How does the signal to noise ratio of a vibration spectrum affect the corresponding cepstral representation?

5. How does the signal to noise ratio of a vibration spectrum affect the corresponding cepstral representation?

- Reference [] http://www.ilearninteractive.com/forum/showthread.php?p=74 provides an interesting response to the question posed of: - How does the signal to noise ratio of a vibration spectrum affect the corresponding cepstral representation?
If you take a spectrum in log amplitude format, and then perform an FFT of that spectrum, you end up with a set of data that will have peaks corresponding to anything periodic in the spectrum. That is cepstrum analysis
- If you were to look at a spectrum with harmonics or sidebands, and forgot for a moment that it was a spectrum and instead thought of the data as a time waveform, the evenly spaced peaks (harmonics or sidebands) could be thought of as periodic events - and if you do an FFT of a time waveform with periodic events you will get a spectrum with a peak that corresponds to the frequency of those events. So the same holds true with spectral data - if you perform an FFT of the spectrum the resulting cepstrum graph will have peaks if the spectrum contained harmonics or sidebands
- Now, if you were to compare a spectrum in linear format to a spectrum in log format, you will notice that it is much easier to see the harmonics and sidebands in the log spectrum. Peaks that are simply too small to see in the linear graph are obvious in the log graph. So that is why we do an FFT on the log spectrum
- However, if you have poor dynamic range, or if the signal to noise ratio is poor, then all of those low amplitude harmonics and/or sidebands may be lost in the noise floor. And if they are lost, then the FFT won't see them, so the cepstrum graph will not have a peak at the harmonic or sideband frequency
- So, that is why I believe the signal to noise ratio is important”

Also so the attachement here...

Cepstrum%20Analysis[1].pdf (21 Kb, 35 downloads)