Differentiation with highpass filter

[georgekar]

Hi, I have position data from a tracker and I want to calculate velocity and acceleration. Simple [x(i)-x(i-1)]/?t and some other formulaes does not give good results.

I want to try to use a highpass filter with slope '1' (20db/dec) from 0 to 10 Hz (my area of interest) to calculate the derivative.

Anyone knows how can I define a filter which will have characteristics close to what I want? How can I specify the slope in a e.g. Butterworth filter.
Can I define a filter with its transfer function (for example the transfer function H=s/(s-10) I think has the impulse response I need.

Thanks a lot for your help in advance.
Regards,
George

 

[IRstuff]

You should be using something akin to a Kalman filter. There are tons of books on that and trackers in general.

A high-pass filter is a derivative in Fourier transform space.

TTFN

 

[electricpete]

5 pages on numerical differentiation here:

http://library.lanl.gov/numerical/bookfpdf/f5-7.pdf

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[electricpete]

The above methods I believe are fairly intuitive.

Also Oppenheimer and Schaffer's "Discrete Time Signal Processing" 2nd ed, p482-485 discusses some more elaborate methods.

One appears to be time domain convolution of your input signal with a non-causal IIR filter defined by equation 7.70. And example using Kaiser window is given.


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[electricpete]

Simple [x(i)-x(i-1)]/dt and some other formulaes does not give good results.[/quoute]

One thing you'll not from the numerical recipes link is that you'll expect significnatly better results using
[x(i+1)-x(i-1)]/[2*dt]


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[GregLocock]

Albeit at the risk of reducing your information bandwidth by a rather hard to work out amount, but roughly 50%

Cheers

Greg Locock

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

 

[electricpete]

Yes I agree.

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[georgekar]

Finally I found my way. The numerical differentiations I tried were really noisy.
A Butterworth high pass filter that I designed with the help of the FDAtool did the trick finally.
Thanks for helping