Optimal sampling and algorihtm

[revesz]

The first Q:
I have an 500kHz ADC, 16 bits, what is the optimal
sampling rate and sample length to measure vibration displacement spectra in the sub Hz- to kHz range?
I am measuring ground and floor vibration using piezoelectric accelerometer.

And the second:
Can anyone point me to a source of algorithm
for the data crunching of the vibration data stream?
(I am doing Windows/Linux programming with GUI)

Thanks a lot for the advice.
Peter

 

[electricpete]

Your sample rate Fsample needs to be at least twice the highest frequency of interest (Fmax) to satisfy Nyquist.

In fact usually more than twice as much to allow for an antialiasing filter with transition band that will pass everything below Fmax and attenuate everything above Fsample/2

"data cruching"... could mean a lot of things. We don't know what you are trying to accomplish.

You might look at:

http://www.dspguide.com

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[revesz]

electricpete thank you for your response.

On data crunching:
My ADC will provide an acceleration vs. time stream.
As I understand the data crunching is the calculation
that converts this into the frequency domain (using FFT)
a(f) = FFT[a(t)],
so then I can recalculate the a(f) into displacement spectrum, d(f) = -a(f)/omega and then subsequently to PSD(f)

So far this seems to be elemental - FFT routines are available all over the place.
But just looking at the some of the vibration-related postings
I can see a number of additional points, like filtering, windowing, averaging etc that also need to be included (are they?) into the calculations. So I am not quite sure I understand the impact of these additional "tunings".

In other words, if I just use FFT to convert to the frequency domain *without* filtering, fancy windowing and averaging what kind of error I will introduce into the
spectrum?

Thanks
Peter

 

[GregLocock]

You need a decent textbook, not a couple of posts on an internet forum. The FAQ section for this Forum has some pointers.

Cheers

Greg Locock

SIGlease see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[IRstuff]

This really needs to be designed from the ground up. In some cases, running the ADC at max rate might well be justified to minimize and spread spectrum the quantization noise. The other consideration is how much frequency resolution you need.

All of this requires you to thoroughly understand the algorithm and its ramifications. As Greg says, this is not something to be answered in a brief forum posting.

TTFN

FAQ731-376

 

[snoopnoon]

In other words, if I just use FFT to convert to the frequency domain *without* filtering, fancy windowing and averaging what kind of error I will introduce into the
spectrum?



With no pre/post processing techniques, ex: window, there will be large errors in the results. In fact when doing ground vibrations, im sure your signal will be mostly random and this will cause extensive leakage without some sort of window. A window weights the ends of your sample less than the middle to account for the begining and end of the sample not being the same. This leakage will give false results because the energy is spread over multiple frequencies.

 

[revesz]

Thank you all for the information.
Peter

 

[electricpete]

One of the most important parameter you will want to decide is the length of the FFT. Longer FFT length gives smaller frequency bin width. Poor selection of window function can be more than compensated by longer FFT.

Also you'll want to decide if you will average multiple FFT's and if so how many averages and what overlap.

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[electricpete]

And yes, I agree with the others. It is not something we can tell you... particularly when you haven't told us a thing about the application or objectives.

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[revesz]

The application:
We have here a number of synchrotron radiation equipments (long beam-pipes, vacuum boxes with water cooling, optical tables, etc.) All of these equipments are to capture X-ray
radiation coming from the synchrotron. Of course everything
everything is coupled together and vibrations coming from different sources (ground, water in cooling lines, AC, fans,
stepping motors, etc, etc) affect the performance of the system.
I have made some preliminary measurement that uses an accelerometer + amplifier, a PCMCA ADC and a labview program to evaluate the acquired vibrational data.
The typical ground vibration PSD at the Hz range is 1E-6 um^2/Hz for modern X-ray light sources (like APS or ESRF)
What I want to do is to make a Windows based vibration measuring system using a DT9834 ADC that has 500kHz multiple simultaneous 16-bit inputs. I am thinking in terms
of having an ovelapped windowed FFT of multiple frames.
The goal is to have a frequency range of Hz-kHz, maybe 0.1Hz to 1 kHz.
I am not sure how to set the frame size, sampling frequency to archive Hz and sub-Hz resolution.
Peter

 

[GregLocock]

The quick, dangerous, answer is that each frame will have to be at least 10 seconds long and will need to be sampled at at least 2 kHz, and many people would say at least 2.5 kHz.

But, just to point out why you need a book:

Do you mean 0.1 Hz line width, or 0.1 Hz resolution?



Cheers

Greg Locock

SIGlease see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[revesz]

Dear Greg,
>>Do you mean 0.1 Hz line width, or 0.1 Hz resolution?

This is how I understand IN GENERAL: resolution is totally instrument related - perhaps when data are obtained the resolution is at best is 1/Fs where Fs is the sampling frequency.
Next, one uses these data and created a spectrum using some kind of binning process. the width of these bins is the line width. The line width depends on how the spectrum is calculated from the data.

Now in the world of signal processing with FFT:
The discrete data stream is converted to a discrete spectrum that contains bars or bins. (Showing a continuous line in spectrum obtaind by FFT is missleading: the calculation results in discrete bins.)
The number of bins in the spectrum is = FFT buffer/2.
The frequency resolution is also related to the number of FFT bins also gives,
and it says how many Hz are represented by a single bin.
Frequency Resolution = Sample Rate / FFT Points = Frequency range / Bins numbers.

So how long it will take to fill the FFT buffer at data acquisition?
Buffer acquisition time = FFT points / Sample Rate = 1 / Frequency resolution.

I am still learning this stuff and I appreciate all your comments and help. Peter

 

[SomptingGuy]

The way I normally try to explain it is that the frequency of the first non-zero bin corresponds to an event the length of the whole sample. The other bins are integer multiples of this frequency, up to half the sample rate.

Trying to remember all the relationships by rote leads to mistakes.

- Steve

 

[electricpete]

You used the word "archive" which suggests this data may be called upon the in the future for further analysis.

If storage is not a big problem, one attractive option is to save the raw time data instead of the processed data.

Then you can go back at any later time and process it however you want. Try multiple ways even on the same data to compare results - you can't make any irrecoverable mistakes in post-processing as long as you don't destroy the original data. The only "error" you can make up front that will limit you later is not storing a long enough time record or not a high enough sample rate. So this approach tends you towards saving long time records sampled at high rates - may not be the most efficient from storage perspective but provides the most flexibility.

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[revesz]

I agree, it is a good idea of archiving data so you can optimize data analysis at post-processing time.
Peter

 

[VibeAC]

If you are trying to do low-amplitude vibration measurements, say for a micro-electronics facility, nano-scale imaging suites, etc, you need to make sure that your accelerometers are sensitive enough. If the vibration levels are very low, you may end up measuring noise and not real data. Typically 10V/g seismic accelerometers are used for this type of work.

If you are doing floor vibration measurements for comparison against the standard velocity criteria lines (Class A to E and below), these criteria are based on 1/3 octave-band velocity spectra and not narrow-band FFT spectra.


Andrew Gorton, MSc
Noise & Vibration Consultant

http://www.PapadimosGroup.com