ch5-delta-sigma.nb

(* Content-type: application/vnd.wolfram.mathematica *)

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

(* CreatedBy='Mathematica 11.2' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       158,          7]
NotebookDataLength[     21908,        551]
NotebookOptionsPosition[     20698,        521]
NotebookOutlinePosition[     21059,        537]
CellTagsIndexPosition[     21016,        534]
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{

Cell[CellGroupData[{
Cell[BoxData[{
 RowBox[{
  RowBox[{
   RowBox[{"ntf", "[", "z_", "]"}], ":=", 
   RowBox[{"1", "-", 
    SuperscriptBox["z", 
     RowBox[{"-", "1"}]]}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{"FullSimplify", "[", 
  RowBox[{"ComplexExpand", "[", 
   RowBox[{"Abs", "[", 
    RowBox[{"ntf", "[", 
     SuperscriptBox["\[ExponentialE]", 
      RowBox[{"\[ImaginaryI]", " ", "\[CapitalOmega]"}]], "]"}], "]"}], "]"}],
   "]"}]}], "Input",
 CellChangeTimes->{{3.763811753678162*^9, 3.7638117724604883`*^9}, {
  3.7638118054978848`*^9, 3.763811809055004*^9}, {3.7638126871121397`*^9, 
  3.7638127422481747`*^9}},ExpressionUUID->"ba026b09-4388-4ba4-be80-\
4a262248cca2"],

Cell[BoxData[
 SqrtBox[
  RowBox[{"2", "-", 
   RowBox[{"2", " ", 
    RowBox[{"Cos", "[", "\[CapitalOmega]", "]"}]}]}]]], "Output",
 CellChangeTimes->{{3.763812740728279*^9, 
  3.763812742701972*^9}},ExpressionUUID->"b54d770a-3a82-4de2-8b09-\
5dfc16742824"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{
   RowBox[{"An", "[", "\[CapitalOmega]_", "]"}], ":=", 
   SqrtBox[
    RowBox[{"2", "-", 
     RowBox[{"2", " ", 
      RowBox[{"Cos", "[", "\[CapitalOmega]", "]"}]}]}]]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"\[Rho]n", "[", "\[CapitalOmega]_", "]"}], ":=", 
   RowBox[{
    SuperscriptBox[
     RowBox[{"An", "[", "\[CapitalOmega]", "]"}], "2"], " ", 
    FractionBox[
     SuperscriptBox["\[Sigma]", "2"], "\[Pi]"]}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{"TrigFactor", "[", 
  RowBox[{"FullSimplify", "[", 
   RowBox[{
    RowBox[{"\[Rho]n", "[", "\[CapitalOmega]", "]"}], ",", 
    RowBox[{"Assumptions", "\[Rule]", 
     RowBox[{
      RowBox[{"\[CapitalOmega]", "\[GreaterEqual]", "0"}], "&&", 
      RowBox[{"\[CapitalOmega]", "<", "\[Pi]"}]}]}]}], "]"}], 
  "]"}], "\[IndentingNewLine]", 
 RowBox[{
  SubsuperscriptBox["\[Integral]", "0", 
   FractionBox["\[Pi]", "R"]], 
  RowBox[{
   RowBox[{"\[Rho]n", "[", "\[CapitalOmega]", "]"}], 
   RowBox[{"\[DifferentialD]", "\[CapitalOmega]"}]}]}]}], "Input",
 CellChangeTimes->{{3.763812766616523*^9, 3.7638129474866037`*^9}, {
  3.763813012108797*^9, 3.763813028816036*^9}, {3.763813063331794*^9, 
  3.7638130746423893`*^9}, {3.7638132289254923`*^9, 3.763813268127249*^9}, {
  3.763813302989893*^9, 3.7638133650977507`*^9}, {3.763813416204055*^9, 
  3.763813418185869*^9}, {3.76381363637467*^9, 3.763813636622324*^9}, {
  3.763813709357101*^9, 3.763813716797261*^9}, {3.763815319429083*^9, 
  3.7638153585768633`*^9}},ExpressionUUID->"d4b3f92d-c509-4c08-98b8-\
0d0006303c8b"],

Cell[BoxData[
 FractionBox[
  RowBox[{"4", " ", 
   SuperscriptBox["\[Sigma]", "2"], " ", 
   SuperscriptBox[
    RowBox[{"Sin", "[", 
     FractionBox["\[CapitalOmega]", "2"], "]"}], "2"]}], "\[Pi]"]], "Output",
 CellChangeTimes->{{3.763812898302814*^9, 3.763812917484065*^9}, 
   3.7638129479434*^9, {3.763813064523367*^9, 3.763813074972405*^9}, {
   3.763813224532035*^9, 3.763813268362009*^9}, 3.763813305053953*^9, 
   3.7638133681167793`*^9, {3.763813400116233*^9, 3.763813418456209*^9}, 
   3.763813639706634*^9, 3.763813674828877*^9, 3.7638137175503597`*^9, {
   3.763815321318963*^9, 
   3.763815358883553*^9}},ExpressionUUID->"fe5a8720-9793-451e-b96c-\
9ef285a78e03"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Plot", "[", 
  RowBox[{
   RowBox[{"An", "[", "\[CapitalOmega]", "]"}], ",", 
   RowBox[{"{", 
    RowBox[{"\[CapitalOmega]", ",", "0", ",", "\[Pi]"}], "}"}], ",", 
   RowBox[{"PlotTheme", "\[Rule]", "\"\<Monochrome\>\""}], ",", 
   RowBox[{"AxesLabel", "\[Rule]", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"Style", "[", 
       RowBox[{
       "\"\<\!\(\*StyleBox[\"\[CapitalOmega]\",FontSlant->\"Italic\"]\)\>\"", 
        ",", 
        RowBox[{"FontFamily", "\[Rule]", "\"\<Times\>\""}], ",", 
        RowBox[{"FontSize", "\[Rule]", "12"}]}], "]"}], ",", 
      RowBox[{"Style", "[", 
       RowBox[{
       "\"\<\!\(\*StyleBox[\"Gain\",FontSlant->\"Italic\"]\)\>\"", ",", 
        RowBox[{"FontFamily", "\[Rule]", "\"\<Times\>\""}], ",", 
        RowBox[{"FontSize", "\[Rule]", "12"}]}], "]"}]}], "}"}]}]}], 
  "]"}]], "Input",
 CellChangeTimes->{{3.763816584616859*^9, 3.763816601188374*^9}, {
  3.763816756469524*^9, 3.763816764708626*^9}, {3.7638168544258547`*^9, 
  3.763816917546034*^9}},ExpressionUUID->"e03fa5fa-c01a-42fe-ae8f-\
5bbafb1d97c0"],

Cell[BoxData[
 GraphicsBox[{{{}, {}, 
    TagBox[
     {GrayLevel[0], AbsoluteThickness[1.6], Opacity[1.], Dashing[{}], CapForm[
      "Butt"], LineBox[CompressedData["
1:eJwt1HlUzssfB/A2z3ceXfdmaREtiuqoRHTpV3w+aEEuFYm00H5DJRXSYi1b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       "]]},
     Annotation[#, "Charting`Private`Tag$163166#1"]& ]}, {}, {}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->{True, True},
  AxesLabel->{
    FormBox[
     StyleBox[
     "\"\\!\\(\\*StyleBox[\\\"\[CapitalOmega]\\\",FontSlant->\\\"Italic\\\"]\\\
)\"", FontFamily -> "Times", FontSize -> 12, StripOnInput -> False], 
     TraditionalForm], 
    FormBox[
     StyleBox[
     "\"\\!\\(\\*StyleBox[\\\"Gain\\\",FontSlant->\\\"Italic\\\"]\\)\"", 
      FontFamily -> "Times", FontSize -> 12, StripOnInput -> False], 
     TraditionalForm]},
  AxesOrigin->{0, 0},
  AxesStyle->GrayLevel[0],
  BaseStyle->GrayLevel[0],
  DisplayFunction->Identity,
  Frame->{{False, False}, {False, False}},
  FrameLabel->{{None, None}, {None, None}},
  FrameStyle->GrayLevel[0],
  FrameTicks->{{Automatic, 
     Charting`ScaledFrameTicks[{Identity, Identity}]}, {Automatic, 
     Charting`ScaledFrameTicks[{Identity, Identity}]}},
  FrameTicksStyle->GrayLevel[0],
  GridLines->{None, None},
  GridLinesStyle->Directive[
    GrayLevel[0], 
    AbsoluteThickness[1], 
    AbsoluteDashing[{1, 2}]],
  ImagePadding->All,
  LabelStyle->{FontFamily -> "Helvetica", 
    GrayLevel[0]},
  Method->{
   "DefaultBoundaryStyle" -> Automatic, "DefaultMeshStyle" -> 
    AbsolutePointSize[6], "ScalingFunctions" -> None, 
    "CoordinatesToolOptions" -> {"DisplayFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& ), "CopiedValueFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& )}},
  PlotRange->
   NCache[{{0, Pi}, {0., 1.9999999999999991`}}, {{0, 3.141592653589793}, {0., 
     1.9999999999999991`}}],
  PlotRangeClipping->True,
  PlotRangePadding->{{
     Scaled[0.02], 
     Scaled[0.02]}, {
     Scaled[0.05], 
     Scaled[0.05]}},
  Ticks->{Automatic, Automatic},
  TicksStyle->GrayLevel[0]]], "Output",
 CellChangeTimes->{{3.763812898302814*^9, 3.763812917484065*^9}, 
   3.7638129479434*^9, {3.763813064523367*^9, 3.763813074972405*^9}, {
   3.763813224532035*^9, 3.763813268362009*^9}, 3.763813305053953*^9, 
   3.7638133681167793`*^9, {3.763813400116233*^9, 3.763813418456209*^9}, 
   3.763813639706634*^9, 3.763813674828877*^9, 3.7638137175503597`*^9, {
   3.763815321318963*^9, 3.763815359847332*^9}, 3.763816603055278*^9, 
   3.763816761383849*^9, {3.763816895186521*^9, 
   3.763816922536252*^9}},ExpressionUUID->"fcf36d87-41e8-40cd-a392-\
530aed5fdbcc"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"\[Sigma]", "=", 
   SqrtBox[
    RowBox[{"1", "/", "12"}]]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"P", "[", "R_", "]"}], ":=", 
   FractionBox[
    RowBox[{"2", " ", 
     SuperscriptBox["\[Sigma]", "2"], " ", 
     RowBox[{"(", 
      RowBox[{"\[Pi]", "-", 
       RowBox[{"R", " ", 
        RowBox[{"Sin", "[", 
         FractionBox["\[Pi]", "R"], "]"}]}]}], ")"}]}], 
    RowBox[{"\[Pi]", " ", "R"}]]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"SNR", "[", "R_", "]"}], ":=", 
   RowBox[{"10", "*", 
    RowBox[{"Log10", "[", 
     FractionBox["0.5", 
      RowBox[{"P", "[", "R", "]"}]], "]"}]}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{"N", "[", 
  RowBox[{"SNR", "[", "1000", "]"}], "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"xticks", "=", 
   RowBox[{"{", 
    RowBox[{
    "1", ",", "2", ",", "5", ",", "10", ",", "100", ",", "1000", ",", "10000",
      ",", "100000"}], "}"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"xgrids", "=", 
   RowBox[{"{", 
    RowBox[{
    "1", ",", "2", ",", "5", ",", "10", ",", "20", ",", "50", ",", "100", ",",
      "200", ",", "500", ",", "1000", ",", "2000", ",", "5000", ",", "10000", 
     ",", "20000", ",", "50000", ",", "100000", ",", "200000"}], "}"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"ygrids", "=", 
   RowBox[{"Table", "[", 
    RowBox[{
     RowBox[{
      RowBox[{"-", "20"}], "+", 
      RowBox[{"10", "*", "k"}]}], ",", 
     RowBox[{"{", 
      RowBox[{"k", ",", "0", ",", "18"}], "}"}]}], "]"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"yticks", "=", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"-", "20"}], ",", "0", ",", "20", ",", "40", ",", "60", ",", 
     "80", ",", "100", ",", "120", ",", "140", ",", "160"}], "}"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{"LogLinearPlot", "[", 
  RowBox[{
   RowBox[{"SNR", "[", "R", "]"}], ",", 
   RowBox[{"{", 
    RowBox[{"R", ",", "1", ",", "200000"}], "}"}], ",", 
   RowBox[{"PlotTheme", "->", "\"\<Monochrome\>\""}], ",", 
   RowBox[{"GridLines", "\[Rule]", 
    RowBox[{"{", 
     RowBox[{"xgrids", ",", "ygrids"}], "}"}]}], ",", 
   RowBox[{"Ticks", "->", 
    RowBox[{"{", 
     RowBox[{"xticks", ",", " ", "yticks"}], "}"}]}], ",", 
   RowBox[{"PlotRange", "\[Rule]", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"{", 
       RowBox[{"1", ",", "200001"}], "}"}], ",", 
      RowBox[{"{", 
       RowBox[{"0", ",", "160"}], "}"}]}], "}"}]}], ",", 
   RowBox[{"AxesLabel", "\[Rule]", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"Style", "[", 
       RowBox[{"\"\<\!\(\*StyleBox[\"R\",FontSlant->\"Italic\"]\)\>\"", ",", 
        RowBox[{"FontFamily", "\[Rule]", "\"\<Times\>\""}], ",", 
        RowBox[{"FontSize", "\[Rule]", "12"}]}], "]"}], ",", 
      RowBox[{"Style", "[", 
       RowBox[{
       "\"\<\!\(\*StyleBox[\"SNR\",FontSlant->\"Italic\"]\)(dB)\>\"", ",", 
        RowBox[{"FontFamily", "\[Rule]", "\"\<Times\>\""}], ",", 
        RowBox[{"FontSize", "\[Rule]", "12"}]}], "]"}]}], "}"}]}]}], 
  "]"}]}], "Input",
 CellChangeTimes->{{3.76381536175247*^9, 3.763815413512062*^9}, {
  3.7638155400749817`*^9, 3.763816250278159*^9}, {3.763816769776761*^9, 
  3.763816842695716*^9}, {3.763817296883831*^9, 3.763817297859309*^9}, {
  3.763817355741679*^9, 3.763817409240745*^9}, {3.763817750023926*^9, 
  3.763817750525879*^9}},ExpressionUUID->"cfc55875-2725-4f79-9f34-\
b16ea3f87058"],

Cell[BoxData["92.60972974062045`"], "Output",
 CellChangeTimes->{{3.763815575460352*^9, 3.763815718985735*^9}, {
   3.763815795484568*^9, 3.763815911837874*^9}, 3.76381602784968*^9, 
   3.7638160647406883`*^9, {3.763816132655259*^9, 3.763816174081702*^9}, {
   3.763816212769074*^9, 3.763816250802528*^9}, {3.763816780747064*^9, 
   3.763816790429029*^9}, {3.763816825749893*^9, 3.763816842927332*^9}, 
   3.763817298231152*^9, {3.763817360693942*^9, 3.763817409621428*^9}, 
   3.7638177508501673`*^9},ExpressionUUID->"e01bf409-a6fe-4f9f-8c48-\
0852899029f7"],

Cell[BoxData[
 GraphicsBox[{{{}, {}, 
    TagBox[
     {GrayLevel[0], AbsoluteThickness[1.6], Opacity[1.], Dashing[{}], CapForm[
      "Butt"], LineBox[CompressedData["
1:eJwdxQ041AcAx/Gj4ayneTkSdyPXuTvvzEtpnv4/kaUrWsN57/hXmJ7yUhqG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       "]]},
     Annotation[#, "Charting`Private`Tag$166951#1"]& ]}, {}, {}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->{True, True},
  AxesLabel->{
    FormBox[
     StyleBox[
     "\"\\!\\(\\*StyleBox[\\\"R\\\",FontSlant->\\\"Italic\\\"]\\)\"", 
      FontFamily -> "Times", FontSize -> 12, StripOnInput -> False], 
     TraditionalForm], 
    FormBox[
     StyleBox[
     "\"\\!\\(\\*StyleBox[\\\"SNR\\\",FontSlant->\\\"Italic\\\"]\\)(dB)\"", 
      FontFamily -> "Times", FontSize -> 12, StripOnInput -> False], 
     TraditionalForm]},
  AxesOrigin->{0, 0},
  AxesStyle->GrayLevel[0],
  BaseStyle->GrayLevel[0],
  CoordinatesToolOptions:>{"DisplayFunction" -> ({
      Exp[
       Part[#, 1]], 
      Part[#, 2]}& ), "CopiedValueFunction" -> ({
      Exp[
       Part[#, 1]], 
      Part[#, 2]}& )},
  DisplayFunction->Identity,
  Frame->{{False, False}, {False, False}},
  FrameLabel->{{None, None}, {None, None}},
  FrameStyle->GrayLevel[0],
  FrameTicks->{{Automatic, Automatic}, {
     Charting`ScaledTicks[{Log, Exp}], 
     Charting`ScaledFrameTicks[{Log, Exp}]}},
  FrameTicksStyle->GrayLevel[0],
  GridLines->NCache[{{0, 
      Log[2], 
      Log[5], 
      Log[10], 
      Log[20], 
      Log[50], 
      Log[100], 
      Log[200], 
      Log[500], 
      Log[1000], 
      Log[2000], 
      Log[5000], 
      Log[10000], 
      Log[20000], 
      Log[50000], 
      Log[100000], 
      Log[200000]}, {-20, -10, 0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 
     110, 120, 130, 140, 150, 160}}, {{
     0, 0.6931471805599453, 1.6094379124341003`, 2.302585092994046, 
      2.995732273553991, 3.912023005428146, 4.605170185988092, 
      5.298317366548036, 6.214608098422191, 6.907755278982137, 
      7.600902459542082, 8.517193191416238, 9.210340371976184, 
      9.903487552536127, 10.819778284410283`, 11.512925464970229`, 
      12.206072645530174`}, {-20, -10, 0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 
     100, 110, 120, 130, 140, 150, 160}}],
  GridLinesStyle->Directive[
    GrayLevel[0], 
    AbsoluteThickness[1], 
    AbsoluteDashing[{1, 2}]],
  ImagePadding->All,
  LabelStyle->{FontFamily -> "Helvetica", 
    GrayLevel[0]},
  Method->{
   "DefaultBoundaryStyle" -> Automatic, "DefaultMeshStyle" -> 
    AbsolutePointSize[6], "ScalingFunctions" -> None},
  PlotRange->NCache[{{0, 
      Log[200001]}, {0, 160}}, {{0, 12.206077645517674`}, {0, 160}}],
  PlotRangeClipping->True,
  PlotRangePadding->{{0, 0}, {0, 0}},
  Ticks->{{{0, 
      FormBox["1", TraditionalForm]}, {
      NCache[
       Log[2], 0.6931471805599453], 
      FormBox["2", TraditionalForm]}, {
      NCache[
       Log[5], 1.6094379124341003`], 
      FormBox["5", TraditionalForm]}, {
      NCache[
       Log[10], 2.302585092994046], 
      FormBox["10", TraditionalForm]}, {
      NCache[
       Log[100], 4.605170185988092], 
      FormBox["100", TraditionalForm]}, {
      NCache[
       Log[1000], 6.907755278982137], 
      FormBox["1000", TraditionalForm]}, {
      NCache[
       Log[10000], 9.210340371976184], 
      FormBox["10000", TraditionalForm]}, {
      NCache[
       Log[100000], 11.512925464970229`], 
      FormBox["100000", TraditionalForm]}}, {{-20, 
      FormBox[
       RowBox[{"-", "20"}], TraditionalForm]}, {0, 
      FormBox["0", TraditionalForm]}, {20, 
      FormBox["20", TraditionalForm]}, {40, 
      FormBox["40", TraditionalForm]}, {60, 
      FormBox["60", TraditionalForm]}, {80, 
      FormBox["80", TraditionalForm]}, {100, 
      FormBox["100", TraditionalForm]}, {120, 
      FormBox["120", TraditionalForm]}, {140, 
      FormBox["140", TraditionalForm]}, {160, 
      FormBox["160", TraditionalForm]}}},
  TicksStyle->GrayLevel[0]]], "Output",
 CellChangeTimes->{{3.763815575460352*^9, 3.763815718985735*^9}, {
   3.763815795484568*^9, 3.763815911837874*^9}, 3.76381602784968*^9, 
   3.7638160647406883`*^9, {3.763816132655259*^9, 3.763816174081702*^9}, {
   3.763816212769074*^9, 3.763816250802528*^9}, {3.763816780747064*^9, 
   3.763816790429029*^9}, {3.763816825749893*^9, 3.763816842927332*^9}, 
   3.763817298231152*^9, {3.763817360693942*^9, 3.763817409621428*^9}, 
   3.763817750906221*^9},ExpressionUUID->"01cdb66c-e0a8-4188-8072-\
33bc213cec01"]
}, Open  ]]
},
WindowSize->{808, 755},
WindowMargins->{{313, Automatic}, {-26, Automatic}},
FrontEndVersion->"11.2 for Mac OS X x86 (32-bit, 64-bit Kernel) (September \
10, 2017)",
StyleDefinitions->"Default.nb"
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[CellGroupData[{
Cell[580, 22, 668, 17, 54, "Input",ExpressionUUID->"ba026b09-4388-4ba4-be80-4a262248cca2"],
Cell[1251, 41, 258, 7, 36, "Output",ExpressionUUID->"b54d770a-3a82-4de2-8b09-5dfc16742824"]
}, Open  ]],
Cell[CellGroupData[{
Cell[1546, 53, 1603, 40, 138, "Input",ExpressionUUID->"d4b3f92d-c509-4c08-98b8-0d0006303c8b"],
Cell[3152, 95, 677, 14, 58, "Output",ExpressionUUID->"fe5a8720-9793-451e-b96c-9ef285a78e03"]
}, Open  ]],
Cell[CellGroupData[{
Cell[3866, 114, 1083, 25, 73, "Input",ExpressionUUID->"e03fa5fa-c01a-42fe-ae8f-5bbafb1d97c0"],
Cell[4952, 141, 5872, 123, 243, "Output",ExpressionUUID->"fcf36d87-41e8-40cd-a392-530aed5fdbcc"]
}, Open  ]],
Cell[CellGroupData[{
Cell[10861, 269, 3463, 95, 356, "Input",ExpressionUUID->"cfc55875-2725-4f79-9f34-b16ea3f87058"],
Cell[14327, 366, 559, 8, 34, "Output",ExpressionUUID->"e01bf409-a6fe-4f9f-8c48-0852899029f7"],
Cell[14889, 376, 5793, 142, 248, "Output",ExpressionUUID->"01cdb66c-e0a8-4188-8072-33bc213cec01"]
}, Open  ]]
}
]
*)