ButterworthFilterModel

ButterworthFilterModel[n]
creates a lowpass Butterworth filter of order n and cutoff frequency of 1.

ButterworthFilterModel[{n, c}]
uses the cutoff frequency .

ButterworthFilterModel[{"type", spec}]
uses the full filter specification .

ButterworthFilterModel[{"type", spec}, var]    
expresses the model in terms of the variable var.

DetailsDetails

  • ButterworthFilterModel returns the filter as a TransferFunctionModel.
  • ButterworthFilterModel[n] uses machine precision to return a filter with attenuation of at frequency 1.
  • In ButterworthFilterModel[{"type", spec}], filter specification can be any of the following:
  • {"Lowpass",{p,s},{ap,as}}lowpass filter specification
    {"Highpass",{s,p},{as,ap}}highpass filter specification
    {"Bandpass",{s1,p1,p2,s2},{as,ap}}bandpass filter specification
    {"Bandstop",{p1,s1,s2,p2},{ap,as}}bandstop filter specification
  • Values and are respectively absolute values of passband and stopband attenuations.
  • Given a gain fraction , the attenuation .

ExamplesExamplesopen allclose all

Basic Examples (2)Basic Examples (2)

A third-order Butterworth filter model with cutoff frequency at :

In[1]:=
Click for copyable input
Out[1]=

Bode plot of the filter:

In[2]:=
Click for copyable input
Out[2]=

A lowpass Butterworth filter using the full specification:

In[1]:=
Click for copyable input
Out[1]=

Magnitude response of the filter showing the ideal filter characteristics:

In[2]:=
Click for copyable input
Out[2]=
New in 9
New to Mathematica? Find your learning path »
Have a question? Ask support »