During parameter study for a project (signal processing applied in mechanical vibration), when I decrease the frequency to a very low value (less than 200 mHz, for a interested range of frequency of a few hundred Herz), the frequency response I have gets "squishy" (instead of a single line going up or down, I have a waveform going up or down).
Checking on some forums online yield me the connection to "dirac delta function", but I do not understand it fully. So I'd like to ask if there is any connection between dirac delta function and frequency resolution, with regards to FFT in vibration analysis. Thanks for your help.
Dear Hoang, Dirac delta functions (more properly, distributions) appear in various situations in Fourier analysis, but I don't see any immediate relationship with your problem.
In my feeling, the problem might be caused by an underresolution of low frequencies. If you want to see a harmonic component at frequency 0.2 Hz in the transform, you must perform DFT or FFT on a time segment of at least 5 seconds, so as to contain at least one period. Is this the case?
Roberto Ferretti Both signal (input and output of the system) finish one period within 2s (the input is an impulse, within a few ms - the output is vibration, begin at 0.3s mark and finish at 1.5s). The current sample/measurement time is 5.12s, more than enough to capture the whole period.
The issue might relate to the generator setting though. With 5.12s measurement time, there would be two input incidents, not one.
And just to make sure we are on the same place, would you mind explain what "under-resolution" means? Thanks
"Underresolution" means that you cannot measure harmonic components at pulsation lower than the inverse of the measurement time, because DFT/FFT need at least one period. In this case, if the measure time is 5.12s, you have the first sample of the FFT at the frequency of 1/5.12=0.195 Hz. You cannot detect harmonic components below this frequency.
Roberto Ferretti
Ah, thanks. For the record, there is no harmonic component (or peak in frequency spectrum)
This is my problem here. For frequency resolution 781.25 mHz (blue line) and 390.625 mHz (orange line), the spectrum is "a single line), but for 195.125 mHz, the spectrum is squishy as seen below. Some other forum mentions connection to dirac delta...
The blue line is hidden under the grey parts, and the orange is pushed down (for some reason). Even if the only thing I change is the number of FFT lines (which would change the frequency resolution). The bandwidth is kept at 10 kHz here.
It's hard to figure out what happens. However, a frequency-periodic component can actually be caused by some spike (=dirac) in the time series. Have you tried windowing the signal?
Roberto Ferretti
Yes. Though the study about window functions comes after this part. As in, for my experiments, I have to choose a bandwidth and FFT line count first, then choose the window function.
For reference, the window function in used of the above graph is Hann. The input is an impulse (or hammer blow, delivered by a shaker)
Dear Hoang, I have thought some times on your results, but could not figure out what is the problem. So sorry.
Roberto Ferretti Don't worry about that. I have a... strange explanation for it. Both in terms of "why the grey line is heavily smeared" and "why do we see peaks at 50 150 Hz and so on".
The first is a combination of very low frequency resolution plus window function. The second... noise. Probably noise. Or some equivalent "freak accident". More recently, I have repeated the experiment under the same conditions, the change is only "hitting different point" - but considering the graph above is the FFT of input force signal, there should be no change. Yet, the recent experiments show practically no such peaks at all.
Another answer (and a more technical one) is the influence of powerline (AC 50 Hz) and some internal harmonic of the measuring system under certain conditions...
Yeah, it is still quite fuzzy.
But still, thanks for your help.
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