Decimation

[AnibalM]

Hi all,

I'm going to sample an acceleration signal at 51,2 kHz and the same signal needs to be integrated at 2 kHz. Should the decimation be applied before or after the integration ? 

Thanks.

[Bob_Schor]

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@AnibalM wrote:

I'm going to sample an acceleration signal at 51,2 kHz and the same signal needs to be integrated at 2 kHz. Should the decimation be applied before or after the integration ? 

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It is not clear what you mean by "integrated at 2 kHz" or "the decimation".  One interpretation of "integration" is "low-pass filtering", and there are numerous low pass filters you could use (see the Signal Processing palette).  Decimation is another form of low-pass filtering (since it lowers the Nyquist frequency).  Not knowing what your goal is, nor how you are using Decimation (are you taking every other point?  every n-th point?), I'd recommend that you "play scientist" and "do an experiment" -- generate a simulated signal + noise and play around with Filters and Decimation to figure out empirically what seems to work for you.  Be sure you evaluate your main question, "Should decimation be applied before or after the integration" ...

Bob Schor

P.S. -- one nice virtue of LabVIEW is that it is fairly easy to set up such "experiments" and kind of fun to "figure it out for myself, based on my actual problem/question/situation".

[altenbach]

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@AnibalM wrote:

I'm going to sample an acceleration signal at 51,2 kHz and the same signal needs to be integrated at 2 kHz. Should the decimation be applied before or after the integration ? 

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Properly done, the integration does not depend on the sampling rate. You seem to entangle two different problems into one:

• integration of the 51.2 kHz signal
• decimation to 2kHz

And the question is what order is more suitable. (Also, "decimation" is not the right term because the dt's are not integer multiples. "Downsampling" is probably what you need)

I would definitely integrate first because it automatically lowers any potential noise and is a relatively cheap operation. Most likely no filtering is needed when downsampling the integrated signal. If you downsample first, you most likely need to filter the signal, which is more expensive. 

What does the data represent? Where does it come from? How big is the data? Do you only need the integrated signal or also the original at the end? What is the datatype? (express, waveform, array, etc.).

We can typically help much more efficiently if you provide more detailed information and maybe even include simplified example code and data.

[AnibalM · Accepted solution]

Hello altenbach,

Thanks for your answer. I'll try to explain a little bit more. The signal comes from an accelerometer mounted on a rotative screw compressor. This machine has a lot of gears and ball/roller bearings. The goal is to detect, monitor and evaluate frequencies and amplitudes. The same signal will have to be analyzed three times:

First, for periodic frequencies :  gear mesh frequency ( 14 kHz and harmonics, in acceleration)

Second, for periodic frequencies: unbalance, looseness, misalignement, etc (till 2 kHz, in velocity).

Third, for transients: impact generated frequencies can be detected from defective bearings and from problems in the gears. These occur till 1 kHz and are treated with Hilbert transform (normally known as "envelope analysis").

I haven't created the VI yet but started thinking about it. Averaging and windowing the signal is important, specially for the acceleration signal. I suppose at least 30 samples have to be averaged, so in the end I'll have a single averaged spectrum for acceleration, another one for velocity and another one for envelope, maybe waveform type. I guess the best way is to create the VI,  follow your recommendations and observe the results.

Thank you.