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# Very low frequency spectral leakage, one-thrid octave band analysis

## Very low frequency spectral leakage, one-thrid octave band analysis

(OP)
As pointed out in the old thread below, it's sort a norm to use 1/3 octave band for environment vibration assessment.

"One-Third-Octaves for Dummies"

The bandwidth increases as central frequency so spectral leakage in high frequency band (>20Hz)is not a concern.
But then it come to very low frequency, this become a serious issue since the bandwidth is so narrow any spectral leakage will distort the picture.

For example, we can see the stairs from very low frequency (<3Hz),and they might be a leakage from a very low frequency (1Hz).

1/3 Octave Band, Main Signal and Ref Signal

Main Signal FFT

Ref Signal FFT

For a normal vibration control, we don't care much about very low frequency area (like the VC-B criterion, the limit went up at very low frequency) and part of the reason is that very low frequency excitation is hard to be isolated. However, for a very stringent vibration control zone, very low frequency is of paramount consideration. My question is how do we distinguish spectral leakage from actual environment noise, and eliminate it, especially at very low frequency bands?

I have thought of windowing, but someone told me that for environment vibration assessment we shall not use other than rectangular window in order not to distort actual environment noise.

### RE: Very low frequency spectral leakage, one-thrid octave band analysis

"someone told me that for environment vibration assessment we shall not use other than rectangular window in order not to distort actual environment noise. "

Well that's why you get leakage innit? Use a Hanning window like normal people, or Blackman Harris if you are feeling posh. I agree there is an issue with calibration, for your stuff I'd use energy compensation rather than peak

There's a couple of other approaches-

1) reduce your sampling frequency, to increase the resolution.
1a) increase the sample time to increase the resolution
2) switch to a time based 1/3 octave filtering system (this introduces the same problems but may simplify your approach)(but it is far more work than the previous ideas)

When I was doing 20-20 kHz third octaves I used three separate sampling frequencies to make sure I got sufficient FFT lines per 1/3 octave, without having too much data, since back then FFT processing was time consuming and disks were small.

Cheers

Greg Locock

New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

### RE: Very low frequency spectral leakage, one-thrid octave band analysis

(OP)
Thanks for your input Greg! You are always the first few to reply.

I have reduced the sampling frequency to the minimum and the sample time to the maximum and test it on a harmonic excitation (built an experiment to verify it). The problem is still exist because we are dealing with extremely low frequency zone (1-20Hz), the 1/3 octave band is very narrow in this zone, and any impact, i.e. footsteps seems to be registered as an low frequency source after FFT.

I would like to try windowing but don't quite understand about energy compensation and calibration. Most of the resources online are talking about calibrating the peak. Do you have any book or article that discuss about energy calibration in details?

### RE: Very low frequency spectral leakage, one-thrid octave band analysis

I am 99% sure that the B&K green book, Frequency Analysis covers it in more detail than any human could bear. Basically all you are trying to do is ensure that the RMS signal is the same in the raw data and the compensated windowed data.

Cheers

Greg Locock

New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

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