2
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enter image description hereI applied the LowpassFilter to my data and it shifted the result. Why is it? How can I filter high frequency oscillations without the shift?

  t = Transpose@
       Join[{Transpose[dat][[1]]}, { 
         LowpassFilter[Transpose[dat][[2]], 0.4]}];
    ListLogPlot[{dat, t}, Joined -> True, ImageSize -> 800]

   dat={{0., 1.}, {0.001, 0.998759}, {0.002, 0.997516}, {0.003, 
      0.996268}, {0.004, 0.995011}, {0.005, 0.993742}, {0.006, 
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$\endgroup$
  • $\begingroup$ Are you asking why its shifted down? I assume that's a result of the power you're removing from the signal by filtering. $\endgroup$ – N.J.Evans Sep 17 '15 at 14:12
  • $\begingroup$ I cut paste your data and code and it plots the filtered curve right through the middle of the data. $\endgroup$ – george2079 Sep 17 '15 at 15:47
  • $\begingroup$ Possible version issue? This works for me with 10.1 (looks nearly the same as Kattern's median filter plot ) $\endgroup$ – george2079 Sep 17 '15 at 16:09
3
$\begingroup$

For understanding the behavior of LowpassFilter[ ]:

First consider a cutoff frequency of 0 : nothing passes, the outcome is a null signal.
Then think of a cutoff frequency of Pi: everything passes, the outcome is the input.

You may experiment it for example with:

n = 30; 
Manipulate[l2 = LowpassFilter[l1 = 
                               Join[ConstantArray[0, n], ConstantArray[1, n]], freq]; 
           ListLinePlot[{l1, l2}],
           {freq, 0, Pi}]

Mathematica graphics

In v9 it gives you:

enter image description here

Edit - Hope you don't mind I'll put this here for comparison: from v10,

l1 = Join[ConstantArray[0, 30], ConstantArray[1, 30]];
Show[Table[ {
    ListLinePlot[LowpassFilter[l1, Exp[logfreq]]] }, {logfreq, -5, 0, .5}]~
       Prepend~ListLinePlot[l1, PlotStyle -> Red], PlotRange -> All]

enter image description here

$\endgroup$
  • $\begingroup$ did you reproduce his error? $\endgroup$ – george2079 Sep 17 '15 at 15:52
  • $\begingroup$ @george2079 I haven't tried the OP code :) $\endgroup$ – Dr. belisarius Sep 17 '15 at 15:58
  • $\begingroup$ @george2079 Well, I did now. I got the same plot posted in the question.V9 here,just in case $\endgroup$ – Dr. belisarius Sep 17 '15 at 16:00
  • $\begingroup$ For your manipulator example in v10, the filtered curve always goes from {0,0} to {60,1} passing through {30,1/2}. What I would "expect", although I don't have the expertise to say what LowpassFilter is supposed to do) $\endgroup$ – george2079 Sep 17 '15 at 16:53
  • $\begingroup$ @george2079 See the uploaded animation $\endgroup$ – Dr. belisarius Sep 17 '15 at 16:58
2
$\begingroup$

MovingAverage may be a possible solution.

mv = MovingAverage[dat[[All, 2]], 5];
ListLogPlot[{dat, MapThread[List, {dat[[;; Length@mv, 1]], mv}]}, 
 Joined -> True, ImageSize -> 800]

mv

$\endgroup$

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