fft result is the complex conjugate fo the first half. (The result would be symmetric about the centre D-C offset using the fftshift function.) This has the effect of distributing the original energy of the signal between the two 'halves' of the discrete Fourier transform. To recover the approximate amplitudes of the original signal components, it is necessary to multiply them by 2. This is a property of the fft calculation, not the result of windowing.

Paul 2025-7-2

在 MATLAB Online 中打开

Hi Lorenz,

If you want the amplitude plot scaled to the magintude of the underlying complex sinusoids, then divide the FFT by the sum of the elements of the window.

t = 0:0.01:1;
x = sin(2*pi*t);
N = numel(x);
X1 = fft(x);
h  = hann(N).';
X2 = fft(x.*h);
f = (0:N-1)/N/0.01;

Without scaling

figure

plot(f,abs(X1),'-o',f,abs(X2),'-x')

●

With scaling. Note that the sum of the elements of the rectangular window is simply N.

figure

plot(f,abs(X1)/N,'-o',f,abs(X2)/sum(h),'-x')

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Is the window function automatically used when doing the fft function, or do I have to enter code to use the window function?

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Is the window function automatically used when doing the fft function, or do I have to enter code to use the window function?

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