Filter periodical sharp spikes in experimental data











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I have experimental data with periodic sharp artefact spikes, which mask the real signal that could be seen as several negative peaks in the first third part on the curve:



enter image description here



Is it possible somehow to filter these spikes? or at least significantly reduce them? Here is data set:



data = {{5.`, 2.41204`}, {10.`, 2.40477`}, {15.`, 2.40154`}, {20.`, 
2.4094`}, {25.`, 2.41592`}, {30.`, 2.40706`}, {35.`,
2.41802`}, {40.`, 2.4171`}, {45.`, 2.40979`}, {50.`,
2.4127`}, {55.`, 2.40254`}, {60.`, 2.40753`}, {65.`,
2.41049`}, {70.`, 2.40521`}, {75.`, 2.40446`}, {80.`,
2.40692`}, {85.`, 2.40509`}, {90.`, 2.40604`}, {95.`,
2.40464`}, {100.`, 2.40448`}, {105.`, 2.41854`}, {110.`,
2.41627`}, {115.`, 2.40941`}, {120.`, 2.40443`}, {125.`,
2.39909`}, {130.`, 2.41194`}, {135.`, 2.40494`}, {140.`,
2.40801`}, {145.`, 2.41532`}, {150.`, 2.41512`}, {155.`,
2.41328`}, {160.`, 2.41383`}, {165.`, 2.40806`}, {170.`,
2.3958`}, {175.`, 2.41296`}, {180.`, 2.41556`}, {185.`,
2.40119`}, {190.`, 2.27056`}, {195.`, 2.51902`}, {200.`,
2.41532`}, {205.`, 2.36206`}, {210.`, 2.37837`}, {215.`,
2.38771`}, {220.`, 2.39959`}, {225.`, 2.40557`}, {230.`,
2.40373`}, {235.`, 2.4045`}, {240.`, 2.39692`}, {245.`,
2.38983`}, {250.`, 2.39646`}, {255.`, 2.40411`}, {260.`,
2.40749`}, {265.`, 2.41679`}, {270.`, 2.42152`}, {275.`,
2.40963`}, {280.`, 2.39891`}, {285.`, 2.39964`}, {290.`,
2.39939`}, {295.`, 2.40453`}, {300.`, 2.40663`}, {305.`,
2.41569`}, {310.`, 2.40495`}, {315.`, 2.40756`}, {320.`,
2.41375`}, {325.`, 2.41212`}, {330.`, 2.41838`}, {335.`,
2.41029`}, {340.`, 2.40475`}, {345.`, 2.40698`}, {350.`,
2.41066`}, {355.`, 2.40286`}, {360.`, 2.40045`}, {365.`,
2.38019`}, {370.`, 2.1133`}, {375.`, 2.74495`}, {380.`,
2.44314`}, {385.`, 2.23574`}, {390.`, 2.26553`}, {395.`,
2.28845`}, {400.`, 2.3039`}, {405.`, 2.32833`}, {410.`,
2.35769`}, {415.`, 2.36831`}, {420.`, 2.38712`}, {425.`,
2.39121`}, {430.`, 2.3947`}, {435.`, 2.39861`}, {440.`,
2.40759`}, {445.`, 2.41661`}, {450.`, 2.41583`}, {455.`,
2.41684`}, {460.`, 2.40925`}, {465.`, 2.40916`}, {470.`,
2.41589`}, {475.`, 2.41347`}, {480.`, 2.40624`}, {485.`,
2.40825`}, {490.`, 2.41021`}, {495.`, 2.40547`}, {500.`,
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2.40647`}, {520.`, 2.40802`}, {525.`, 2.41601`}, {530.`,
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2.38785`}, {550.`, 2.1242`}, {555.`, 2.74989`}, {560.`,
2.47186`}, {565.`, 2.22649`}, {570.`, 2.25904`}, {575.`,
2.27855`}, {580.`, 2.30019`}, {585.`, 2.31269`}, {590.`,
2.33149`}, {595.`, 2.35533`}, {600.`, 2.37581`}, {605.`,
2.38236`}, {610.`, 2.39662`}, {615.`, 2.38875`}, {620.`,
2.3945`}, {625.`, 2.40292`}, {630.`, 2.41223`}, {635.`,
2.41755`}, {640.`, 2.41581`}, {645.`, 2.42747`}, {650.`,
2.42243`}, {655.`, 2.40486`}, {660.`, 2.41097`}, {665.`,
2.41289`}, {670.`, 2.4112`}, {675.`, 2.41057`}, {680.`,
2.40854`}, {685.`, 2.40255`}, {690.`, 2.40663`}, {695.`,
2.41292`}, {700.`, 2.39958`}, {705.`, 2.40153`}, {710.`,
2.41089`}, {715.`, 2.41834`}, {720.`, 2.41014`}, {725.`,
2.38069`}, {730.`, 2.18214`}, {735.`, 2.78697`}, {740.`,
2.43799`}, {745.`, 2.2292`}, {750.`, 2.2685`}, {755.`,
2.27852`}, {760.`, 2.29429`}, {765.`, 2.31846`}, {770.`,
2.33485`}, {775.`, 2.34926`}, {780.`, 2.36237`}, {785.`,
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2.408`}, {820.`, 2.40672`}, {825.`, 2.4003`}, {830.`,
2.40356`}, {835.`, 2.40439`}, {840.`, 2.41256`}, {845.`,
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2.41221`}, {880.`, 2.41353`}, {885.`, 2.40919`}, {890.`,
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2.36319`}, {910.`, 2.232`}, {915.`, 2.83176`}, {920.`,
2.40338`}, {925.`, 2.24156`}, {930.`, 2.26923`}, {935.`,
2.27405`}, {940.`, 2.29832`}, {945.`, 2.32295`}, {950.`,
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2.39735`}, {1165.`, 2.40887`}, {1170.`, 2.40433`}, {1175.`,
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2.39176`}, {1225.`, 2.40127`}, {1230.`, 2.41093`}, {1235.`,
2.41167`}, {1240.`, 2.41547`}, {1245.`, 2.41724`}, {1250.`,
2.41734`}, {1255.`, 2.41807`}, {1260.`, 2.40711`}, {1265.`,
2.32865`}, {1270.`, 2.33615`}, {1275.`, 2.83364`}, {1280.`,
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2.30539`}, {1300.`, 2.30546`}, {1305.`, 2.32279`}, {1310.`,
2.34521`}, {1315.`, 2.35093`}, {1320.`, 2.36876`}, {1325.`,
2.38492`}, {1330.`, 2.38044`}, {1335.`, 2.38815`}, {1340.`,
2.38348`}, {1345.`, 2.40065`}, {1350.`, 2.39982`}, {1355.`,
2.39992`}, {1360.`, 2.4054`}, {1365.`, 2.40309`}, {1370.`,
2.40594`}, {1375.`, 2.4014`}, {1380.`, 2.40763`}, {1385.`,
2.40742`}, {1390.`, 2.40345`}, {1395.`, 2.41129`}, {1400.`,
2.41493`}, {1405.`, 2.41004`}, {1410.`, 2.41289`}, {1415.`,
2.41294`}, {1420.`, 2.4068`}, {1425.`, 2.4041`}, {1430.`,
2.39989`}, {1435.`, 2.41382`}, {1440.`, 2.4151`}, {1445.`,
2.28722`}, {1450.`, 2.41435`}, {1455.`, 2.8229`}, {1460.`,
2.34602`}, {1465.`, 2.27485`}, {1470.`, 2.28696`}, {1475.`,
2.30587`}, {1480.`, 2.32392`}, {1485.`, 2.33769`}, {1490.`,
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2.35091`}, {2020.`, 2.35177`}, {2025.`, 2.368`}, {2030.`,
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share|improve this question


















  • 1




    You could try LowpassFilter. For example, with y = data[[1 ;; 400, 2]] (to see better) and Manipulate[LowpassFilter[y, t] // ListLinePlot, {t, 0, 3}], you can see that t=0.375 is not a too bad choice (I got rid of the $x$ values so of course you should compensate for that).
    – anderstood
    Dec 12 at 22:18















up vote
3
down vote

favorite












I have experimental data with periodic sharp artefact spikes, which mask the real signal that could be seen as several negative peaks in the first third part on the curve:



enter image description here



Is it possible somehow to filter these spikes? or at least significantly reduce them? Here is data set:



data = {{5.`, 2.41204`}, {10.`, 2.40477`}, {15.`, 2.40154`}, {20.`, 
2.4094`}, {25.`, 2.41592`}, {30.`, 2.40706`}, {35.`,
2.41802`}, {40.`, 2.4171`}, {45.`, 2.40979`}, {50.`,
2.4127`}, {55.`, 2.40254`}, {60.`, 2.40753`}, {65.`,
2.41049`}, {70.`, 2.40521`}, {75.`, 2.40446`}, {80.`,
2.40692`}, {85.`, 2.40509`}, {90.`, 2.40604`}, {95.`,
2.40464`}, {100.`, 2.40448`}, {105.`, 2.41854`}, {110.`,
2.41627`}, {115.`, 2.40941`}, {120.`, 2.40443`}, {125.`,
2.39909`}, {130.`, 2.41194`}, {135.`, 2.40494`}, {140.`,
2.40801`}, {145.`, 2.41532`}, {150.`, 2.41512`}, {155.`,
2.41328`}, {160.`, 2.41383`}, {165.`, 2.40806`}, {170.`,
2.3958`}, {175.`, 2.41296`}, {180.`, 2.41556`}, {185.`,
2.40119`}, {190.`, 2.27056`}, {195.`, 2.51902`}, {200.`,
2.41532`}, {205.`, 2.36206`}, {210.`, 2.37837`}, {215.`,
2.38771`}, {220.`, 2.39959`}, {225.`, 2.40557`}, {230.`,
2.40373`}, {235.`, 2.4045`}, {240.`, 2.39692`}, {245.`,
2.38983`}, {250.`, 2.39646`}, {255.`, 2.40411`}, {260.`,
2.40749`}, {265.`, 2.41679`}, {270.`, 2.42152`}, {275.`,
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2.28845`}, {400.`, 2.3039`}, {405.`, 2.32833`}, {410.`,
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share|improve this question


















  • 1




    You could try LowpassFilter. For example, with y = data[[1 ;; 400, 2]] (to see better) and Manipulate[LowpassFilter[y, t] // ListLinePlot, {t, 0, 3}], you can see that t=0.375 is not a too bad choice (I got rid of the $x$ values so of course you should compensate for that).
    – anderstood
    Dec 12 at 22:18













up vote
3
down vote

favorite









up vote
3
down vote

favorite











I have experimental data with periodic sharp artefact spikes, which mask the real signal that could be seen as several negative peaks in the first third part on the curve:



enter image description here



Is it possible somehow to filter these spikes? or at least significantly reduce them? Here is data set:



data = {{5.`, 2.41204`}, {10.`, 2.40477`}, {15.`, 2.40154`}, {20.`, 
2.4094`}, {25.`, 2.41592`}, {30.`, 2.40706`}, {35.`,
2.41802`}, {40.`, 2.4171`}, {45.`, 2.40979`}, {50.`,
2.4127`}, {55.`, 2.40254`}, {60.`, 2.40753`}, {65.`,
2.41049`}, {70.`, 2.40521`}, {75.`, 2.40446`}, {80.`,
2.40692`}, {85.`, 2.40509`}, {90.`, 2.40604`}, {95.`,
2.40464`}, {100.`, 2.40448`}, {105.`, 2.41854`}, {110.`,
2.41627`}, {115.`, 2.40941`}, {120.`, 2.40443`}, {125.`,
2.39909`}, {130.`, 2.41194`}, {135.`, 2.40494`}, {140.`,
2.40801`}, {145.`, 2.41532`}, {150.`, 2.41512`}, {155.`,
2.41328`}, {160.`, 2.41383`}, {165.`, 2.40806`}, {170.`,
2.3958`}, {175.`, 2.41296`}, {180.`, 2.41556`}, {185.`,
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2.40346`}, {6535.`, 2.40558`}};









share|improve this question













I have experimental data with periodic sharp artefact spikes, which mask the real signal that could be seen as several negative peaks in the first third part on the curve:



enter image description here



Is it possible somehow to filter these spikes? or at least significantly reduce them? Here is data set:



data = {{5.`, 2.41204`}, {10.`, 2.40477`}, {15.`, 2.40154`}, {20.`, 
2.4094`}, {25.`, 2.41592`}, {30.`, 2.40706`}, {35.`,
2.41802`}, {40.`, 2.4171`}, {45.`, 2.40979`}, {50.`,
2.4127`}, {55.`, 2.40254`}, {60.`, 2.40753`}, {65.`,
2.41049`}, {70.`, 2.40521`}, {75.`, 2.40446`}, {80.`,
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2.40346`}, {6535.`, 2.40558`}};






filtering






share|improve this question













share|improve this question











share|improve this question




share|improve this question










asked Dec 12 at 21:25









Филипп Цветков

1,389721




1,389721








  • 1




    You could try LowpassFilter. For example, with y = data[[1 ;; 400, 2]] (to see better) and Manipulate[LowpassFilter[y, t] // ListLinePlot, {t, 0, 3}], you can see that t=0.375 is not a too bad choice (I got rid of the $x$ values so of course you should compensate for that).
    – anderstood
    Dec 12 at 22:18














  • 1




    You could try LowpassFilter. For example, with y = data[[1 ;; 400, 2]] (to see better) and Manipulate[LowpassFilter[y, t] // ListLinePlot, {t, 0, 3}], you can see that t=0.375 is not a too bad choice (I got rid of the $x$ values so of course you should compensate for that).
    – anderstood
    Dec 12 at 22:18








1




1




You could try LowpassFilter. For example, with y = data[[1 ;; 400, 2]] (to see better) and Manipulate[LowpassFilter[y, t] // ListLinePlot, {t, 0, 3}], you can see that t=0.375 is not a too bad choice (I got rid of the $x$ values so of course you should compensate for that).
– anderstood
Dec 12 at 22:18




You could try LowpassFilter. For example, with y = data[[1 ;; 400, 2]] (to see better) and Manipulate[LowpassFilter[y, t] // ListLinePlot, {t, 0, 3}], you can see that t=0.375 is not a too bad choice (I got rid of the $x$ values so of course you should compensate for that).
– anderstood
Dec 12 at 22:18










3 Answers
3






active

oldest

votes

















up vote
5
down vote














Is it possible somehow to filter these spikes?




In that question "filter" can be interpreted in several ways. Instead of signal filtering (used in the previous answers) you can identify and remove the outliers.



Import["https://raw.githubusercontent.com/antononcube/MathematicaForPrediction/master/OutlierIdentifiers.m"]

(* This finds the outliers positions. *)
otlPos = OutlierPosition[data[[All, 2]], SPLUSQuartileIdentifierParameters];

(* Plot the data in blue and the outliers in red. *)
Show[ListLinePlot[data, PlotRange -> All],
ListPlot[data[[otlPos]], PlotStyle -> {Red}]]


enter image description here



(* Plot the data with the outliers removed. *)
ListLinePlot[data[[Complement[Range[Length[data]], otlPos]]],
PlotRange -> All]


enter image description here






share|improve this answer






























    up vote
    4
    down vote













    You might try a "moving median". Unfortunately the decision for an optimal window width is "I'll know it when I see it" kinda thing. In other words, it takes subject matter expertise and restraint.



    Manipulate[
    ListPlot[Table[{data[[n, 1]], Median[data[[n - ww ;; n + ww, 2]]]},
    {n, ww + 1, Length[data] - ww}], Joined -> True, PlotRange -> All],
    {{ww, 2, "Window width"}, 2, 200, 2, Appearance -> "Labeled"}]


    Moving median and window width 2



    Moving median and window width 130






    share|improve this answer




























      up vote
      3
      down vote













      How about a running median filter?



      With[{
      time = Median /@ Partition[data[[All, 1]], 5, 1],
      ampl = Median /@ Partition[data[[All, 2]], 5, 1]},
      ListPlot[Transpose[{time, ampl}], Joined -> True, PlotRange -> All]]


      enter image description here






      share|improve this answer





















      • +1 Beat me by 30 seconds!
        – JimB
        Dec 12 at 22:21











      Your Answer





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      3 Answers
      3






      active

      oldest

      votes








      3 Answers
      3






      active

      oldest

      votes









      active

      oldest

      votes






      active

      oldest

      votes








      up vote
      5
      down vote














      Is it possible somehow to filter these spikes?




      In that question "filter" can be interpreted in several ways. Instead of signal filtering (used in the previous answers) you can identify and remove the outliers.



      Import["https://raw.githubusercontent.com/antononcube/MathematicaForPrediction/master/OutlierIdentifiers.m"]

      (* This finds the outliers positions. *)
      otlPos = OutlierPosition[data[[All, 2]], SPLUSQuartileIdentifierParameters];

      (* Plot the data in blue and the outliers in red. *)
      Show[ListLinePlot[data, PlotRange -> All],
      ListPlot[data[[otlPos]], PlotStyle -> {Red}]]


      enter image description here



      (* Plot the data with the outliers removed. *)
      ListLinePlot[data[[Complement[Range[Length[data]], otlPos]]],
      PlotRange -> All]


      enter image description here






      share|improve this answer



























        up vote
        5
        down vote














        Is it possible somehow to filter these spikes?




        In that question "filter" can be interpreted in several ways. Instead of signal filtering (used in the previous answers) you can identify and remove the outliers.



        Import["https://raw.githubusercontent.com/antononcube/MathematicaForPrediction/master/OutlierIdentifiers.m"]

        (* This finds the outliers positions. *)
        otlPos = OutlierPosition[data[[All, 2]], SPLUSQuartileIdentifierParameters];

        (* Plot the data in blue and the outliers in red. *)
        Show[ListLinePlot[data, PlotRange -> All],
        ListPlot[data[[otlPos]], PlotStyle -> {Red}]]


        enter image description here



        (* Plot the data with the outliers removed. *)
        ListLinePlot[data[[Complement[Range[Length[data]], otlPos]]],
        PlotRange -> All]


        enter image description here






        share|improve this answer

























          up vote
          5
          down vote










          up vote
          5
          down vote










          Is it possible somehow to filter these spikes?




          In that question "filter" can be interpreted in several ways. Instead of signal filtering (used in the previous answers) you can identify and remove the outliers.



          Import["https://raw.githubusercontent.com/antononcube/MathematicaForPrediction/master/OutlierIdentifiers.m"]

          (* This finds the outliers positions. *)
          otlPos = OutlierPosition[data[[All, 2]], SPLUSQuartileIdentifierParameters];

          (* Plot the data in blue and the outliers in red. *)
          Show[ListLinePlot[data, PlotRange -> All],
          ListPlot[data[[otlPos]], PlotStyle -> {Red}]]


          enter image description here



          (* Plot the data with the outliers removed. *)
          ListLinePlot[data[[Complement[Range[Length[data]], otlPos]]],
          PlotRange -> All]


          enter image description here






          share|improve this answer















          Is it possible somehow to filter these spikes?




          In that question "filter" can be interpreted in several ways. Instead of signal filtering (used in the previous answers) you can identify and remove the outliers.



          Import["https://raw.githubusercontent.com/antononcube/MathematicaForPrediction/master/OutlierIdentifiers.m"]

          (* This finds the outliers positions. *)
          otlPos = OutlierPosition[data[[All, 2]], SPLUSQuartileIdentifierParameters];

          (* Plot the data in blue and the outliers in red. *)
          Show[ListLinePlot[data, PlotRange -> All],
          ListPlot[data[[otlPos]], PlotStyle -> {Red}]]


          enter image description here



          (* Plot the data with the outliers removed. *)
          ListLinePlot[data[[Complement[Range[Length[data]], otlPos]]],
          PlotRange -> All]


          enter image description here







          share|improve this answer














          share|improve this answer



          share|improve this answer








          edited Dec 13 at 20:52

























          answered Dec 13 at 14:11









          Anton Antonov

          22.4k164111




          22.4k164111






















              up vote
              4
              down vote













              You might try a "moving median". Unfortunately the decision for an optimal window width is "I'll know it when I see it" kinda thing. In other words, it takes subject matter expertise and restraint.



              Manipulate[
              ListPlot[Table[{data[[n, 1]], Median[data[[n - ww ;; n + ww, 2]]]},
              {n, ww + 1, Length[data] - ww}], Joined -> True, PlotRange -> All],
              {{ww, 2, "Window width"}, 2, 200, 2, Appearance -> "Labeled"}]


              Moving median and window width 2



              Moving median and window width 130






              share|improve this answer

























                up vote
                4
                down vote













                You might try a "moving median". Unfortunately the decision for an optimal window width is "I'll know it when I see it" kinda thing. In other words, it takes subject matter expertise and restraint.



                Manipulate[
                ListPlot[Table[{data[[n, 1]], Median[data[[n - ww ;; n + ww, 2]]]},
                {n, ww + 1, Length[data] - ww}], Joined -> True, PlotRange -> All],
                {{ww, 2, "Window width"}, 2, 200, 2, Appearance -> "Labeled"}]


                Moving median and window width 2



                Moving median and window width 130






                share|improve this answer























                  up vote
                  4
                  down vote










                  up vote
                  4
                  down vote









                  You might try a "moving median". Unfortunately the decision for an optimal window width is "I'll know it when I see it" kinda thing. In other words, it takes subject matter expertise and restraint.



                  Manipulate[
                  ListPlot[Table[{data[[n, 1]], Median[data[[n - ww ;; n + ww, 2]]]},
                  {n, ww + 1, Length[data] - ww}], Joined -> True, PlotRange -> All],
                  {{ww, 2, "Window width"}, 2, 200, 2, Appearance -> "Labeled"}]


                  Moving median and window width 2



                  Moving median and window width 130






                  share|improve this answer












                  You might try a "moving median". Unfortunately the decision for an optimal window width is "I'll know it when I see it" kinda thing. In other words, it takes subject matter expertise and restraint.



                  Manipulate[
                  ListPlot[Table[{data[[n, 1]], Median[data[[n - ww ;; n + ww, 2]]]},
                  {n, ww + 1, Length[data] - ww}], Joined -> True, PlotRange -> All],
                  {{ww, 2, "Window width"}, 2, 200, 2, Appearance -> "Labeled"}]


                  Moving median and window width 2



                  Moving median and window width 130







                  share|improve this answer












                  share|improve this answer



                  share|improve this answer










                  answered Dec 12 at 22:20









                  JimB

                  16.7k12662




                  16.7k12662






















                      up vote
                      3
                      down vote













                      How about a running median filter?



                      With[{
                      time = Median /@ Partition[data[[All, 1]], 5, 1],
                      ampl = Median /@ Partition[data[[All, 2]], 5, 1]},
                      ListPlot[Transpose[{time, ampl}], Joined -> True, PlotRange -> All]]


                      enter image description here






                      share|improve this answer





















                      • +1 Beat me by 30 seconds!
                        – JimB
                        Dec 12 at 22:21















                      up vote
                      3
                      down vote













                      How about a running median filter?



                      With[{
                      time = Median /@ Partition[data[[All, 1]], 5, 1],
                      ampl = Median /@ Partition[data[[All, 2]], 5, 1]},
                      ListPlot[Transpose[{time, ampl}], Joined -> True, PlotRange -> All]]


                      enter image description here






                      share|improve this answer





















                      • +1 Beat me by 30 seconds!
                        – JimB
                        Dec 12 at 22:21













                      up vote
                      3
                      down vote










                      up vote
                      3
                      down vote









                      How about a running median filter?



                      With[{
                      time = Median /@ Partition[data[[All, 1]], 5, 1],
                      ampl = Median /@ Partition[data[[All, 2]], 5, 1]},
                      ListPlot[Transpose[{time, ampl}], Joined -> True, PlotRange -> All]]


                      enter image description here






                      share|improve this answer












                      How about a running median filter?



                      With[{
                      time = Median /@ Partition[data[[All, 1]], 5, 1],
                      ampl = Median /@ Partition[data[[All, 2]], 5, 1]},
                      ListPlot[Transpose[{time, ampl}], Joined -> True, PlotRange -> All]]


                      enter image description here







                      share|improve this answer












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                      answered Dec 12 at 22:19









                      John Doty

                      6,5641924




                      6,5641924












                      • +1 Beat me by 30 seconds!
                        – JimB
                        Dec 12 at 22:21


















                      • +1 Beat me by 30 seconds!
                        – JimB
                        Dec 12 at 22:21
















                      +1 Beat me by 30 seconds!
                      – JimB
                      Dec 12 at 22:21




                      +1 Beat me by 30 seconds!
                      – JimB
                      Dec 12 at 22:21


















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