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butter

Butterworth IIR digital filter design

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Syntax

butterFilter = butter(designSpecs,SystemObject=true)
butterFilter = butter(designSpecs,designoption=value,... SystemObject=true)
butterFilter = design(designSpecs,'butter',SystemObject=true)

Description

butterFilter = butter(designSpecs,SystemObject=true) designs a Butterworth IIR digital filter using specifications in the object designSpecs.

Depending on the filter specification object designSpecs, the butter design method might not be valid. Use designmethods with the filter specification object to determine if a Butterworth IIR digital filter design is possible.

designmethods(designSpecs,SystemObject=true)

butterFilter = butter(designSpecs,designoption=value,... SystemObject=true) returns a Butterworth IIR filter with one or more specified designed options and the corresponding values.

To view a list of available design options, run the designoptions function on the specification object. The function also lists the default design options the filter uses.

designoptions(designSpecs,'butter')

butterFilter = design(designSpecs,'butter',SystemObject=true) is an alternative syntax for designing the Butterworth IIR digital filter.

For complete help about using the butter design method for a specification object, designSpecs, enter the following at the MATLAB® command prompt.

help(designSpecs,'butter')

example

Examples

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Open Live Script

Design a Butterworth filter with lowpass and highpass frequency responses. The filter design procedure is:

  1. Specify the filter design specifications using a fdesign function.

  2. Pick a design method provided by the designmethods function.

  3. To determine the available design options to choose from, use the designoptions function.

  4. Design the filter using the design function.

Lowpass Filter

Construct a default lowpass filter design specification object using fdesign.lowpass.

designSpecs = fdesign.lowpass
designSpecs = 
  lowpass with properties:

               Response: 'Lowpass'
          Specification: 'Fp,Fst,Ap,Ast'
            Description: {4x1 cell}
    NormalizedFrequency: 1
                  Fpass: 0.4500
                  Fstop: 0.5500
                  Apass: 1
                  Astop: 60

Determine the available design methods using the designmethods function. To design a Butterworth filter, pick butter.

designmethods(designSpecs,SystemObject=true)
Design Methods that support System objects for class fdesign.lowpass (Fp,Fst,Ap,Ast):


butter
cheby1
cheby2
ellip
equiripple
ifir
kaiserwin
multistage

While designing the filter, you can specify additional design options. View a list of the options using the designoptions function. This function also shows the default design options the filter uses.

designoptions(designSpecs,'butter',SystemObject=true)
ans = struct with fields:
           FilterStructure: {'df1sos'  'df2sos'  'df1tsos'  'df2tsos'  'cascadeallpass'  'cascadewdfallpass'}
              SOSScaleNorm: 'ustring'
              SOSScaleOpts: 'fdopts.sosscaling'
              MatchExactly: {'passband'  'stopband'}
    DefaultFilterStructure: 'df2sos'
       DefaultMatchExactly: 'stopband'
       DefaultSOSScaleNorm: ''
       DefaultSOSScaleOpts: [1x1 fdopts.sosscaling]

Use the design function to design the filter. Pass 'butter' and the specifications given by variable designSpecs, as input arguments. Specify the 'matchexactly' design option to 'passband'. 

lpFilter = design(designSpecs,'butter',matchexactly='passband',SystemObject=true)
lpFilter = 
  dsp.SOSFilter with properties:

            Structure: 'Direct form II'
    CoefficientSource: 'Property'
            Numerator: [13x3 double]
          Denominator: [13x3 double]
       HasScaleValues: true
          ScaleValues: [0.4095 0.3669 0.3330 0.3059 0.2841 0.2666 0.2525 0.2414 0.2328 0.2263 0.2219 0.2193 0.4674 1]

  Use get to show all properties

Visualize the frequency response of the designed filter.

filterAnalyzer(lpFilter)

Highpass Filter

Construct a highpass filter design specification object using fdesign.highpass. Specify the order to be 7 and the 3 dB frequency to be 0.6π radians/sample.

designSpecs = fdesign.highpass('N,F3dB',7,.6)
designSpecs = 
  highpass with properties:

          Specification: 'N,F3dB'
               Response: 'Highpass'
            Description: {2x1 cell}
    NormalizedFrequency: 1
            FilterOrder: 7
                   F3dB: 0.6000

Determine the available design methods. To design a Butterworth filter, pick butter.

designmethods(designSpecs,SystemObject=true)
Design Methods that support System objects for class fdesign.highpass (N,F3dB):


butter
maxflat

While designing the filter, you can specify additional design options. View a list of the options using the designoptions function. This function also shows the default design options the filter uses.

designoptions(designSpecs,'butter',SystemObject=true)
ans = struct with fields:
           FilterStructure: {'df1sos'  'df2sos'  'df1tsos'  'df2tsos'  'cascadeallpass'  'cascadewdfallpass'}
              SOSScaleNorm: 'ustring'
              SOSScaleOpts: 'fdopts.sosscaling'
    DefaultFilterStructure: 'df2sos'
       DefaultSOSScaleNorm: ''
       DefaultSOSScaleOpts: [1x1 fdopts.sosscaling]

To design the Butterworth filter, use the design function and specify 'butter' as an input. Set 'FilterStructure' to 'cascadeallpass'.

hpFilter = design(designSpecs,'butter',FilterStructure='cascadeallpass',SystemObject=true)
hpFilter = 
  dsp.CoupledAllpassFilter with properties:

               Structure: 'Minimum multiplier'
         PureDelayBranch: 0
    AllpassCoefficients1: {2x1 cell}
    AllpassCoefficients2: {2x1 cell}
                   Gain1: '-1'
                   Gain2: '1'

Visualize the highpass frequency response.

filterAnalyzer(hpFilter)

Input Arguments

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Filter specification object, specified as one of the following:

Output Arguments

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Butterworth IIR filter, returned as a filter System object. The System object and the values of its properties depend on the input designSpecs object and the other design options specified to the function.

Version History

Introduced in R2011a

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See Also

Functions

Objects