(* Content-type: application/mathematica *)

(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)

(* CreatedBy='Mathematica 6.0' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       145,          7]
NotebookDataLength[     62007,       1434]
NotebookOptionsPosition[     58310,       1307]
NotebookOutlinePosition[     59641,       1352]
CellTagsIndexPosition[     59536,       1346]
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{

Cell[CellGroupData[{
Cell["\<\
Smoothing noisy digital signal
using moving average\
\>", "MainTitle",
 CellChangeTimes->{{3.413454371744011*^9, 3.413454378673976*^9}, {
   3.4134544243997264`*^9, 3.4134544498363028`*^9}, {3.413454504805344*^9, 
   3.413454541277789*^9}, {3.41347048347281*^9, 3.4134704905029182`*^9}, {
   3.4134705992292595`*^9, 3.4134706022836514`*^9}, {3.663079418413989*^9, 
   3.663079472650916*^9}, {3.6630795067775297`*^9, 3.6630795134184637`*^9}, 
   3.6630820289560575`*^9, {3.663082105475685*^9, 3.6630821373678117`*^9}, 
   3.663331430676668*^9},
 CellTags->"part-1"],

Cell[CellGroupData[{

Cell["Preparation", "MainSection",
 CellChangeTimes->{{3.6630800352221127`*^9, 3.6630800511447425`*^9}, {
   3.663080157446235*^9, 3.6630801589150505`*^9}, 3.6630813225628495`*^9, {
   3.66308175292638*^9, 3.663081787990533*^9}, {3.6630819956107454`*^9, 
   3.6630820075956545`*^9}, {3.663082999140499*^9, 3.6630830024219084`*^9}}],

Cell["\<\
The signal has some random noises. There are several methods to filter the \
noises (see NCIS...). Similar methods ar also used in image processing.
One of them, is the simple moving average. \
\>", "Text",
 CellChangeTimes->{{3.6630804049766436`*^9, 3.663080456604082*^9}, {
  3.6630807726648445`*^9, 3.663080849668091*^9}, {3.6630816946424675`*^9, 
  3.6630817768493886`*^9}, {3.6630827792235537`*^9, 3.6630829025422025`*^9}}],

Cell[CellGroupData[{

Cell["Digitalize and save the analogous signal", "Section",
 CellChangeTimes->{{3.413453734908286*^9, 3.413453738833931*^9}, {
  3.6630795666553497`*^9, 3.6630795811869516`*^9}, {3.663079798712512*^9, 
  3.6630798020095425`*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"analogsignal", "[", "t_", "]"}], ":=", 
   RowBox[{
    RowBox[{"Sin", "[", 
     RowBox[{"Pi", " ", "t"}], "]"}], "+", 
    RowBox[{"0.3", " ", 
     RowBox[{"Cos", "[", 
      RowBox[{"5", "Pi", " ", "t"}], "]"}]}]}]}], ";", 
  RowBox[{
   RowBox[{"randomsignal", "[", "t_", "]"}], ":=", 
   RowBox[{
    RowBox[{"Sin", "[", 
     RowBox[{"Pi", " ", "t"}], "]"}], "+", 
    RowBox[{"0.3", " ", 
     RowBox[{"Cos", "[", 
      RowBox[{"5", "Pi", " ", "t"}], "]"}]}], "+", 
    RowBox[{"RandomReal", "[", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"-", "0.3"}], ",", "0.3"}], "}"}], "]"}]}]}], ";"}]], "Input",
 CellChangeTimes->{{3.6630796442524233`*^9, 3.6630796723474874`*^9}, {
  3.6630824535380487`*^9, 3.663082480351244*^9}, {3.6630825128996534`*^9, 
  3.6630825216344366`*^9}, {3.6630825651833687`*^9, 3.663082626748762*^9}, {
  3.6630826706090574`*^9, 3.663082712282895*^9}}],

Cell[BoxData[{
 RowBox[{
  RowBox[{"dt", "=", "0.05"}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"signal", "=", 
   RowBox[{"Table", "[", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"t", ",", 
       RowBox[{"randomsignal", "[", "t", "]"}]}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"t", ",", "0", ",", "2", ",", "dt"}], "}"}]}], "]"}]}], 
  ";"}]}], "Input",
 CellChangeTimes->{{3.663079586796583*^9, 3.663079634361329*^9}, 
   3.6630797066772385`*^9, {3.663079738069343*^9, 3.6630797608201027`*^9}, {
   3.663080977236586*^9, 3.6630809780647507`*^9}, {3.663082494383151*^9, 
   3.6630824958988495`*^9}, 3.6630825486982117`*^9}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Show", "[", 
  RowBox[{
   RowBox[{"Plot", "[", 
    RowBox[{
     RowBox[{"analogsignal", "[", "t", "]"}], ",", 
     RowBox[{"{", 
      RowBox[{"t", ",", "0", ",", "2"}], "}"}]}], "]"}], ",", 
   RowBox[{"ListPlot", "[", "signal", "]"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.6630797745863667`*^9, 3.663079783430542*^9}, {
  3.663082636342967*^9, 3.6630826617492657`*^9}}],

Cell[BoxData[
 GraphicsBox[{{{}, {}, 
    {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], Opacity[
     1.], LineBox[CompressedData["
1:eJwUV3k81F8XFhVFi7InCkn2SiXbUQqhku0nURJZimxZK1Qke5aUJHvWkkoi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      "]]}}, {{}, {{}, 
     {RGBColor[0.368417, 0.506779, 0.709798], PointSize[
      0.012833333333333334`], AbsoluteThickness[1.6], PointBox[CompressedData["
1:eJxTTMoPSmViYGDQBGIQDQMV4d8Uf2xZaT9rJgistBf7p7iXrfMmlL/TXvvd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       "]]}, {}}, {}}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->{True, True},
  AxesLabel->{None, None},
  AxesOrigin->{0, 0},
  DisplayFunction->Identity,
  Frame->{{False, False}, {False, False}},
  FrameLabel->{{None, None}, {None, None}},
  FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}},
  GridLines->{None, None},
  GridLinesStyle->Directive[
    GrayLevel[0.5, 0.4]],
  Method->{
   "DefaultBoundaryStyle" -> Automatic, "DefaultMeshStyle" -> 
    AbsolutePointSize[6], "ScalingFunctions" -> None},
  PlotRange->{{0, 2}, {-1.2567174392745, 1.2567175448910282`}},
  PlotRangeClipping->True,
  PlotRangePadding->{{
     Scaled[0.02], 
     Scaled[0.02]}, {
     Scaled[0.05], 
     Scaled[0.05]}},
  Ticks->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{{3.6630826624055343`*^9, 3.663082717314371*^9}}]
}, Open  ]],

Cell[BoxData[
 RowBox[{
  RowBox[{"SetDirectory", "[", 
   RowBox[{"NotebookDirectory", "[", "]"}], "]"}], ";"}]], "Input",
 CellChangeTimes->{{3.663079808978613*^9, 3.663079834292307*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Export", "[", 
  RowBox[{"\"\<data//randomsignal.xlsx\>\"", ",", "signal"}], "]"}]], "Input",
 CellChangeTimes->{{3.663079849621154*^9, 3.663079887826089*^9}, {
  3.6630827280492725`*^9, 3.663082737080949*^9}}],

Cell[BoxData["\<\"data//randomsignal.xlsx\"\>"], "Output",
 CellChangeTimes->{
  3.6630798997016244`*^9, 3.6630809943155136`*^9, {3.6630810485822926`*^9, 
   3.6630810563326416`*^9}, 3.6630810896154604`*^9, 3.6630827451906786`*^9}]
}, Open  ]]
}, Closed]]
}, Closed]],

Cell[CellGroupData[{

Cell["The algorithm of Moving average", "MainSection",
 CellChangeTimes->{{3.6630829177460437`*^9, 3.6630829312623053`*^9}}],

Cell[CellGroupData[{

Cell["The  simplest way", "Section",
 CellChangeTimes->{{3.6630829909994946`*^9, 3.663083035000906*^9}, {
  3.663083239853795*^9, 3.6630832622142296`*^9}}],

Cell["Take the average of the elements in the neighborhood:", "Text",
 CellChangeTimes->{{3.6630829909994946`*^9, 3.663083035000906*^9}, {
  3.6630831252551727`*^9, 3.6630832225248585`*^9}, {3.6630832654331264`*^9, 
  3.663083266292548*^9}}],

Cell[TextData[{
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "j"], TraditionalForm]]],
 " \[Rule]",
 Cell[BoxData[
  FormBox[
   RowBox[{" ", 
    FractionBox[
     RowBox[{" ", 
      RowBox[{
       SubscriptBox["x", 
        RowBox[{"j", "-", "1"}]], "+", " ", 
       SubscriptBox["x", "j"], "+", " ", 
       SubscriptBox["x", 
        RowBox[{"j", "+", "1"}]]}]}], "3"]}], TraditionalForm]]],
 "   \t",
 Cell[BoxData[
  FormBox[
   RowBox[{"(", 
    RowBox[{
     RowBox[{"j", "=", "2"}], ",", "...", ",", " ", 
     RowBox[{"n", "-", "1"}]}], ")"}], TraditionalForm]],
  FormatType->"TraditionalForm"]
}], "Text",
 CellChangeTimes->{{3.6630829909994946`*^9, 3.663083035000906*^9}, {
  3.6630831252551727`*^9, 3.6630832225248585`*^9}, {3.6630832696051974`*^9, 
  3.663083285059051*^9}, {3.6630835298359923`*^9, 3.6630835544762487`*^9}}]
}, Open  ]],

Cell[CellGroupData[{

Cell["The  weighted average", "Section",
 CellChangeTimes->{{3.6630829909994946`*^9, 3.663083035000906*^9}, {
  3.663083239853795*^9, 3.663083247229143*^9}}],

Cell["\<\
Take the weighted average of the elements in the neighborhood:\
\>", "Text",
 CellChangeTimes->{{3.6630829909994946`*^9, 3.663083035000906*^9}, {
  3.6630831252551727`*^9, 3.6630832225248585`*^9}}],

Cell[TextData[{
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "j"], TraditionalForm]]],
 " \[Rule]",
 Cell[BoxData[
  FormBox[
   RowBox[{" ", 
    FractionBox[
     RowBox[{
      RowBox[{
       SubscriptBox["w", 
        RowBox[{"-", "1"}]], " ", 
       SubscriptBox["x", 
        RowBox[{"j", "-", "1"}]]}], "+", " ", 
      RowBox[{
       SubscriptBox["w", "0"], 
       SubscriptBox["x", "j"]}], "+", " ", 
      RowBox[{
       SubscriptBox["w", "1"], 
       SubscriptBox["x", 
        RowBox[{"j", "+", "1"}]]}]}], 
     RowBox[{
      SubscriptBox["w", 
       RowBox[{"-", "1"}]], "+", 
      SubscriptBox["w", "0"], "+", 
      SubscriptBox["w", "1"]}]]}], TraditionalForm]]],
 "   \t",
 Cell[BoxData[
  FormBox[
   RowBox[{"(", 
    RowBox[{
     RowBox[{"j", "=", "2"}], ",", "...", ",", " ", 
     RowBox[{"n", "-", "1"}]}], ")"}], TraditionalForm]]]
}], "Text",
 CellChangeTimes->{{3.6630829909994946`*^9, 3.663083035000906*^9}, {
  3.6630831252551727`*^9, 3.6630832225248585`*^9}, {3.663083475833455*^9, 
  3.6630834774116535`*^9}, {3.6630835150696692`*^9, 3.66308352071056*^9}, {
  3.6630835666643214`*^9, 3.663083579743037*^9}, {3.6630836121508408`*^9, 
  3.6630836121508408`*^9}}]
}, Open  ]],

Cell[CellGroupData[{

Cell["The  general weighted average", "Section",
 CellChangeTimes->{{3.6630829909994946`*^9, 3.663083035000906*^9}, {
  3.663083239853795*^9, 3.663083247229143*^9}, {3.663083303856815*^9, 
  3.6630833056850224`*^9}}],

Cell["\<\
Take the weighted average of the elements in the neighborhood of length k:\
\>", "Text",
 CellChangeTimes->{{3.6630829909994946`*^9, 3.663083035000906*^9}, {
  3.6630831252551727`*^9, 3.6630832225248585`*^9}, {3.6630833329675617`*^9, 
  3.6630833417336006`*^9}}],

Cell[BoxData[
 FormBox[
  RowBox[{
   SubscriptBox["x", "j"], " ", "\[Rule]", " ", 
   RowBox[{
    FractionBox[
     RowBox[{
      UnderoverscriptBox["\[Sum]", 
       RowBox[{"i", "=", 
        RowBox[{"-", "k"}]}], "k"], 
      RowBox[{
       SubscriptBox["w", "i"], " ", 
       SubscriptBox["x", 
        RowBox[{"j", "-", "i"}]]}]}], 
     RowBox[{
      UnderoverscriptBox["\[Sum]", 
       RowBox[{"i", "=", 
        RowBox[{"-", "k"}]}], "k"], 
      SubscriptBox["w", 
       RowBox[{"-", "i"}]], " "}]], "   \t", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{"j", "=", 
       RowBox[{"k", "+", "1"}]}], ",", "...", ",", " ", 
      RowBox[{"n", "-", "k", "-", "1"}]}], ")"}]}]}], 
  TraditionalForm]], "DisplayFormula",
 CellChangeTimes->{{3.6630829909994946`*^9, 3.663083035000906*^9}, {
   3.6630831252551727`*^9, 3.6630832225248585`*^9}, {3.663083359140649*^9, 
   3.6630834588638954`*^9}, {3.6630834919123325`*^9, 3.663083499631451*^9}, 
   3.663083599869006*^9}]
}, Open  ]]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["", "SlideShowNavigationBar",
 CellTags->"SlideShowHeader"],

Cell[CellGroupData[{

Cell["Apply the algorithm", "MainSection",
 CellChangeTimes->{{3.6630836722005386`*^9, 3.6630836767476325`*^9}}],

Cell["Apply the averaging method:", "Text",
 CellChangeTimes->{{3.4140878726552577`*^9, 3.414087905893051*^9}, {
  3.663083714343154*^9, 3.6630837145306535`*^9}}],

Cell[CellGroupData[{

Cell["Data import from Excel", "Section",
 CellChangeTimes->{{3.413453734908286*^9, 3.413453738833931*^9}, {
  3.663079945452281*^9, 3.663079948061776*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{"SetDirectory", "[", 
   RowBox[{"NotebookDirectory", "[", "]"}], "]"}], ";"}]], "Input",
 CellChangeTimes->{{3.663079808978613*^9, 3.663079834292307*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"randomdata", "=", 
  RowBox[{
   RowBox[{"Import", "[", "\"\<data//randomsignal.xlsx\>\"", "]"}], "[", 
   RowBox[{"[", "1", "]"}], "]"}]}]], "Input",
 CellChangeTimes->{{3.663079849621154*^9, 3.663079887826089*^9}, {
  3.663079982391522*^9, 3.6630800058457427`*^9}, {3.6630827546599016`*^9, 
  3.6630827556911964`*^9}, {3.6630837263761296`*^9, 3.663083728063733*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"0.`", ",", "0.05020881094530599`"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0.05`", ",", "0.3989884230613553`"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0.1`", ",", "0.387768272135619`"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0.15000000000000002`", ",", "0.4125212090694186`"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0.2`", ",", "0.34277016883179695`"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0.25`", ",", "0.2876337427784966`"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0.30000000000000004`", ",", "0.8522244422404938`"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0.35000000000000003`", ",", "1.3167812212126129`"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0.4`", ",", "1.2562266984086854`"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0.45`", ",", "0.9327723392955614`"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0.5`", ",", "1.0300496098644811`"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0.55`", ",", "0.5358168029296169`"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0.6000000000000001`", ",", "0.8784013239975694`"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0.65`", ",", "0.8986743128371504`"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0.7000000000000001`", ",", "0.9904193894540598`"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0.75`", ",", "1.061452752706311`"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0.8`", ",", "1.0901752526100827`"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0.8500000000000001`", ",", "0.6710086862439532`"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0.9`", ",", "0.21247289703046957`"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0.9500000000000001`", ",", 
     RowBox[{"-", "0.04042445142644285`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1.`", ",", 
     RowBox[{"-", "0.1764932222863303`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1.05`", ",", 
     RowBox[{"-", "0.5734927263569197`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1.1`", ",", 
     RowBox[{"-", "0.5986615827328186`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1.1500000000000001`", ",", 
     RowBox[{"-", "0.001483985458080761`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1.2000000000000002`", ",", 
     RowBox[{"-", "0.21823179408259435`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1.25`", ",", 
     RowBox[{"-", "0.2660659373909254`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1.3`", ",", 
     RowBox[{"-", "0.5543010443040204`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1.35`", ",", 
     RowBox[{"-", "1.2786054195393501`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1.4000000000000001`", ",", 
     RowBox[{"-", "1.353476207215398`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1.4500000000000002`", ",", 
     RowBox[{"-", "1.236678958581745`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1.5`", ",", 
     RowBox[{"-", "1.237048985874879`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1.55`", ",", 
     RowBox[{"-", "0.8201987364133096`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1.6`", ",", 
     RowBox[{"-", "0.5276254614557605`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1.6500000000000001`", ",", 
     RowBox[{"-", "0.6283498275377862`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1.7000000000000002`", ",", 
     RowBox[{"-", "0.7653169799595918`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1.75`", ",", 
     RowBox[{"-", "0.7517140613853441`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1.8`", ",", 
     RowBox[{"-", "1.120424357444063`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1.85`", ",", 
     RowBox[{"-", "0.5919448126527974`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1.9000000000000001`", ",", 
     RowBox[{"-", "0.5990018148019106`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1.9500000000000002`", ",", 
     RowBox[{"-", "0.11688582183272275`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"2.`", ",", "0.08512937597897025`"}], "}"}]}], "}"}]], "Output",
 CellChangeTimes->{
  3.6630798997016244`*^9, {3.6630799992204175`*^9, 3.6630800070332813`*^9}, 
   3.663081118163678*^9, 3.6630827568787303`*^9, 3.6630837301263103`*^9, 
   3.664046876882169*^9, 3.681140498733321*^9}]
}, Open  ]],

Cell["First we recall how to fill in lists of experimental data.", "Text",
 CellChangeTimes->{{3.4134537016104064`*^9, 3.413453714418824*^9}, {
  3.4134539626056995`*^9, 3.4134539796301794`*^9}}]
}, Open  ]],

Cell[CellGroupData[{

Cell["A random list", "Section"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"p", "=", 
  RowBox[{"ListPlot", "[", "randomdata", "]"}]}]], "Input",
 CellChangeTimes->{
  3.391399998185582*^9, {3.6630837454082937`*^9, 3.663083747517776*^9}}],

Cell[BoxData[
 GraphicsBox[{{}, {{}, 
    {RGBColor[0.368417, 0.506779, 0.709798], PointSize[0.012833333333333334`],
      AbsoluteThickness[1.6], PointBox[CompressedData["
1:eJxTTMoPSmViYGDQBGIQDQMV4d8Uf2xZaT9rJgistBf7p7iXrfMmlL/TXvvd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      "]]}, {}}, {}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->{True, True},
  AxesLabel->{None, None},
  AxesOrigin->{0, 0},
  DisplayFunction->Identity,
  Frame->{{False, False}, {False, False}},
  FrameLabel->{{None, None}, {None, None}},
  FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}},
  GridLines->{None, None},
  GridLinesStyle->Directive[
    GrayLevel[0.5, 0.4]],
  ImagePadding->All,
  Method->{"CoordinatesToolOptions" -> {"DisplayFunction" -> ({
        (Part[{{Identity, Identity}, {Identity, Identity}}, 1, 2][#]& )[
         Part[#, 1]], 
        (Part[{{Identity, Identity}, {Identity, Identity}}, 2, 2][#]& )[
         Part[#, 2]]}& ), "CopiedValueFunction" -> ({
        (Part[{{Identity, Identity}, {Identity, Identity}}, 1, 2][#]& )[
         Part[#, 1]], 
        (Part[{{Identity, Identity}, {Identity, Identity}}, 2, 2][#]& )[
         Part[#, 2]]}& )}},
  PlotRange->{{0, 2.}, {-1.353476207215398, 1.3167812212126129`}},
  PlotRangeClipping->True,
  PlotRangePadding->{{
     Scaled[0.02], 
     Scaled[0.02]}, {
     Scaled[0.05], 
     Scaled[0.05]}},
  Ticks->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{
  3.391399999187022*^9, 3.3991412322536416`*^9, 3.3995495108860064`*^9, 
   3.3995495694702463`*^9, 3.6630837486115575`*^9, 3.663083913040161*^9, {
   3.6811404989182234`*^9, 3.6811405054981384`*^9}}]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["The averaging", "Section"],

Cell[BoxData[
 RowBox[{
  RowBox[{"k", "=", "1"}], ";"}]], "Input",
 CellChangeTimes->{{3.663083885758666*^9, 3.6630838922589626`*^9}, {
  3.6630841446135077`*^9, 3.6630841531920357`*^9}, {3.66308425696255*^9, 
  3.6630842697747927`*^9}, {3.663084337918626*^9, 3.663084346184643*^9}, {
  3.681140541192773*^9, 3.681140541508421*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"smootheddata", "=", 
  RowBox[{"Table", "[", 
   RowBox[{
    RowBox[{
     RowBox[{"(", 
      RowBox[{"Apply", "[", 
       RowBox[{"Plus", ",", 
        RowBox[{"Take", "[", 
         RowBox[{"randomdata", ",", 
          RowBox[{"{", 
           RowBox[{
            RowBox[{"j", "-", "k"}], ",", 
            RowBox[{"j", "+", "k"}]}], "}"}]}], "]"}]}], "]"}], ")"}], "/", 
     RowBox[{"(", 
      RowBox[{
       RowBox[{"2", "k"}], "+", "1"}], ")"}]}], ",", 
    RowBox[{"{", 
     RowBox[{"j", ",", 
      RowBox[{"k", "+", "1"}], ",", 
      RowBox[{
       RowBox[{"Length", "[", "randomdata", "]"}], "-", "k", "-", "1"}]}], 
     "}"}]}], "]"}]}]], "Input",
 CellChangeTimes->{{3.6630838319904985`*^9, 3.6630838522570877`*^9}, {
  3.663083952823306*^9, 3.6630840915953803`*^9}, {3.663084130440955*^9, 
  3.663084234414613*^9}, {3.663084352809951*^9, 3.663084355825732*^9}, {
  3.6630844315636697`*^9, 3.663084440735977*^9}, {3.6630883224421444`*^9, 
  3.6630883301300015`*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"0.05`", ",", "0.27898850204742676`"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0.1`", ",", "0.3997593014221309`"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0.15`", ",", "0.38101988334561154`"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0.2`", ",", "0.3476417068932374`"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0.25`", ",", "0.4942094512835958`"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0.30000000000000004`", ",", "0.818879802077201`"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0.3500000000000001`", ",", "1.1417441206205972`"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0.39999999999999997`", ",", "1.1685934196389531`"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0.45`", ",", "1.0730162158562426`"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0.5`", ",", "0.8328795840298865`"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0.55`", ",", "0.8147559122638892`"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0.6000000000000001`", ",", "0.7709641465881122`"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0.65`", ",", "0.9224983420962598`"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0.7`", ",", "0.9835154849991736`"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0.75`", ",", "1.047349131590151`"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0.8`", ",", "0.9408788971867823`"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0.8500000000000001`", ",", "0.6578856119615017`"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0.9`", ",", "0.2810190439493266`"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0.95`", ",", 
     RowBox[{"-", "0.0014815922274345286`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1.`", ",", 
     RowBox[{"-", "0.2634701333565643`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1.0499999999999998`", ",", 
     RowBox[{"-", "0.4495491771253562`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1.1`", ",", 
     RowBox[{"-", "0.391212764849273`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1.15`", ",", 
     RowBox[{"-", "0.2727924540911646`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1.2000000000000002`", ",", 
     RowBox[{"-", "0.16192723897720016`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1.25`", ",", 
     RowBox[{"-", "0.3461995919258467`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1.2999999999999998`", ",", 
     RowBox[{"-", "0.6996574670780986`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1.35`", ",", 
     RowBox[{"-", "1.0621275570195894`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1.4`", ",", 
     RowBox[{"-", "1.2895868617788309`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1.4500000000000002`", ",", 
     RowBox[{"-", "1.2757347172240074`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1.5`", ",", 
     RowBox[{"-", "1.097975560289978`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1.55`", ",", 
     RowBox[{"-", "0.8616243945813162`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1.6`", ",", 
     RowBox[{"-", "0.6587246751356188`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1.65`", ",", 
     RowBox[{"-", "0.6404307563177127`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1.7000000000000002`", ",", 
     RowBox[{"-", "0.7151269562942406`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1.75`", ",", 
     RowBox[{"-", "0.879151799596333`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1.8`", ",", 
     RowBox[{"-", "0.8213610771607348`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1.85`", ",", 
     RowBox[{"-", "0.770456994966257`"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1.9`", ",", 
     RowBox[{"-", "0.43594414976247686`"}]}], "}"}]}], "}"}]], "Output",
 CellChangeTimes->{{3.6630842189607334`*^9, 3.6630842353365097`*^9}, 
   3.6630842735405765`*^9, 3.663084356997635*^9, 3.663084441407858*^9, 
   3.6640468843825207`*^9, 3.68114054447853*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"p1", "=", 
   RowBox[{"ListPlot", "[", 
    RowBox[{"smootheddata", ",", 
     RowBox[{"PlotStyle", "\[Rule]", 
      RowBox[{"{", 
       RowBox[{"Hue", "[", "0", "]"}], "}"}]}]}], "]"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{"Show", "[", 
  RowBox[{"p", ",", "p1"}], "]"}]}], "Input",
 CellChangeTimes->{{3.391400010112733*^9, 3.391400015800912*^9}, 
   3.663083862538822*^9, 3.663084374420353*^9}],

Cell[BoxData[
 GraphicsBox[{{{}, {{}, 
     {RGBColor[0.368417, 0.506779, 0.709798], PointSize[
      0.012833333333333334`], AbsoluteThickness[1.6], PointBox[CompressedData["
1:eJxTTMoPSmViYGDQBGIQDQMV4d8Uf2xZaT9rJgistBf7p7iXrfMmlL/TXvvd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       "]]}, {}}, {}}, {{}, {{}, 
     {Hue[0, 1, 1], PointSize[0.012833333333333334`], AbsoluteThickness[1.6], 
      PointBox[CompressedData["
1:eJxTTMoPSmViYGBQA2IQPWsmCKy0F7AVmP7p1kV7CH+n/Sz/Cs4VU2/aG4PB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       "]]}, {}}, {}}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->{True, True},
  AxesLabel->{None, None},
  AxesOrigin->{0, 0},
  DisplayFunction->Identity,
  Frame->{{False, False}, {False, False}},
  FrameLabel->{{None, None}, {None, None}},
  FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}},
  GridLines->{None, None},
  GridLinesStyle->Directive[
    GrayLevel[0.5, 0.4]],
  ImagePadding->All,
  Method->{"CoordinatesToolOptions" -> {"DisplayFunction" -> ({
        (Part[{{Identity, Identity}, {Identity, Identity}}, 1, 2][#]& )[
         Part[#, 1]], 
        (Part[{{Identity, Identity}, {Identity, Identity}}, 2, 2][#]& )[
         Part[#, 2]]}& ), "CopiedValueFunction" -> ({
        (Part[{{Identity, Identity}, {Identity, Identity}}, 1, 2][#]& )[
         Part[#, 1]], 
        (Part[{{Identity, Identity}, {Identity, Identity}}, 2, 2][#]& )[
         Part[#, 2]]}& )}},
  PlotRange->{{0, 2.}, {-1.353476207215398, 1.3167812212126129`}},
  PlotRangeClipping->True,
  PlotRangePadding->{{
     Scaled[0.02], 
     Scaled[0.02]}, {
     Scaled[0.05], 
     Scaled[0.05]}},
  Ticks->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{{3.3914000108638124`*^9, 3.3914000165720205`*^9}, 
   3.399141250950526*^9, 3.3995495206500463`*^9, 3.399549578433134*^9, 
   3.663083863226331*^9, 3.663083897477946*^9, 3.6630842808221664`*^9, {
   3.6630843593883734`*^9, 3.6630843753578873`*^9}, 3.6630844446267643`*^9, 
   3.6811405487493925`*^9}]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["Change the averaging window", "Section",
 CellChangeTimes->{{3.6630843833426504`*^9, 3.663084406421846*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Manipulate", "[", "\[IndentingNewLine]", 
  RowBox[{
   RowBox[{"Show", "[", 
    RowBox[{
     RowBox[{"ListPlot", "[", "randomdata", "]"}], ",", "\[IndentingNewLine]", 
     RowBox[{"Graphics", "[", 
      RowBox[{"{", 
       RowBox[{"Red", ",", 
        RowBox[{"Point", "[", 
         RowBox[{"Table", "[", 
          RowBox[{
           RowBox[{
            RowBox[{"(", 
             RowBox[{"Apply", "[", 
              RowBox[{"Plus", ",", 
               RowBox[{"Take", "[", 
                RowBox[{"randomdata", ",", 
                 RowBox[{"{", 
                  RowBox[{
                   RowBox[{"j", "-", "k"}], ",", 
                   RowBox[{"j", "+", "k"}]}], "}"}]}], "]"}]}], "]"}], ")"}], 
            "/", 
            RowBox[{"(", 
             RowBox[{
              RowBox[{"2", "k"}], "+", "1"}], ")"}]}], ",", 
           RowBox[{"{", 
            RowBox[{"j", ",", 
             RowBox[{"k", "+", "1"}], ",", 
             RowBox[{
              RowBox[{"Length", "[", "randomdata", "]"}], "-", "k", "-", 
              "1"}]}], "}"}]}], "]"}], "]"}]}], "}"}], "]"}]}], "]"}], ",", 
   "\[IndentingNewLine]", 
   RowBox[{"{", 
    RowBox[{"k", ",", "0", ",", " ", "5", ",", "1"}], "}"}], ",", 
   RowBox[{"SaveDefinitions", "\[Rule]", "True"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.66308445765879*^9, 3.663084524974464*^9}, {
  3.6630845590229473`*^9, 3.6630846307449737`*^9}, {3.663084669778058*^9, 
  3.6630846732157288`*^9}, {3.664046861303322*^9, 3.664046868334903*^9}}],

Cell[BoxData[
 TagBox[
  StyleBox[
   DynamicModuleBox[{$CellContext`k$$ = 2, Typeset`show$$ = True, 
    Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", 
    Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = 
    "\"untitled\"", Typeset`specs$$ = {{
      Hold[$CellContext`k$$], 0, 5, 1}}, Typeset`size$$ = {
    558., {163., 175.}}, Typeset`update$$ = 0, Typeset`initDone$$, 
    Typeset`skipInitDone$$ = False, $CellContext`k$41121$$ = 0}, 
    DynamicBox[Manipulate`ManipulateBoxes[
     1, StandardForm, "Variables" :> {$CellContext`k$$ = 0}, 
      "ControllerVariables" :> {
        Hold[$CellContext`k$$, $CellContext`k$41121$$, 0]}, 
      "OtherVariables" :> {
       Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, 
        Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, 
        Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$,
         Typeset`skipInitDone$$}, "Body" :> Show[
        ListPlot[$CellContext`randomdata], 
        Graphics[{Red, 
          Point[
           Table[Apply[Plus, 
              
              Take[$CellContext`randomdata, {$CellContext`j - \
$CellContext`k$$, $CellContext`j + $CellContext`k$$}]]/(2 $CellContext`k$$ + 
            1), {$CellContext`j, $CellContext`k$$ + 1, 
             Length[$CellContext`randomdata] - $CellContext`k$$ - 1}]]}]], 
      "Specifications" :> {{$CellContext`k$$, 0, 5, 1}}, "Options" :> {}, 
      "DefaultOptions" :> {}],
     ImageSizeCache->{638., {235., 248.}},
     SingleEvaluation->True],
    Deinitialization:>None,
    DynamicModuleValues:>{},
    Initialization:>({$CellContext`randomdata = CompressedData["
1:eJxTTMoPSmViYGDQBGIQDQMV4d8Uf2xZaT9rJgistBf7p7iXrfMmlL/TXvvd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        "], $CellContext`k$$ = 2}; Typeset`initDone$$ = True),
    SynchronousInitialization->True,
    UndoTrackedVariables:>{Typeset`show$$, Typeset`bookmarkMode$$},
    UnsavedVariables:>{Typeset`initDone$$},
    UntrackedVariables:>{Typeset`size$$}], "Manipulate",
   Deployed->True,
   StripOnInput->False],
  Manipulate`InterpretManipulate[1]]], "Output",
 CellChangeTimes->{
  3.663084525599472*^9, {3.6630845595385685`*^9, 3.663084586242955*^9}, {
   3.663084623432207*^9, 3.6630846317918797`*^9}, 3.6630846765752354`*^9, 
   3.664046890867202*^9}]
}, Open  ]]
}, Open  ]]
}, Open  ]]
}, Open  ]],

Cell["", "SlideShowNavigationBar",
 CellTags->"SlideShowHeader"]
},
AutoGeneratedPackage->None,
ScreenStyleEnvironment->"SlideShow",
WindowSize->{1280, 677},
WindowMargins->{{-8, Automatic}, {Automatic, 0}},
PrintingCopies->1,
PrintingPageRange->{Automatic, Automatic},
PageHeaders->{{Inherited, Inherited, 
   Cell[
    TextData[{"Impulz\[IAcute]v jelens\[EAcute]gek matematikai modelljei"}], 
    "Header"]}, {
   Cell[
    TextData[{
     "Adatbevitel, \[AAcute]br\[AAcute]zol\[AAcute]s, transzform\[AAcute]ci\
\[OAcute]k"}], "Header"], Inherited, Inherited}},
PrintingOptions->{"FirstPageFace"->Left,
"PrintCellBrackets"->False,
"PrintMultipleHorizontalPages"->False,
"PrintRegistrationMarks"->False,
"PrintingMargins"->{{54, 54}, {54, 54}}},
Magnification:>1.55 Inherited,
FrontEndVersion->"10.4 for Microsoft Windows (64-bit) (February 25, 2016)",
StyleDefinitions->"Modelstyle-EN.nb"
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{
 "part-1"->{
  Cell[567, 22, 574, 11, 206, "MainTitle",
   CellTags->"part-1"]},
 "SlideShowHeader"->{
  Cell[36418, 745, 64, 1, 1, "SlideShowNavigationBar",
   CellTags->"SlideShowHeader"],
  Cell[58242, 1304, 64, 1, 1, "SlideShowNavigationBar",
   CellTags->"SlideShowHeader"]}
 }
*)
(*CellTagsIndex
CellTagsIndex->{
 {"part-1", 59245, 1335},
 {"SlideShowHeader", 59335, 1338}
 }
*)
(*NotebookFileOutline
Notebook[{
Cell[CellGroupData[{
Cell[567, 22, 574, 11, 206, "MainTitle",
 CellTags->"part-1"],
Cell[CellGroupData[{
Cell[1166, 37, 331, 4, 85, "MainSection"],
Cell[1500, 43, 438, 7, 189, "Text"],
Cell[CellGroupData[{
Cell[1963, 54, 229, 3, 125, "Section"],
Cell[2195, 59, 938, 25, 418, "Input"],
Cell[3136, 86, 648, 16, 418, "Input"],
Cell[CellGroupData[{
Cell[3809, 106, 402, 10, 303, "Input"],
Cell[4214, 118, 26867, 452, 1489, "Output"]
}, Open  ]],
Cell[31096, 573, 189, 4, 220, "Input"],
Cell[CellGroupData[{
Cell[31310, 581, 234, 4, 303, "Input"],
Cell[31547, 587, 231, 3, 175, "Output"]
}, Open  ]]
}, Closed]]
}, Closed]],
Cell[CellGroupData[{
Cell[31839, 597, 124, 1, 85, "MainSection"],
Cell[CellGroupData[{
Cell[31988, 602, 155, 2, 85, "Section"],
Cell[32146, 606, 241, 3, 66, "Text"],
Cell[32390, 611, 844, 27, 83, "Text"]
}, Open  ]],
Cell[CellGroupData[{
Cell[33271, 643, 157, 2, 85, "Section"],
Cell[33431, 647, 207, 4, 66, "Text"],
Cell[33641, 653, 1203, 39, 89, "Text"]
}, Open  ]],
Cell[CellGroupData[{
Cell[34881, 697, 216, 3, 85, "Section"],
Cell[35100, 702, 272, 5, 66, "Text"],
Cell[35375, 709, 982, 29, 110, "DisplayFormula"]
}, Open  ]]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[36418, 745, 64, 1, 1, "SlideShowNavigationBar",
 CellTags->"SlideShowHeader"],
Cell[CellGroupData[{
Cell[36507, 750, 112, 1, 84, "MainSection"],
Cell[36622, 753, 162, 2, 66, "Text"],
Cell[CellGroupData[{
Cell[36809, 759, 156, 2, 84, "Section"],
Cell[36968, 763, 189, 4, 94, "Input"],
Cell[CellGroupData[{
Cell[37182, 771, 392, 7, 94, "Input"],
Cell[37577, 780, 4233, 109, 590, "Output"]
}, Open  ]],
Cell[41825, 892, 195, 2, 66, "Text"]
}, Open  ]],
Cell[CellGroupData[{
Cell[42057, 899, 32, 0, 84, "Section"],
Cell[CellGroupData[{
Cell[42114, 903, 186, 4, 94, "Input"],
Cell[42303, 909, 2257, 49, 389, "Output"]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[44609, 964, 32, 0, 84, "Section"],
Cell[44644, 966, 333, 6, 94, "Input"],
Cell[CellGroupData[{
Cell[45002, 976, 1013, 27, 173, "Input"],
Cell[46018, 1005, 3871, 101, 551, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[49926, 1111, 443, 12, 134, "Input"],
Cell[50372, 1125, 3171, 64, 389, "Output"]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[53592, 1195, 114, 1, 84, "Section"],
Cell[CellGroupData[{
Cell[53731, 1200, 1537, 38, 290, "Input"],
Cell[55271, 1240, 2920, 58, 536, "Output"]
}, Open  ]]
}, Open  ]]
}, Open  ]]
}, Open  ]],
Cell[58242, 1304, 64, 1, 1, "SlideShowNavigationBar",
 CellTags->"SlideShowHeader"]
}
]
*)

