butter

Butterworth IIR digital filter design

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')

Examples

Design Butterworth Filter

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: {4×1 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: [1×1 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: [13×3 double]
          Denominator: [13×3 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]

  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 $0.6\pi$ radians/sample.

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

designSpecs = 
  highpass with properties:

          Specification: 'N,F3dB'
               Response: 'Highpass'
            Description: {2×1 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: [1×1 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: {2×1 cell}
    AllpassCoefficients2: {2×1 cell}
                   Gain1: '-1'
                   Gain2: '1'

Visualize the highpass frequency response.

filterAnalyzer(hpFilter)

Input Arguments

designSpecs — Filter specification object

object

Filter specification object, specified as one of the following:

• fdesign.bandpass

• fdesign.bandstop

• fdesign.comb

• fdesign.decimator

• fdesign.halfband

• fdesign.highpass

• fdesign.interpolator

• fdesign.lowpass

• fdesign.notch

• fdesign.nyquist

• fdesign.peak

Output Arguments

butterFilter — Butterworth IIR filter

System object™

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

R2024b: dsp.BiquadFilter object warns

The dsp.BiquadFilter object and the UseLegacyBiquadFilter flag will be removed in a future release.

R2023b: dsp.BiquadFilter object will be removed

The dsp.BiquadFilter object and the UseLegacyBiquadFilter argument will be removed in a future release.

R2022b: Designs dsp.SOSFilter object instead of dsp.BiquadFilter object

The butter design method now generates a dsp.SOSFilter object in the designs which previously generated a dsp.BiquadFilter object.

Initialize the default fdesign.lowpass filter specification object. Use the design function with the SystemObject=true flag to design a dsp.SOSFilter filter object.

designSpecs = fdesign.lowpass;
filtObj = design(designSpecs,'butter',SystemObject=true)

filtObj = 

  dsp.SOSFilter with properties:

            Structure: 'Direct form II'
    CoefficientSource: 'Property'
            Numerator: [13×3 double]
          Denominator: [13×3 double]
       HasScaleValues: true
          ScaleValues: [0.4151 0.3718 0.3374 0.3099 0.2878 0.2701 0.2558 … ]

  Show all properties

To design a dsp.BiquadFilter object instead of the dsp.SOSFilter object, you can use the UseLegacyBiquadFilter flag and set it to true.

filtObj = design(designSpecs,'butter',SystemObject=true,...
UseLegacyBiquadFilter=true)

filtObj = 

  dsp.BiquadFilter with properties:

                   Structure: 'Direct form II'
             SOSMatrixSource: 'Property'
                   SOSMatrix: [13×6 double]
                 ScaleValues: [14×1 double]
           InitialConditions: 0
    OptimizeUnityScaleValues: true

  Show all properties