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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, 0.992457}, {0.007, 0.991152}, {0.008, 0.989824}, {0.009, 0.988466}, {0.01, 0.987075}, {0.011, 0.985644}, {0.012, 0.984167}, {0.013, 0.982637}, {0.014, 0.981046}, {0.015, 0.979383}, {0.016, 0.977638}, {0.017, 0.975797}, {0.018, 0.973843}, {0.019, 0.971757}, {0.02, 0.969513}, {0.021, 0.967081}, {0.022, 0.964421}, {0.023, 0.96148}, {0.024, 0.958187}, {0.025, 0.954446}, {0.026, 0.950115}, {0.027, 0.944986}, {0.028, 0.938726}, {0.029, 0.930769}, {0.03, 0.920047}, {0.031, 0.904209}, {0.032, 0.876587}, {0.033, 0.804836}, {0.034, 0.500818}, {0.035, 0.308999}, {0.036, 0.217665}, {0.037, 0.164207}, {0.038, 0.130845}, {0.039, 0.106335}, {0.04, 0.0861833}, {0.041, 0.0731473}, {0.042, 0.0631012}, {0.043, 0.0519342}, {0.044, 0.0453451}, 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  • $\begingroup$ Are you asking why its shifted down? I assume that's a result of the power you're removing from the signal by filtering. $\endgroup$ Commented Sep 17, 2015 at 14:12
  • $\begingroup$ I cut paste your data and code and it plots the filtered curve right through the middle of the data. $\endgroup$ Commented Sep 17, 2015 at 15:47
  • $\begingroup$ Possible version issue? This works for me with 10.1 (looks nearly the same as Kattern's median filter plot ) $\endgroup$ Commented Sep 17, 2015 at 16:09

2 Answers 2

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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

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  • $\begingroup$ did you reproduce his error? $\endgroup$ Commented Sep 17, 2015 at 15:52
  • $\begingroup$ @george2079 I haven't tried the OP code :) $\endgroup$ Commented Sep 17, 2015 at 15:58
  • $\begingroup$ @george2079 Well, I did now. I got the same plot posted in the question.V9 here,just in case $\endgroup$ Commented Sep 17, 2015 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) $\endgroup$ Commented Sep 17, 2015 at 16:53
  • $\begingroup$ @george2079 See the uploaded animation $\endgroup$ Commented Sep 17, 2015 at 16:58
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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

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