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Ex: We're measuring vibration Frequency response of a structure, and at the same time there is a constant source of vibration (noise) from a pump. The pump is exciting the structure by sinusoid correspond to its constant rotational speed.

Is it possible to remove the sinusoid which is induced by the pump using averaging technique (Signal averaging)?

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    $\begingroup$ It is much better if you can provide more details about your application, your setup, the signal of interest, and the contamination considered as non-random noise. Their time domain and spectral descirptions are critically important. Your application requirements and your overall goals are equivalently important before designing any solutions to your problem. $\endgroup$ – Fat32 Feb 12 at 11:24
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    $\begingroup$ Like said above, more details for a full answer including what do you mean by averaging? Do you mean averaging multiple measurement signals or averaging across a single measurement signal (moving average)? $\endgroup$ – Engineer Feb 12 at 13:00
  • $\begingroup$ You can use an adaptive filter I think, it has been a while but I believe a similar technique is used to remove AC sinusoid from sensitive equipment. $\endgroup$ – FourierFlux Feb 14 at 9:14
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Window-average filter is an example of lowpass filter. That means, if interesting frequencies in your signal are few times lower than noise, then yes, you can do that.

If they are close or higher, then no.

Use bandstop/highpass filter if your signal frequencies are much higher than noise, or adaptive filter like Recursive Least Squares instead, if your signal and noise frequencies overlap.

And don't forget, that your filter will affect your FRF measurements, so if you sample over the range that includes constant noise frequency, I'd suggest going with adaptive filter.

See also: What is the cut-off frequency of a moving average filter?

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The random does not play a role when averaging is used to remove the noise. The distribution of noise does. Averaging works when the mean of the noise is zero. The assumption is that averaging noise that has a zero mean results in canceling noise component while the signal components remain mostly unchanged.

Take for example the power line noise as 60Hz sinusoid. If your band of interest small and compared to band that is affected by averaging (low pass filter cut-off frequency), by averaging and taking long enough window all of that elements added by that 60Hz power line noise can be removed. A sinusoid noise is not a random noise.

That being said in you case a notch filter might do the trick.

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