3
$\begingroup$

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.`, 
2.37218`}, {790.`, 2.37895`}, {795.`, 2.38696`}, {800.`, 
2.39067`}, {805.`, 2.40635`}, {810.`, 2.40362`}, {815.`, 
2.408`}, {820.`, 2.40672`}, {825.`, 2.4003`}, {830.`, 
2.40356`}, {835.`, 2.40439`}, {840.`, 2.41256`}, {845.`, 
2.40369`}, {850.`, 2.40362`}, {855.`, 2.40254`}, {860.`, 
2.40808`}, {865.`, 2.41858`}, {870.`, 2.42083`}, {875.`, 
2.41221`}, {880.`, 2.41353`}, {885.`, 2.40919`}, {890.`, 
2.40225`}, {895.`, 2.40183`}, {900.`, 2.41031`}, {905.`, 
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.`, 
2.34304`}, {955.`, 2.35416`}, {960.`, 2.36042`}, {965.`, 
2.37545`}, {970.`, 2.37944`}, {975.`, 2.38077`}, {980.`, 
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2.38268`}, {1150.`, 2.39181`}, {1155.`, 2.39219`}, {1160.`, 
2.39735`}, {1165.`, 2.40887`}, {1170.`, 2.40433`}, {1175.`, 
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2.40641`}, {1195.`, 2.40956`}, {1200.`, 2.4138`}, {1205.`, 
2.42494`}, {1210.`, 2.41362`}, {1215.`, 2.40338`}, {1220.`, 
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.`, 
2.35782`}, {1285.`, 2.2653`}, {1290.`, 2.30087`}, {1295.`, 
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.`, 
2.34829`}, {1495.`, 2.35833`}, {1500.`, 2.36606`}, {1505.`, 
2.38031`}, {1510.`, 2.3882`}, {1515.`, 2.38575`}, {1520.`, 
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2.39511`}, {1705.`, 2.40145`}, {1710.`, 2.41432`}, {1715.`, 
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2.4009`}, {1795.`, 2.39214`}, {1800.`, 2.41367`}, {1805.`, 
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2.35331`}, {1825.`, 2.33172`}, {1830.`, 2.34277`}, {1835.`, 
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2.36269`}, {1855.`, 2.36324`}, {1860.`, 2.37877`}, {1865.`, 
2.38914`}, {1870.`, 2.39899`}, {1875.`, 2.41142`}, {1880.`, 
2.40601`}, {1885.`, 2.40194`}, {1890.`, 2.39789`}, {1895.`, 
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2.39888`}, {1915.`, 2.40384`}, {1920.`, 2.40937`}, {1925.`, 
2.40709`}, {1930.`, 2.3954`}, {1935.`, 2.41691`}, {1940.`, 
2.41117`}, {1945.`, 2.4113`}, {1950.`, 2.41505`}, {1955.`, 
2.41613`}, {1960.`, 2.39838`}, {1965.`, 2.41402`}, {1970.`, 
2.42415`}, {1975.`, 2.40659`}, {1980.`, 2.40548`}, {1985.`, 
2.21571`}, {1990.`, 2.65837`}, {1995.`, 2.73631`}, {2000.`, 
2.35978`}, {2005.`, 2.34484`}, {2010.`, 2.35112`}, {2015.`, 
2.35091`}, {2020.`, 2.35177`}, {2025.`, 2.368`}, {2030.`, 
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2.35285`}, {2200.`, 2.36043`}, {2205.`, 2.36718`}, {2210.`, 
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2.40045`}, {2410.`, 2.40662`}, {2415.`, 2.39452`}, {2420.`, 
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$\endgroup$
  • 1
    $\begingroup$ 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). $\endgroup$ – anderstood Dec 12 '18 at 22:18
5
$\begingroup$

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

$\endgroup$
4
$\begingroup$

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

$\endgroup$
3
$\begingroup$

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

$\endgroup$
  • $\begingroup$ +1 Beat me by 30 seconds! $\endgroup$ – JimB Dec 12 '18 at 22:21

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