zero lag Butterworth filter
in [DSP]
|
Prev: CompIMAGE 2010: Call for Short Communications
Next: Please help a newbie: Matlab freqz.m -- Plotting a functions frequency response
From: adamchapman on 25 Jan 2010 15:55 Im trying to implement a zero-lag butterworth Filtert as described in tha paper at http://www3.uta.edu/faculty/ricard/Grad%20Biomech/Pezzack/Robertson%20(2003)%20Design%20and%20responses%20of%20butterworth%20filters.pdf My understanding is that the output of the filter needs to be reversed and passed back through the filter a second time, but this time with the data in reverse. I think that in eqn(7) of the paper; for the second pass trought the filter, I just replace the x's with the output of the first filter pass, but the data multiplied by the "b" coefficients puzzle me. I suppose they would be replaced with previous outputs of the second filter pass. However, I don't see how the data is reversed for this second pass. Any help is greatly appreciated.
From: Tim Wescott on 25 Jan 2010 17:39 On Mon, 25 Jan 2010 12:55:46 -0800, adamchapman wrote: > Im trying to implement a zero-lag butterworth Filtert as described in > tha paper at > http://www3.uta.edu/faculty/ricard/Grad%20Biomech/Pezzack/Robertson%20 (2003)%20Design%20and%20responses%20of%20butterworth%20filters.pdf > > My understanding is that the output of the filter needs to be reversed > and passed back through the filter a second time, but this time with the > data in reverse. Correct. > > I think that in eqn(7) of the paper; for the second pass through the > filter, I just replace the x's with the output of the first filter pass, > but the data multiplied by the "b" coefficients puzzle me. I suppose > they would be replaced with previous outputs of the second filter pass. Yes. The filter itself does not change, just the data that you pass through it. > However, I don't see how the data is reversed for this second pass. You have a vector of data x, with elements x[0] through x[n]. You run that through the filter specified by (7) once to get a filtered vector y. Then you set x[0] = y[n], x[1] = y[n-1], etc. to x[n] = y[0]. Then you run this new x through the _same_ filter to get the filtered vector y (which is in reverse time). Then you time-reverse y _again_ to get the answer you're looking for. In case this wasn't clear before, this algorithm only works after the fact -- you can't apply it in real time. -- www.wescottdesign.com
From: adamchapman on 27 Jan 2010 06:19 > In case this wasn't clear before, this algorithm only works after the > fact -- you can't apply it in real time. Ah, I suppose it's useless for following stock prices then
From: Rune Allnor on 27 Jan 2010 07:32 On 27 Jan, 12:19, adamchapman <adamchapman1...(a)hotmail.co.uk> wrote: > > In case this wasn't clear before, this algorithm only works after the > > fact -- you can't apply it in real time. > > Ah, I suppose it's useless for following stock prices then Well - yes. And it has nothing to do with the filter being zero phase or real time or anything like that. Filters as used in DSP are designed from the assumption that the data are stationary, which stock market data are not. Stock market data are, to some extent, similar to random walk data, which DSP filters are not very well suited to deal with. So if you want to mess with data with random walk-type characteristics, you might want to find analysis methods that are better suited to random walk-type data. Rune
From: Jerry Avins on 27 Jan 2010 09:04
Rune Allnor wrote: > On 27 Jan, 12:19, adamchapman <adamchapman1...(a)hotmail.co.uk> wrote: >>> In case this wasn't clear before, this algorithm only works after the >>> fact -- you can't apply it in real time. >> Ah, I suppose it's useless for following stock prices then > > Well - yes. > > And it has nothing to do with the filter being zero phase > or real time or anything like that. Filters as used in DSP > are designed from the assumption that the data are stationary, > which stock market data are not. > > Stock market data are, to some extent, similar to random > walk data, which DSP filters are not very well suited to > deal with. So if you want to mess with data with random > walk-type characteristics, you might want to find analysis > methods that are better suited to random walk-type data. I want a filter that will tell me the name of a winner at the track tomorrow. If the stock market, why not the racetrack? Jerry -- Engineering is the art of making what you want from things you can get. ����������������������������������������������������������������������� |