Fourier transform of a noisy signal 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
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.