(* Content-type: application/vnd.wolfram.cdf.text *) (*** Wolfram CDF File ***) (* http://www.wolfram.com/cdf *) (* CreatedBy='Mathematica 8.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 150, 7] NotebookDataLength[ 17983, 379] NotebookOptionsPosition[ 17704, 365] NotebookOutlinePosition[ 18059, 381] CellTagsIndexPosition[ 18016, 378] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`porZ$$ = { True, False, False, True}, $CellContext`showEqAnswer$$ = False, $CellContext`showGuess$$ = False, $CellContext`showMPPlot$$ = True, $CellContext`showPlot$$ = False, $CellContext`y$$ = {{ 3.141592653589793, 3.141592653589793}, {-3.16, -0.16999999999999993`}, {-3.141592653589793, \ -3.141592653589793}}, $CellContext`z$$ = {{0, Pi}, {Pi, 0}, {0, 0}}, $CellContext`zinit$$ = {{0, Pi}, {Pi, 0}, {0, 0}}, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{ Hold[ Row[{ Style["Guess(f) =", 15], Dynamic[ Text[ ToString[ If[$CellContext`showGuess$$, Product[E^(((I 2) Pi) $CellContext`f) - Part[$CellContext`yzero, $CellContext`n, 1] - I Part[$CellContext`yzero, $CellContext`n, 2], {$CellContext`n, 1, $CellContext`yq}]/Product[ E^(((I 2) Pi) $CellContext`f) - Part[$CellContext`ypole, $CellContext`n, 1] - I Part[$CellContext`ypole, $CellContext`n, 2], {$CellContext`n, 1, $CellContext`yp}], " "], StandardForm]]], Style["H(f) =", 15], Dynamic[ Text[ ToString[ If[$CellContext`showEqAnswer$$, Product[E^(((I 2) Pi) $CellContext`f) - Part[$CellContext`zero, $CellContext`n, 1] - I Part[$CellContext`zero, $CellContext`n, 2], {$CellContext`n, 1, $CellContext`q}]/Product[ E^(((I 2) Pi) $CellContext`f) - Part[$CellContext`pole, $CellContext`n, 1] - I Part[$CellContext`pole, $CellContext`n, 2], {$CellContext`n, 1, $CellContext`p}], ""], StandardForm]]]}, ImageSize -> {600, 40}]], Manipulate`Dump`ThisIsNotAControl}, {{ Hold[$CellContext`z$$], {{0, Pi}, {Pi, 0}, {0, 0}}}, { Rational[-3, 2] Pi, Rational[-3, 2] Pi}, { Rational[3, 2] Pi, Rational[3, 2] Pi}, Null}, {{ Hold[$CellContext`y$$], {{Pi, Pi}, {-Pi, -Pi}, {-Pi, -Pi}}}, { Rational[-3, 2] Pi, Rational[-3, 2] Pi}, { Rational[3, 2] Pi, Rational[3, 2] Pi}}, {{ Hold[$CellContext`showGuess$$], False, " Show Guess Equation"}, {True, False}}, {{ Hold[$CellContext`showEqAnswer$$], False, " Show Answer Equation"}, { True, False}}, {{ Hold[$CellContext`showMPPlot$$], False, " Show Mag/Phase Answer Plot"}, {True, False}}, {{ Hold[$CellContext`showPlot$$], False, " Show Answer Plot"}, { True, False}}, { Hold[ Row[{ Manipulate`Place[1], Manipulate`Place[2], Manipulate`Place[3], Manipulate`Place[4]}]], Manipulate`Dump`ThisIsNotAControl}, {{ Hold[$CellContext`porZ$$], {True, False, True, True}}}, { Hold[$CellContext`zinit$$]}}, Typeset`size$$ = { 608., {245.84375, 251.15625}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = False, $CellContext`z$32493$$ = 0, $CellContext`y$32494$$ = {0, 0}, $CellContext`showGuess$32495$$ = False, $CellContext`showEqAnswer$32496$$ = False, $CellContext`showMPPlot$32497$$ = False, $CellContext`showPlot$32498$$ = False}, DynamicBox[Manipulate`ManipulateBoxes[ 2, StandardForm, "Variables" :> {$CellContext`porZ$$ = { True, False, True, True}, $CellContext`showEqAnswer$$ = False, $CellContext`showGuess$$ = False, $CellContext`showMPPlot$$ = False, $CellContext`showPlot$$ = False, $CellContext`y$$ = {{ Pi, Pi}, {-Pi, -Pi}, {-Pi, -Pi}}, $CellContext`z$$ = {{0, Pi}, { Pi, 0}, {0, 0}}, $CellContext`zinit$$ = Null}, "ControllerVariables" :> { Hold[$CellContext`z$$, $CellContext`z$32493$$, 0], Hold[$CellContext`y$$, $CellContext`y$32494$$, {0, 0}], Hold[$CellContext`showGuess$$, $CellContext`showGuess$32495$$, False], Hold[$CellContext`showEqAnswer$$, $CellContext`showEqAnswer$32496$$, False], Hold[$CellContext`showMPPlot$$, $CellContext`showMPPlot$32497$$, False], Hold[$CellContext`showPlot$$, $CellContext`showPlot$32498$$, False]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> ($CellContext`zinit$$ = $CellContext`z$$; $CellContext`pole = Part[$CellContext`z$$, Select[ Table[$CellContext`k, {$CellContext`k, Length[$CellContext`z$$]}], Part[$CellContext`porZ$$, #]& ]]; $CellContext`p = Length[$CellContext`pole]; $CellContext`zero = Part[$CellContext`z$$, Select[ Table[$CellContext`k, {$CellContext`k, Length[$CellContext`z$$]}], Not[ Part[$CellContext`porZ$$, #]]& ]]; $CellContext`q = Length[$CellContext`zero]; $CellContext`yinit = $CellContext`zinit$$; \ $CellContext`ypole = Part[$CellContext`y$$, Select[ Table[$CellContext`k, {$CellContext`k, Length[$CellContext`y$$]}], Part[$CellContext`porZ$$, #]& ]]; $CellContext`yp = Length[$CellContext`ypole]; $CellContext`yzero = Part[$CellContext`y$$, Select[ Table[$CellContext`k, {$CellContext`k, Length[$CellContext`y$$]}], Not[ Part[$CellContext`porZ$$, #]]& ]]; $CellContext`yq = Length[$CellContext`yzero]; Grid[{{ Graphics[{ AbsolutePointSize[12], {Green, Point[$CellContext`ypole]}, {Blue, Point[$CellContext`yzero]}, Circle[{0, 0}, Pi]}, PlotRange -> 3 (Pi/2), Frame -> True, GridLines -> { Table[ If[$CellContext`n == 0, {$CellContext`n, Thick}, Pi ($CellContext`n/10)], {$CellContext`n, -14, 14}], Table[ If[$CellContext`n == 0, {$CellContext`n, Thick}, Pi ($CellContext`n/10)], {$CellContext`n, -14, 14}]}, FrameTicks -> Automatic, ImageSize -> {240, 240}], Grid[{{ Plot[{ Abs[ $CellContext`H[$CellContext`freq, $CellContext`yp, \ $CellContext`yq, $CellContext`ypole, $CellContext`yzero]]}, \ {$CellContext`freq, -(Pi/2), Pi/2}, PlotStyle -> { RGBColor[1, 0, 1]}, PlotRange -> All, PlotLabel -> "Magnitude", GridLines -> Automatic, ImageSize -> {360, 120}, AspectRatio -> 9/16]}, { Plot[ Arg[ $CellContext`H[$CellContext`freq, $CellContext`yp, \ $CellContext`yq, $CellContext`ypole, $CellContext`yzero]], \ {$CellContext`freq, -(Pi/2), Pi/2}, PlotStyle -> { RGBColor[1, 0, 0]}, PlotRange -> {All, {-Pi, Pi}}, PlotLabel -> "Phase", GridLines -> { Automatic, {-Pi, -(3 (Pi/4)), -(Pi/2), -(Pi/4), Pi/4, Pi/2, 3 (Pi/4), Pi}}, ImageSize -> {360, 120}, AspectRatio -> 9/16]}}]}, { If[$CellContext`showPlot$$, Graphics[{ AbsolutePointSize[12], {Green, Point[$CellContext`pole]}, {Blue, Point[$CellContext`zero]}, Circle[{0, 0}, Pi]}, PlotRange -> 3 (Pi/2), Frame -> True, GridLines -> { Table[ If[$CellContext`n == 0, {$CellContext`n, Thick}, Pi ($CellContext`n/10)], {$CellContext`n, -14, 14}], Table[ If[$CellContext`n == 0, {$CellContext`n, Thick}, Pi ($CellContext`n/10)], {$CellContext`n, -14, 14}]}, FrameTicks -> Automatic, ImageSize -> {240, 240}], Null], Grid[{{ If[$CellContext`showMPPlot$$, Plot[{ Abs[ $CellContext`H[$CellContext`freq, $CellContext`p, \ $CellContext`q, $CellContext`pole, $CellContext`zero]]}, {$CellContext`freq, \ (-Pi)/2, Pi/2}, PlotStyle -> { RGBColor[1, 0, 1]}, PlotRange -> All, PlotLabel -> "Magnitude", GridLines -> Automatic, ImageSize -> {360, 120}, AspectRatio -> 9/16], Null]}, { If[$CellContext`showMPPlot$$, Plot[ Arg[ $CellContext`H[$CellContext`freq, $CellContext`p, \ $CellContext`q, $CellContext`pole, $CellContext`zero]], {$CellContext`freq, -( Pi/2), Pi/2}, PlotStyle -> { RGBColor[1, 0, 0]}, PlotRange -> {All, {-Pi, Pi}}, PlotLabel -> "Phase", GridLines -> { Automatic, {-Pi, -(3 (Pi/4)), -(Pi/2), -(Pi/4), Pi/4, Pi/2, 3 (Pi/4), Pi}}, ImageSize -> {360, 120}, AspectRatio -> 9/16], Null]}}]}}]), "Specifications" :> { Row[{ Style["Guess(f) =", 15], Dynamic[ Text[ ToString[ If[$CellContext`showGuess$$, Product[E^(((I 2) Pi) $CellContext`f) - Part[$CellContext`yzero, $CellContext`n, 1] - I Part[$CellContext`yzero, $CellContext`n, 2], {$CellContext`n, 1, $CellContext`yq}]/Product[ E^(((I 2) Pi) $CellContext`f) - Part[$CellContext`ypole, $CellContext`n, 1] - I Part[$CellContext`ypole, $CellContext`n, 2], {$CellContext`n, 1, $CellContext`yp}], " "], StandardForm]]], Style["H(f) =", 15], Dynamic[ Text[ ToString[ If[$CellContext`showEqAnswer$$, Product[E^(((I 2) Pi) $CellContext`f) - Part[$CellContext`zero, $CellContext`n, 1] - I Part[$CellContext`zero, $CellContext`n, 2], {$CellContext`n, 1, $CellContext`q}]/Product[ E^(((I 2) Pi) $CellContext`f) - Part[$CellContext`pole, $CellContext`n, 1] - I Part[$CellContext`pole, $CellContext`n, 2], {$CellContext`n, 1, $CellContext`p}], ""], StandardForm]]]}, ImageSize -> {600, 40}], {{$CellContext`z$$, {{0, Pi}, {Pi, 0}, {0, 0}}}, { Rational[-3, 2] Pi, Rational[-3, 2] Pi}, { Rational[3, 2] Pi, Rational[3, 2] Pi}, Null, ControlType -> None}, {{$CellContext`y$$, {{Pi, Pi}, {-Pi, -Pi}, {-Pi, -Pi}}}, { Rational[-3, 2] Pi, Rational[-3, 2] Pi}, { Rational[3, 2] Pi, Rational[3, 2] Pi}, ControlType -> Locator, LocatorAutoCreate -> {1, DirectedInfinity[1]}}, {{$CellContext`showGuess$$, False, " Show Guess Equation"}, {True, False}, ControlPlacement -> 1}, {{$CellContext`showEqAnswer$$, False, " Show Answer Equation"}, {True, False}, ControlPlacement -> 2}, {{$CellContext`showMPPlot$$, False, " Show Mag/Phase Answer Plot"}, {True, False}, ControlPlacement -> 3}, {{$CellContext`showPlot$$, False, " Show Answer Plot"}, { True, False}, ControlPlacement -> 4}, Row[{ Manipulate`Place[1], Manipulate`Place[2], Manipulate`Place[3], Manipulate`Place[4]}], {{$CellContext`porZ$$, { True, False, True, True}}, ControlType -> None}, {$CellContext`zinit$$, ControlType -> None}}, "Options" :> {FrameLabel -> {"", "", Style["Pole-Zero Drill", Large], ""}, TrackedSymbols -> Manipulate, AutorunSequencing -> {1, 2, 3, 5}, ControllerLinking -> False}, "DefaultOptions" :> {}], ImageSizeCache->{673., {330., 336.}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, Initialization:>({{$CellContext`pole = {{Pi, 0}}, $CellContext`p = 1, $CellContext`zero = {{Pi, Pi}, {0, -Pi}}, $CellContext`q = 2, $CellContext`yinit = {{Pi, 0}, {Pi, Pi}, { 0, -Pi}}, $CellContext`ypole = {{0, Pi}}, $CellContext`yp = 1, $CellContext`yzero = {{0, 0}, {0, -Pi}}, $CellContext`yq = 2, Attributes[PlotRange] = {ReadProtected}, $CellContext`n = 50, $CellContext`H[ Pattern[$CellContext`freq, Blank[]], Pattern[$CellContext`p, Blank[]], Pattern[$CellContext`q, Blank[]], Pattern[$CellContext`pole, Blank[]], Pattern[$CellContext`zero, Blank[]]] := Product[E^((I 2) $CellContext`freq) - Part[$CellContext`zero, $CellContext`n, 1] - I Part[$CellContext`zero, $CellContext`n, 2], {$CellContext`n, 1, $CellContext`q}]/Product[ E^((I 2) $CellContext`freq) - Part[$CellContext`pole, $CellContext`n, 1] - I Part[$CellContext`pole, $CellContext`n, 2], {$CellContext`n, 1, $CellContext`p}], $CellContext`showPlot$$ = False}; {$CellContext`porZ$$ = { RandomChoice[{True, False}], RandomChoice[{True, False}], RandomChoice[{True, False}], RandomChoice[{True, False}]}, $CellContext`zrand = RandomInteger[{1, 4}], $CellContext`H[ Pattern[$CellContext`freq, Blank[]], Pattern[$CellContext`p, Blank[]], Pattern[$CellContext`q, Blank[]], Pattern[$CellContext`pole, Blank[]], Pattern[$CellContext`zero, Blank[]]] := Product[E^((I 2) $CellContext`freq) - Part[$CellContext`zero, $CellContext`n, 1] - I Part[$CellContext`zero, $CellContext`n, 2], {$CellContext`n, 1, $CellContext`q}]/Product[ E^((I 2) $CellContext`freq) - Part[$CellContext`pole, $CellContext`n, 1] - I Part[$CellContext`pole, $CellContext`n, 2], {$CellContext`n, 1, $CellContext`p}]}}; Typeset`initDone$$ = True), SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "PluginEmbeddedContent", CellChangeTimes->{ 3.5196681441798553`*^9, {3.519668286927987*^9, 3.519668296789662*^9}, 3.519668529193877*^9, {3.519668679095642*^9, 3.519668749498166*^9}, 3.519668779692584*^9, 3.519668862595276*^9, {3.519668918242216*^9, 3.519668956405912*^9}, 3.5196690177325087`*^9, 3.5196693606650553`*^9, 3.519669491881207*^9, 3.5196695968139277`*^9, {3.5196696860649557`*^9, 3.5196697266836042`*^9}, {3.5196698216127777`*^9, 3.51966984802975*^9}, 3.519669884157634*^9, 3.5196703112196693`*^9, 3.519670442643238*^9, { 3.519670483261984*^9, 3.5196704966155767`*^9}, {3.519670638687541*^9, 3.5196706440490637`*^9}, {3.519670678661929*^9, 3.519670810575378*^9}, { 3.519670846640164*^9, 3.5196708707130632`*^9}, 3.5196709136442013`*^9, { 3.519671144563849*^9, 3.5196711652080383`*^9}, 3.519671435482562*^9, { 3.519671521211371*^9, 3.519671541878167*^9}, 3.5196715814794083`*^9, 3.519671633408435*^9, {3.5196716669491167`*^9, 3.519671678689343*^9}, 3.519671793855797*^9, {3.519671830528823*^9, 3.5196718474717083`*^9}, { 3.519671891214995*^9, 3.519671903598275*^9}, {3.519671981381616*^9, 3.5196720834496107`*^9}, {3.51967214514193*^9, 3.5196721511150427`*^9}, 3.5196722651095123`*^9, 3.519672387282987*^9, 3.519672956583558*^9, 3.5197303077481203`*^9, 3.519730354306732*^9, {3.5197304304719267`*^9, 3.519730447382532*^9}, 3.5197305883610563`*^9, {3.5197314171721077`*^9, 3.5197314256127872`*^9}, 3.519731470471702*^9, 3.519731701507824*^9, 3.5197317674624233`*^9, 3.5197318102100763`*^9, 3.5197318445360117`*^9, 3.519731883272099*^9, 3.519732278377419*^9, 3.51973234395693*^9, { 3.5197323740174217`*^9, 3.519732399281109*^9}, {3.519732525771018*^9, 3.519732571829791*^9}, {3.519732979019101*^9, 3.5197329862010393`*^9}, 3.519733105399024*^9, 3.519733179947586*^9, {3.519733223301386*^9, 3.519733240583074*^9}, {3.519733281326461*^9, 3.519733312599038*^9}, 3.519733377643392*^9, 3.519733430000722*^9, 3.519733510998725*^9, 3.519733544216049*^9, {3.519734238292161*^9, 3.519734287087229*^9}, 3.519734321710479*^9, 3.519734357131864*^9, 3.51973442094792*^9, 3.5227725148631487`*^9}] }, WindowSize->{997, 750}, WindowMargins->{{88, Automatic}, {Automatic, 0}}, FrontEndVersion->"8.0 for Mac OS X x86 (32-bit, 64-bit Kernel) (November 6, \ 2010)", StyleDefinitions->"Default.nb" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[550, 20, 17150, 343, 668, "PluginEmbeddedContent"] } ] *) (* End of internal cache information *) (* NotebookSignature su0LwrFJcavgdBKzF4K#Qwa5 *)