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When you say Fourier Transform (FT) it usually implies the continuous case. When you have discrete samples, the Discrete Fourier Transform is used. They are very similar, but it is important to keep them distinct as concepts do not directly translate from one to the other. The DFT is a mathematical transform that does not care about the units of the ...

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hFilt = designfilt('hilbertfir','FilterOrder',n,'TransitionWidth',TW); n is the order of the filter and TW is the transition width. d = fdesign.hilbert b = firpm(n,f,fresp,w,'hilbert') n - order of the filter f - normalized frequency points for transition bandwidth w - weight of the points

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One technique that I've seen used in determining bearing faults is using the kurtosis of the vibration signal. You can track as a function of time what Wikipedia calls the sample excess kurtosis. This is the kurtosis that is different from the kurtosis you would see if the signal was Gaussian distributed. The sample excess kurtosis is defined as:  \frac{...

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(I am relatively new to this field of study as well, but here is my input which I hope is of help). Frequency analysis techniques should be chosen that reflect the characteristics of the system you use. Fourier analysis in this way assumes that the data is stationary for each sample interval over which the data is collected. As you only take the data in 10 ...

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I'm not that familiar with the Hilbert-Huang transform, so I won't comment on that. You seem to be under the impression that the DFT "suffers from the uncertainty principle". This is not true. Don't feel bad about thinking that as it is a widespread misunderstanding. This is a quote from an email to me from a well known expert in the field after I tried ...

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