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Built-in Signal Processing
Create Filters from a Lowpass Prototype
Create an analog lowpass Butterworth filter and transform it to other types.
In[1]:=
X
lowpass = ButterworthFilterModel[3, s]; highpass = TransferFunctionTransform[1/# &, lowpass]; bandpass = TransferFunctionTransform[(#^2 + 1)/(2 #) &, lowpass]; bandstop = TransferFunctionTransform[(2 #)/(#^2 + 1) &, lowpass];
In[2]:=
X
Plot[{Abs[lowpass[I x]], Abs[highpass[I x]], Abs[bandpass[I x]], Abs[bandstop[I x]]}, {x, 0, 5}, PlotRange -> All, PlotStyle -> {Thick, Automatic, Automatic, Automatic}, PlotLegends -> {"lowpass", "highpass", "bandpass", "bandstop"}]
Out[2]=
