ButterworthFilterModel

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

ButterworthFilterModel[{n,ωc}]
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",{ωp,ωs},{ap,as}}lowpass filter specification
    {"Highpass",{ωs,ωp},{as,ap}}highpass filter specification
    {"Bandpass",{ωs1,ωp1,ωp2,ωs2},{as,ap}}bandpass filter specification
    {"Bandstop",{ωp1,ωs1,ωs2,ωp2},{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 :

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Bode plot of the filter:

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A lowpass Butterworth filter using the full specification:

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Magnitude response of the filter showing the ideal filter characteristics:

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Introduced in 2012
(9.0)