Poles of a Butterworth Filter 

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X Manipulate[Module[{tf, poles}, tf = ButterworthFilterModel[n, s]; poles = Flatten@TransferFunctionPoles[tf]; Switch[view, "3D view", Plot3D[Evaluate[ Abs@tf[\[Sigma] + I \[Omega]][[1, 1]]], {\[Sigma], -1.5, 0.5}, {\[Omega], -1.5, 1.5}, PlotRange -> {0, n^2.6}, Mesh -> False, AxesLabel -> {\[Sigma], \[Omega], None}, ImageSize -> {300, 300}], "2D view", ListPlot[Transpose[{Re[poles], Im[poles]}], PlotRange -> 1.1 {{-1, 1}, {-1, 1}}, AspectRatio -> Automatic, PlotStyle -> {PointSize[Large]}, Epilog -> {Dashed, Pink, Circle[]}, ImageSize -> {300, 300}]]], {{n, 9, "order"}, 1, 13, 1, Appearance -> "Labeled"}, {{view, "3D view", ""}, {"2D view", "3D view"}}]

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