Savitzky golay filter for finding second derivative

Hello friends,
I want to find second derivative using Savitzky golay filter for the data as shown in image.
Three different spacings are used.
Region AB and EF= ∆f1
Region BC and DE=∆f2
Region CD=∆f3
Can some one help me to understand to to decide side points and polynomial order for my input data.?
Thanks in advance.

The polynomial order must be at least one larger than the highest derivative. So a third order polynomial is required for a second deriviative. In general it is better to keep the polynomial order as low as possible while getting a good fit to the data.
The number of side points is somewhat arbitrary and depends on how much smoothing is needed. Often some experimentation and judgement is required.
Have you considered resampling the data to create a new dataset with uniform sampling throughout? That might be easier than trying to match derivatives at the transition points.There are several resampling VIs available.
How many data points do you have in each segment?
Lynn

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Attachments:
Savitzky-Golan Derivatives2.jpg ‏56 KB
PD_DEPTH.jpg ‏96 KB

I can't see anything wrong with your implementation of the SG filter (except that you should consider using the "Savitzky Golay Filter PtByPt.vi" which is intended for this kind of real-time use), but I wonder if SG is the best for your application. The velocity you get from your VI is an estimate of the velocity at the middle of your 2k+1 data-point array (ie. k intervals in the past), rather than the best estimate of velocity at the time of most recent reading. With very noisy data you will have to use quite a large value of k to get a meaningful value, and thus will be controlling your vehicle with outdated velocity values. You might be better off with a filter that is designed to provide an estimate of current velocity, such as an exponentially-weighted moving average.
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Savitzky Golay Differentiator PtByPt.vi ‏21 KB

I replied a tad too soon. I discovered that the amplitude output from the derivative had been scaled down by (100/2xPI) for some reason I don't understand, so I updated both the test harness and the point by point vi and attached them.
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Attachments:
TestSVDerivPntByPnt.vi ‏42 KB
Savitzky Golay Differentiator PtByPt.vi ‏21 KB

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Thanks for the reply. The problem was that I had not updated to version
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"iainhp" wrote in message
news:[email protected]..
> Well it ain't obvious, that's for sure.
>
> 1. In the "diagram" window click on "Window" then "Show Functions
> Palette".
>
> 2. On the palette that pops up click on the large magniying glass at
> the top.
>
> 3. On the index line type "savitzky" and that should bring up the
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>
> Well hidden, Ehhh?

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I can't see anything wrong with your implementation of the SG filter (except that you should consider using the "Savitzky Golay Filter PtByPt.vi" which is intended for this kind of real-time use), but I wonder if SG is the best for your application. The velocity you get from your VI is an estimate of the velocity at the middle of your 2k+1 data-point array (ie. k intervals in the past), rather than the best estimate of velocity at the time of most recent reading. With very noisy data you will have to use quite a large value of k to get a meaningful value, and thus will be controlling your vehicle with outdated velocity values. You might be better off with a filter that is designed to provide an estimate of current velocity, such as an exponentially-weighted moving average.
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Savitzky golay filter for finding second derivative

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