BUILT-IN MATHEMATICA SYMBOL

# ButterworthFilterModel

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.
• 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 :

 Out[1]=

Bode plot of the filter:

 Out[2]=

A lowpass Butterworth filter using the full specification:

 Out[1]=

Magnitude response of the filter showing the ideal filter characteristics:

 Out[2]=