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I have a variable in time and I calculated its mean which is 9.5. I have done the Fourier Transform of this variable, using the FFT in matlab. I would like to consider only a range of frequencies, so I substituted with zero all the frequencies that I have excluded. After this I did the ifft of this, obtaining again a variable in time. I calculated its mean and now is 9.5. I am surprised because I supposed that it should have been a lower value because the signal does not include some frequencies.

Maybe substituting with 0 the value in the frequencies that I don't want to include is not the right procedure. Can you help me?

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    $\begingroup$ Don't zero out FFT bins to filter. You can convolve the signal with a sine wave and it's equivalent to multiplication a delta function in the frequency domain. $\endgroup$
    – ZR Han
    Jul 21 at 9:36
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[Pictures to follow] Let us start with a thought experiment (which can be simulated): imagine a constant signal with value $c$. Add a full period of a pure sine with non-zero frequency. If you can remove this harmonic contribution by zeroing out its frequency bin in the Fourier domain, then the resulting inverse Fourier signal will still have mean $c$. So remove "some frequency" does not reduce the mean per se.

Now remember that, in the Fourier domain, the "O-th" frequency ought to be equal (up to a constant scale factor) to the average of the signal. This is consistent with the above. The pure sine period has equally distributed values above and below $0$, so this does not contribute to the signal's average.

Then, imagine that the observation time frame only encloses the first positive half of the "one-period sine", or the second one. Zeroing its frequency will sure remove frequency components, yet parts of the "not-otherwise" compensated sine bumps may remain, and modify the amplitude, both ways. Therefore, if everything has been done right, your experiment is not totally surprising.

Finally: if removing or cancelling frequency terms in an FFT was a generic cure (panacea), I would not have the my job, and this site would be leaner. As suggested by @ZRHan, to zero out FFT coefficients is quite dangerous.

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