# When to zero-mean a signal?

I have two sets of signals. The first is a noisy sinewave, which I zero-mean before taking the FFT since I need to find the amplitude.

The other is essentially noise with a gaussian distribution. I'm unsure whether to zero-mean this before taking the FFT (I think I do to remove the 0 Hz reponse.) Do I zero-mean before applying the statistical analysis?

When do you zero-mean a signal?

• why would you need to apply an FFT to find the amplitude of a sine wave? and: what good would zero-meaning do? Why are you doing that? Aug 16, 2021 at 11:52
• @MarcusMüller It's a very noisy sine wave signal. I needed to get the amplitude of the response. To be honest, that is not the issue, it is more whether to zero-mean the noise signal when describing it statistically. Aug 16, 2021 at 14:50
• well, what is the actual problem then? because what you need to do depends on what you want to do, and you seem to be describing something else in your question! Aug 16, 2021 at 15:27

First of all, if you have a whole number of periods, the FFT of your sine wave will have no spectral leakage and no DC bias caused by the spectral leakage. That being said, if your sine wave has been acquired via an analog chain and an ADC, the DC bias could be caused by the analog input chain and the ADC.

Second, the presence of a DC bias will no affect the amplitude of the other FFT bins, therefore removing the mean will not yield a better amplitude estimate.

Third, if you don't have a whole number of periods, the FFT is probably not the right tool to estimate the amplitude of a sine wave.

Finally, I don't know how your gaussian noise was generated. It should be zero-mean. That being said, it's possible that there could be some DC bias especially if your noise sequence is short.

• The noise is a signal response of measured turbulence. It has a gaussian distribution, but I was wondering if I should zero-mean it considering I zero-meaned the noisy sine wave since the noise is supposedly the underlying noise in the sine wave signal? Aug 16, 2021 at 15:09
• What do you hope to accomplish by removing the mean?
– Ben
Aug 16, 2021 at 19:00
• What am trying to achieve is (1) statistical analysis of the noise signal (2) Determine the type of noise (3) removing some component and see how that affects it. Since removing the mean for the sine wave i assumed i had to remove from the noise signal analysis aswell Aug 17, 2021 at 8:19