ButterworthFilterModel

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

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

ButterworthFilterModel[{"type",spec}]
creates a filter of a given "type" using the specified parameters spec.

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

DetailsDetails

  • ButterworthFilterModel returns the filter as a TransferFunctionModel.
  • ButterworthFilterModel[{n,ω}] returns a lowpass filter with attenuation of (approximately 3 dB) at frequency ω.
  • ButterworthFilterModel[n] uses the cutoff frequency of 1.
  • Lowpass filter specification {"type",spec} can be any of the following:
  • {"Lowpass",n}lowpass filter of order n and cutoff frequency 1
    {"Lowpass",n,ωp}use cutoff frequency ωp
    {"Lowpass",{ωp,ωs},{ap,as}}use full filter specification giving passband and stopband frequencies and attenuations
  • Highpass filter specifications:
  • {"Highpass",n}highpass filter with cutoff frequency 1
    {"Highpass",n,ωp}use cutoff frequency ωp
    {"Highpass",{ωs,ωp},{as,ap}}full filter specification
  • Bandpass filter specifications:
  • {"Bandpass",n,{ωp1,ωp2}}bandpass filter with passband frequencies ωp1 and ωp2
    {"Bandpass",n,{{ω,q}}}use center frequency ω and quality factor q
    {"Bandpass",{ωs1,ωp1,ωp2,ωs2},{as,ap}}full filter specification
  • Bandstop filter specifications:
  • {"Bandstop",n,{ωp1,ωp2}}bandstop filter with passband frequencies ωp1 and ωp2
    {"Bandstop",n,{{ω,q}}}use center frequency ω and quality factor q
    {"Bandstop",{ωp1,ωs1,ωs2,ωp2},{ap,as}}full filter specification
  • Values ap and as are, respectively, absolute values of passband and stopband attenuations.
  • Given a gain fraction , the attenuation is .
  • The quality factor q is defined as , with being the center frequency of a bandpass or bandstop filter. Higher values of q give narrower filters.

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)
| Updated in 2015
(10.2)
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