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Let's suppose i have a sensor that measures the output of a process and this cause a not negligible noise that affects my signal. My goal is to analyze the process signal in order to find faults. How can i deal with noise ? Is it possible to apply the fourier transform to the signal with noise or i have to filter it in advance? Maybe is possible to deduce which frequencies does the noise affect...

If i have to filter the noise, which are the techniques to do it ? Thanks

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Usually, there are two types of noise that you can eliminate by using the spectrum.

One type is a noise that is in a different frequency band than the signal (it can be a high-frequency noise). In such a case, there is a clear separation between the signal content and the noise in the spectrum and you have to do nothing.

The second case is when the noise is in the same frequency band as the signal and then you can perform Welch's method of averaging the spectrums to reduce the noise component.

In case you have a dynamic model of the signal generator, you can reduce the noise using some kind of adaptive filter such as Kalman-filter prior to the evaluation of the spectrum.

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You can first find the frequency response using FFT. There will be a peak at the signal frequency with noise around. You can filter the narrow band signal and perform inverse FFT to get a cleaner signal.

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  • $\begingroup$ Hi Anushka! Could you elaborate on how you find a frequency response of a time--continuous system using an FFT? This is not obvious to me here. Then, it seems like you're proposing filtering in (discrete) frequency domain, and that's generally a bad idea. $\endgroup$ Mar 5 '20 at 12:40
  • $\begingroup$ Thank you for the article. I meant FFT after discretization but that seems to be a bad idea. $\endgroup$
    – DSP Novice
    Mar 9 '20 at 12:59

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