Differentiation with highpass filter
Differentiation with highpass filter
(OP)
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
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





RE: Differentiation with highpass filter
A high-pass filter is a derivative in Fourier transform space.
TTFN
RE: Differentiation with highpass filter
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RE: Differentiation with highpass filter
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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RE: Differentiation with highpass filter
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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RE: Differentiation with highpass filter
Cheers
Greg Locock
Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.
RE: Differentiation with highpass filter
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RE: Differentiation with highpass filter
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 ;)