designfilt

Design digital filter

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designfilt no longer assists in correcting calls to the function within a script or function. For more information, see Version History.

Syntax

d = designfilt(resp,Name,Value)
designfilt(d)

Description

d = designfilt(resp,Name,Value) designs a digitalFilter object or a filter System object™ with response type resp. Examples of resp are 'lowpassfir' and 'bandstopiir'. Specify the filter further using a set of Name-Value Arguments. The allowed specification sets depend on resp and consist of combinations of these:

  • Frequency Constraints correspond to the frequencies at which a filter exhibits a desired behavior. Examples include 'PassbandFrequency' and 'CutoffFrequency'. You must always specify the frequency constraints.

  • Magnitude Constraints describe the filter behavior at particular frequency ranges. Examples include 'PassbandRipple' and 'StopbandAttenuation'. designfilt provides default values for magnitude constraints left unspecified. In arbitrary-magnitude designs you must always specify the vectors of desired amplitudes.

  • Filter Order: Some design methods let you specify the order. Others produce minimum-order designs. That is, they generate the smallest filters that satisfy the specified constraints.

  • Design Method is the algorithm used to design the filter. Examples include constrained least squares ('cls') and Kaiser windowing ('kaiserwin'). For some specification sets, there are multiple design methods available to choose from. In other cases, you can use only one method to meet the desired specifications.

  • Design Method Options are parameters specific to a given design method. Examples include 'Window' for the 'window' method and optimization 'Weights' for arbitrary-magnitude equiripple designs. designfilt provides default values for design options left unspecified.

  • Sample Rate is the frequency at which the filter operates. designfilt has a default sample rate of 2 Hz. Using this value is equivalent to working with normalized frequencies.

  • Implementation parameters determine how the designfilt function implements the filter design. (since R2023b)

Note

If you specify an incomplete or inconsistent set of name-value arguments at the command line, designfilt offers to open a Filter Design Assistant. The assistant helps you design the filter and pastes the corrected MATLAB® code to the command line.

If you call designfilt from a script or function with an incorrect set of specifications, designfilt issues an error message with a link to open a Filter Design Assistant. The assistant helps you design the filter and pastes the corrected MATLAB code on the command line. The designed filter is saved to the workspace.

  • If d is a digitalFilter object, use the filter function in the form of dataOut = filter(d,dataIn) to filter an input signal dataIn. For IIR filters, the filter function uses a direct-form II implementation. You can also use the filtfilt and fftfilt functions with digitalFilter objects.

    If d is a filter System object, pass the input data to the object and run the object algorithm: filtObj = dsp.FIRFilter; dataOut = filtObj(dataIn). (since R2023b)

  • Use Filter Analyzer to visualize the filter d.

  • If d is a digitalFilter object, type d.Numerator and d.Denominator to obtain the numerator and denominator coefficients of the filter. For IIR filters, the coefficients are expressed as second-order cascaded transfer functions.

    If d is an FIR filter System object such as the dsp.FIRFilter object, type d.Numerator to obtain the filter coefficients. If d is an IIR filter System object such as the dsp.SOSFilter object, type d.Numerator and d.Denominator to obtain the numerator and denominator coefficients of the filter. (since R2023b)

  • See digitalFilter for a list of the filtering and analysis functions you can use with the digitalFilter object.

    For a list of filtering and analysis functions supported by filter System objects in DSP System Toolbox™, see Analysis Functions for Filter System Objects. (since R2023b)

example

designfilt(d) lets you edit an existing digital filter d. It opens a Filter Design Assistant populated with the filter specifications, which you can then modify. This is the only way you can edit a digitalFilter object. Its properties are otherwise read-only.

Examples

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Since R2023b

Open Live Script

Design a lowpass FIR filter using the designfilt function.

The filter is a minimum order filter with a passband frequency of 0.45 and a stopband frequency of 0.55 in normalized frequency units. The passband ripple is 1 dB and the stopband attenuation is 60 dB. Use the Kaiser window design method and set the SystemObject argument to true.

With these specifications, the designfilt function generates a dsp.FIRFilter System object™.

lpFIRFilter = designfilt("lowpassfir", ...
    PassbandFrequency=0.45,StopbandFrequency=0.55, ...
    PassbandRipple=1,StopbandAttenuation=60, ...
    DesignMethod="kaiserwin",SystemObject=true)
lpFIRFilter = 
  dsp.FIRFilter with properties:

            Structure: 'Direct form'
      NumeratorSource: 'Property'
            Numerator: [1.2573e-04 -1.9141e-04 -2.7282e-04 3.7207e-04 4.9141e-04 -6.3325e-04 -8.0016e-04 9.9490e-04 0.0012 -0.0015 -0.0018 0.0021 0.0025 -0.0029 -0.0034 0.0040 0.0046 -0.0053 -0.0060 0.0069 0.0079 -0.0090 -0.0102 0.0116 … ] (1×74 double)
    InitialConditions: 0

  Show all properties

Visualize the magnitude and phase responses of this filter using freqz.

freqz(lpFIRFilter.Numerator)

Figure contains 2 axes objects. Axes object 1 with title Phase, xlabel Normalized Frequency (\times\pi rad/sample), ylabel Phase (degrees) contains an object of type line. Axes object 2 with title Magnitude, xlabel Normalized Frequency (\times\pi rad/sample), ylabel Magnitude (dB) contains an object of type line.

Since R2023b

Open Live Script

Design a highpass IIR filter using the designfilt function.

The filter is a 20th order highpass IIR filter with a sample rate of 44.1 kHz. The stopband frequency of the filter is 3 kHz and the passband frequency is 8 kHz. Use the IIR least p-norm design method and set the L-infinity norm to 120. Set the SystemObject argument to true.

With these specifications, the designfilt function generates a dsp.SOSFilter System object™.

hpIIRFilter = designfilt('highpassiir', ...
    FilterOrder=20,StopbandFrequency=3000, ...
    PassbandFrequency=8000,SampleRate=44100, ...
    Norm=120,SystemObject=true)
hpIIRFilter = 
  dsp.SOSFilter with properties:

            Structure: 'Direct form II'
    CoefficientSource: 'Property'
            Numerator: [10×3 double]
          Denominator: [10×3 double]
       HasScaleValues: true
          ScaleValues: [0.5812 1 1 1 1 1 1 1 1 1 14.8291]

  Show all properties

Visualize the frequency response of this filter.

freqz(hpIIRFilter,[],44100)

Figure contains 2 axes objects. Axes object 1 with title Phase, xlabel Frequency (kHz), ylabel Phase (degrees) contains an object of type line. Axes object 2 with title Magnitude, xlabel Frequency (kHz), ylabel Magnitude (dB) contains an object of type line.

Input Arguments

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Filter response and type, specified as a character vector or string scalar.

Select this option to design a finite impulse response (FIR) lowpass filter. This example uses the fifth specification set from the table.

d = designfilt('lowpassfir', ...        % Response type
       'FilterOrder',25, ...            % Filter order
       'PassbandFrequency',400, ...     % Frequency constraints
       'StopbandFrequency',550, ...
       'DesignMethod','ls', ...         % Design method
       'PassbandWeight',1, ...          % Design method options
       'StopbandWeight',2, ...
       'SampleRate',2000)               % Sample rate

  • If you omit 'FilterOrder' (when required), or any of the frequency constraints, designfilt generates an error.

  • If you omit the magnitude constraints, designfilt uses default values.

  • If you omit 'DesignMethod', designfilt uses the default design method for the specification set.

  • If you omit the design method options, designfilt uses the default values for the design method that you have selected.

  • If you omit 'SampleRate', designfilt sets it to 2 Hz.

Filter Order Argument NamesFrequency Constraint Argument NamesMagnitude Constraint Argument Names'DesignMethod' Argument ValuesDesign Option Argument Names

N/A (Minimum-order design)

'PassbandFrequency'

'StopbandFrequency'

'PassbandRipple'

'StopbandAttenuation'

'equiripple' (default)

N/A

'kaiserwin'

'MinOrder'

'ScalePassband'

'FilterOrder'

'HalfPowerFrequency'

N/A

'maxflat'

N/A

'FilterOrder'

'CutoffFrequency'

N/A

'window'

'Window'

'ScalePassband'

'FilterOrder'

'CutoffFrequency'

'PassbandRipple'

'StopbandAttenuation'

'cls'

'PassbandOffset'

'ZeroPhase'

'FilterOrder'

'PassbandFrequency'

'StopbandFrequency'

N/A

'equiripple' (default)

'PassbandWeight'

'StopbandWeight'

'ls'

'PassbandWeight'

'StopbandWeight'

If you have a DSP System Toolbox license, the designfilt function supports these additional design specifications. (since R2023b)

Filter Order Argument NamesFrequency Constraint Argument NamesMagnitude Constraint Argument Names'DesignMethod' Argument ValuesDesign Option Argument Names

N/A (Minimum-order design) (since R2024a)

'PassbandFrequency'

'StopbandFrequency'

'PassbandRipple'

'StopbandAttenuation'

'equiripple'

'MinOrder'

'PhaseConstraint'

N/A (Minimum-order design) (since R2025a)

'PassbandFrequency'

'StopbandFrequency'

'PassbandRipple'

'StopbandAttenuation'

'equiripple'

'StopbandShape''StopbandDecay'

N/A (Minimum-order design) (since R2025a)

'PassbandFrequency'

'StopbandFrequency'

'PassbandRipple'

'StopbandAttenuation'

'ifir' (since R2025a)

'InterpolationFactor'

'JointOptimization'

SystemObject flag is always true.

'FilterOrder' (since R2024a)

'PassbandFrequency'

'StopbandFrequency'

N/A

'equiripple'

'PassbandWeight'

'StopbandWeight'

'PhaseConstraint'

'FilterOrder'

'PassbandFrequency'

'StopbandFrequency'

'PassbandRipple'

'equiripple'

'PhaseConstraint' (since R2024a)

'FilterOrder'

'PassbandFrequency'

'StopbandFrequency'

'StopbandAttenuation'

'equiripple'

'PhaseConstraint' (since R2024a)

'FilterOrder'

'PassbandFrequency'

'PassbandRipple'

'StopbandAttenuation'

'equiripple'

N/A

'FilterOrder'

'StopbandFrequency'

'PassbandRipple'

'StopbandAttenuation'

'equiripple'

N/A

'FilterOrder'

'CutoffFrequency'

'PassbandRipple'

'StopbandAttenuation'

'equiripple'

N/A

'FilterOrder' (since R2025a)

'PassbandFrequency'

'StopbandFrequency'

N/A

'lpnorm'

'Norm'

'DensityFactor'

'InitialNorm'

'InitialNumerator'

'PassbandWeight'

'StopbandWeight'

'PhaseConstraint'

Select this option to design an infinite impulse response (IIR) lowpass filter. This example uses the first specification set from the table.

d = designfilt('lowpassiir', ...        % Response type
       'PassbandFrequency',400, ...     % Frequency constraints
       'StopbandFrequency',550, ...
       'PassbandRipple',4, ...          % Magnitude constraints
       'StopbandAttenuation',55, ...
       'DesignMethod','ellip', ...      % Design method
       'MatchExactly','passband', ...   % Design method options
       'SampleRate',2000)               % Sample rate

  • If you omit 'FilterOrder' (when required), or any of the frequency constraints, designfilt generates an error.

  • If you omit the magnitude constraints, designfilt uses default values.

  • If you omit 'DesignMethod', designfilt uses the default design method for the specification set.

  • If you omit the design method options, designfilt uses the default values for the design method that you have selected.

  • If you omit 'SampleRate', designfilt sets it to 2 Hz.

Filter Order Argument NamesFrequency Constraint Argument NamesMagnitude Constraint Argument Names'DesignMethod' Argument ValuesDesign Option Argument Names

N/A (Minimum-order design)

'PassbandFrequency'

'StopbandFrequency'

'PassbandRipple'

'StopbandAttenuation'

'butter' (default)

'MatchExactly'

'cheby1'

'MatchExactly'

'cheby2'

'MatchExactly'

'ellip'

'MatchExactly'

'FilterOrder'

'HalfPowerFrequency'

N/A

'butter'

N/A

'FilterOrder'

'PassbandFrequency'

'PassbandRipple'

'cheby1'

N/A

'FilterOrder'

'PassbandFrequency'

'PassbandRipple'

'StopbandAttenuation'

'ellip'

N/A

'FilterOrder'

'StopbandFrequency'

'StopbandAttenuation'

'cheby2'

N/A

'NumeratorOrder'

'DenominatorOrder'

'HalfPowerFrequency'

N/A

'butter'

N/A

If you have a DSP System Toolbox license, the designfilt function supports these additional design specifications. (since R2023b)

Filter Order Argument NamesFrequency Constraint Argument NamesMagnitude Constraint Argument Names'DesignMethod' Argument ValuesDesign Option Argument Names

'NumeratorOrder'

'DenominatorOrder'

'PassbandFrequency'

'StopbandFrequency'

N/A

'lpnorm'

'Norm'

'PassbandWeight'

'StopbandWeight'

'FilterOrder' (since R2025a)

'PassbandFrequency'

'StopbandFrequency'

N/A

'lpnorm'

'Norm'

'DensityFactor'

'MaxPoleRadius'

'InitialNorm'

'InitialNumerator'

'InitialDenominator'

'PassbandWeight'

'StopbandWeight'

'FilterOrder'

'PassbandFrequency'

'StopbandFrequency'

'PassbandRipple'

'ellip'

N/A

'FilterOrder'

'PassbandFrequency'

'HalfPowerFrequency'

N/A

'cheby1'

N/A

'FilterOrder'

'HalfPowerFrequency'

'PassbandRipple'

'cheby1'

N/A

'FilterOrder'

'HalfPowerFrequency'

'StopbandAttenuation'

'cheby2'

N/A

'FilterOrder'

'HalfPowerFrequency'

'PassbandRipple'

'StopbandAttenuation'

'ellip'

N/A

'FilterOrder'

'HalfPowerFrequency'

'StopbandFrequency'

N/A

'cheby2'

N/A

Since R2025a

Select this option to design an inverse sinc lowpass finite impulse response (FIR) filter. This example uses the first specification set from the table.

d = designfilt('isinclpfir', ...          % Response type
       'PassbandFrequency',0.45, ...      % Frequency constraints
       'StopbandFrequency',0.55 , ...
       'PassbandRipple',1, ...
       'StopbandAttenuation',60, ...
       'DesignMethod','equiripple', ...   % Design method
       'DensityFactor',16, ...            % Design options
       'MinOrder','any', ...
       'StopbandShape','flat', ...
       'SincFrequencyFactor',0.5, ...
       'SincPower',1, ...
       'PhaseConstraint','linear',...
       'SystemObject',true)

  • If you omit 'FilterOrder' (when required), or any of the required frequency constraints, designfilt generates an error.

  • If you omit the magnitude constraints, designfilt uses default values.

  • If you omit 'DesignMethod', designfilt uses the default design method for the specification set.

  • If you omit the design method options, designfilt uses the default values for the design method that you have selected.

  • If you omit 'SampleRate', designfilt sets it to 2 Hz.

  • To generate a filter System object, set the 'SystemObject' argument to true.

Filter Order Argument NamesFrequency Constraint Argument NamesMagnitude Constraint Argument Names'DesignMethod' Argument ValuesDesign Option Argument Names

N/A (Minimum-order design)

'PassbandFrequency'

'StopbandFrequency'

'PassbandRipple'

'StopbandAttenuation'

'equiripple'

'DensityFactor'

'MinOrder'

'StopbandShape'

'StopbandDecay'

'SincFrequencyFactor'

'SincPower'

'PhaseConstraint'

'FilterOrder'

'PassbandFrequency'

'StopbandFrequency'

N/A

'equiripple'

'DensityFactor'

'PassbandWeight'

'StopbandWeight'

'StopbandShape'

'StopbandDecay'

'SincFrequencyFactor'

'SincPower'

'PhaseConstraint'

'FilterOrder'

'PassbandFrequency'

'PassbandRipple'

'StopbandAttenuation'

'equiripple'

'StopbandShape'

'StopbandDecay'

'SincFrequencyFactor'

'SincPower'

'FilterOrder'

'StopbandFrequency'

'PassbandRipple'

'StopbandAttenuation'

'equiripple'

'StopbandShape'

'StopbandDecay'

'SincFrequencyFactor'

'SincPower'

'FilterOrder'

'CutoffFrequency'

'PassbandRipple'

'StopbandAttenuation'

'equiripple'

'StopbandShape'

'StopbandDecay'

'SincFrequencyFactor'

'SincPower'

Select this option to design a finite impulse response (FIR) highpass filter. This example uses the first specification set from the table.

d = designfilt('highpassfir', ...       % Response type
       'StopbandFrequency',400, ...     % Frequency constraints
       'PassbandFrequency',550, ...
       'StopbandAttenuation',55, ...    % Magnitude constraints
       'PassbandRipple',4, ...
       'DesignMethod','kaiserwin', ...  % Design method
       'ScalePassband',false, ...       % Design method options
       'SampleRate',2000)               % Sample rate

  • If you omit 'FilterOrder' (when required), or any of the frequency constraints, designfilt generates an error.

  • If you omit the magnitude constraints, designfilt uses default values.

  • If you omit 'DesignMethod', designfilt uses the default design method for the specification set.

  • If you omit the design method options, designfilt uses the default values for the design method that you have selected.

  • If you omit 'SampleRate', designfilt sets it to 2 Hz.

Filter Order Argument NamesFrequency Constraint Argument NamesMagnitude Constraint Argument Names'DesignMethod' Argument ValuesDesign Option Argument Names

N/A (Minimum-order design)

'StopbandFrequency'

'PassbandFrequency'

'StopbandAttenuation'

'PassbandRipple'

'equiripple' (default)

N/A

'kaiserwin'

'MinOrder'

'ScalePassband'

'FilterOrder'

'CutoffFrequency'

N/A

'window'

'Window'

'ScalePassband'

'FilterOrder'

'CutoffFrequency'

'StopbandAttenuation'

'PassbandRipple'

'cls'

'PassbandOffset'

'ZeroPhase'

'FilterOrder'

'StopbandFrequency'

'PassbandFrequency'

N/A

'equiripple' (default)

'PassbandWeight'

'StopbandWeight'

'ls'

'PassbandWeight'

'StopbandWeight'

If you have a DSP System Toolbox license, the designfilt function supports these additional design specifications. (since R2023b)

Filter Order Argument NamesFrequency Constraint Argument NamesMagnitude Constraint Argument Names'DesignMethod' Argument ValuesDesign Option Argument Names

N/A (Minimum-order design) (since R2024a)

'StopbandFrequency'

'PassbandFrequency'

'StopbandAttenuation'

'PassbandRipple'

'equiripple'

'MinOrder'

'PhaseConstraint'

N/A (Minimum-order design) (since R2025a)

'StopbandFrequency'

'PassbandFrequency'

'StopbandAttenuation'

'PassbandRipple'

'equiripple'

'StopbandShape'

'StopbandDecay'

N/A (Minimum-order design) (since R2025a)

'StopbandFrequency'

'PassbandFrequency'

'StopbandAttenuation'

'PassbandRipple'

'ifir' (since R2025a)

'InterpolationFactor'

'JointOptimization'

SystemObject flag is always true.

'FilterOrder' (since R2024a)

'PassbandFrequency'

'StopbandFrequency'

N/A

'equiripple'

'PassbandWeight'

'StopbandWeight'

'PhaseConstraint'

'FilterOrder'

'PassbandFrequency'

'StopbandFrequency'

'PassbandRipple'

'equiripple'

'PhaseConstraint' (since R2024a)

'FilterOrder'

'PassbandFrequency'

'StopbandFrequency'

'StopbandAttenuation'

'equiripple'

'PhaseConstraint' (since R2024a)

'FilterOrder'

'PassbandFrequency'

'PassbandRipple'

'StopbandAttenuation'

'equiripple'

N/A

'FilterOrder'

'StopbandFrequency'

'PassbandRipple'

'StopbandAttenuation'

'equiripple'

N/A

'FilterOrder'

'CutoffFrequency'

'PassbandRipple'

'StopbandAttenuation'

'equiripple'

N/A

'FilterOrder' (since R2025a)

'PassbandFrequency'

'StopbandFrequency'

N/A

'lpnorm'

'Norm'

'DensityFactor'

'InitialNorm'

'InitialNumerator'

'PassbandWeight'

'StopbandWeight'

'PhaseConstraint'

Select this option to design an infinite impulse response (IIR) highpass filter. This example uses the first specification set from the table.

d = designfilt('highpassiir', ...       % Response type
       'StopbandFrequency',400, ...     % Frequency constraints
       'PassbandFrequency',550, ...
       'StopbandAttenuation',55, ...    % Magnitude constraints
       'PassbandRipple',4, ...
       'DesignMethod','cheby1', ...     % Design method
       'MatchExactly','stopband', ...   % Design method options
       'SampleRate',2000)               % Sample rate

  • If you omit 'FilterOrder' (when required), or any of the frequency constraints, designfilt generates an error.

  • If you omit the magnitude constraints, designfilt uses default values.

  • If you omit 'DesignMethod', designfilt uses the default design method for the specification set.

  • If you omit the design method options, designfilt uses the default values for the design method that you have selected.

  • If you omit 'SampleRate', designfilt sets it to 2 Hz.

Filter Order Argument NamesFrequency Constraint Argument NamesMagnitude Constraint Argument Names'DesignMethod' Argument ValuesDesign Option Argument Names

N/A (Minimum-order design)

'StopbandFrequency'

'PassbandFrequency'

'StopbandAttenuation'

'PassbandRipple'

'butter' (default)

'MatchExactly'

'cheby1'

'MatchExactly'

'cheby2'

'MatchExactly'

'ellip'

'MatchExactly'

'FilterOrder'

'HalfPowerFrequency'

N/A

'butter'

N/A

'FilterOrder'

'PassbandFrequency'

'PassbandRipple'

'cheby1'

N/A

'FilterOrder'

'PassbandFrequency'

'StopbandAttenuation'

'PassbandRipple'

'ellip'

N/A

'FilterOrder'

'StopbandFrequency'

'StopbandAttenuation'

'cheby2'

N/A

'NumeratorOrder'

'DenominatorOrder'

'HalfPowerFrequency'

N/A

'butter'

N/A

If you have a DSP System Toolbox license, the designfilt function supports these additional design specifications. (since R2023b)

Filter Order Argument NamesFrequency Constraint Argument NamesMagnitude Constraint Argument Names'DesignMethod' Argument ValuesDesign Option Argument Names

'NumeratorOrder'

'DenominatorOrder'

'StopbandFrequency'

'PassbandFrequency'

N/A

'lpnorm'

'Norm'

'PassbandWeight'

'StopbandWeight'

'FilterOrder' (since R2025a)

'StopbandFrequency'

'PassbandFrequency'

N/A

'lpnorm'

'Norm'

'DensityFactor'

'MaxPoleRadius'

'InitialNorm'

'InitialNumerator'

'InitialDenominator'

'StopbandWeight'

'PassbandWeight'

'FilterOrder'

'StopbandFrequency'

'PassbandFrequency'

'PassbandRipple'

'ellip'

N/A

'FilterOrder'

'StopbandFrequency'

'HalfPowerFrequency'

N/A

'cheby2'

N/A

'FilterOrder'

'HalfPowerFrequency'

'PassbandRipple'

'cheby1'

N/A

'FilterOrder'

'HalfPowerFrequency'

'StopbandAttenuation'

'cheby2'

N/A

'FilterOrder'

'HalfPowerFrequency'

'StopbandAttenuation'

'PassbandRipple'

'ellip'

N/A

'FilterOrder'

'HalfPowerFrequency'

'PassbandFrequency'

N/A

'cheby1'

N/A

Since R2025a

Select this option to design an inverse sinc highpass finite impulse response (FIR) filter. This example uses the first specification set from the table.

d = designfilt('isinchpfir', ...          % Response type
       'StopbandFrequency',0.45 , ...     % Frequency constraints
       'PassbandFrequency',0.55, ...             
       'PassbandRipple',1, ...            % Magnitude constraints
       'StopbandAttenuation',60, ...
       'DesignMethod','equiripple', ...   % Design method
       'DensityFactor',16, ...            % Design options
       'MinOrder','any', ...
       'StopbandShape','flat', ...
       'SincFrequencyFactor',0.5, ...
       'SincPower',1, ...
       'PhaseConstraint','linear',...
       'SystemObject',true)

  • If you omit 'FilterOrder' (when required), or any of the required frequency constraints, designfilt generates an error.

  • If you omit the magnitude constraints, designfilt uses default values.

  • If you omit 'DesignMethod', designfilt uses the default design method for the specification set.

  • If you omit the design method options, designfilt uses the default values for the design method that you have selected.

  • If you omit 'SampleRate', designfilt sets it to 2 Hz.

  • To generate a filter System object, set the 'SystemObject' argument to true.

Filter Order Argument NamesFrequency Constraint Argument NamesMagnitude Constraint Argument Names'DesignMethod' Argument ValuesDesign Option Argument Names

N/A (Minimum-order design)

'StopbandFrequency'

'PassbandFrequency'

'StopbandAttenuation'

'PassbandRipple'

'equiripple'

'DensityFactor'

'MinOrder'

'StopbandShape'

'StopbandDecay'

'SincFrequencyFactor'

'SincPower'

'PhaseConstraint'

'FilterOrder'

'StopbandFrequency'

'PassbandFrequency'

N/A

'equiripple'

'DensityFactor'

'PassbandWeight'

'StopbandWeight'

'StopbandShape'

'StopbandDecay'

'SincFrequencyFactor'

'SincPower'

'PhaseConstraint'

'FilterOrder'

'PassbandFrequency'

'StopbandAttenuation'

'PassbandRipple'

'equiripple'

'StopbandShape'

'StopbandDecay'

'SincFrequencyFactor'

'SincPower'

'FilterOrder'

'StopbandFrequency'

'StopbandAttenuation'

'PassbandRipple'

'equiripple'

'StopbandShape'

'StopbandDecay'

'SincFrequencyFactor'

'SincPower'

'FilterOrder'

'CutoffFrequency'

'StopbandAttenuation'

'PassbandRipple'

'equiripple'

'StopbandShape'

'StopbandDecay'

'SincFrequencyFactor'

'SincPower'

Select this option to design a finite impulse response (FIR) bandpass filter. This example uses the fourth specification set from the table.

d = designfilt('bandpassfir', ...       % Response type
       'FilterOrder',86, ...            % Filter order
       'StopbandFrequency1',400, ...    % Frequency constraints
       'PassbandFrequency1',450, ...
       'PassbandFrequency2',600, ...
       'StopbandFrequency2',650, ...
       'DesignMethod','ls', ...         % Design method
       'StopbandWeight1',1, ...         % Design method options
       'PassbandWeight', 2, ...
       'StopbandWeight2',3, ...
       'SampleRate',2000)               % Sample rate

  • If you omit 'FilterOrder' (when required), or any of the frequency constraints, designfilt generates an error.

  • If you omit the magnitude constraints, designfilt uses default values.

  • If you omit 'DesignMethod', designfilt uses the default design method for the specification set.

  • If you omit the design method options, designfilt uses the default values for the design method that you have selected.

  • If you omit 'SampleRate', designfilt sets it to 2 Hz.

Filter Order Argument NamesFrequency Constraint Argument NamesMagnitude Constraint Argument Names'DesignMethod' Argument ValuesDesign Option Argument Names

N/A (Minimum-order design)

'StopbandFrequency1'

'PassbandFrequency1'

'PassbandFrequency2'

'StopbandFrequency2'

'StopbandAttenuation1'

'PassbandRipple'

'StopbandAttenuation2'

'equiripple' (default)

N/A

'kaiserwin'

'MinOrder'

'ScalePassband'

'FilterOrder'

'CutoffFrequency1'

'CutoffFrequency2'

N/A

'window'

'Window'

'ScalePassband'

'FilterOrder'

'CutoffFrequency1'

'CutoffFrequency2'

'StopbandAttenuation1'

'PassbandRipple'

'StopbandAttenuation2'

'cls'

'PassbandOffset'

'ZeroPhase'

'FilterOrder'

'StopbandFrequency1'

'PassbandFrequency1'

'PassbandFrequency2'

'StopbandFrequency2'

N/A

'equiripple' (default)

'StopbandWeight1'

'PassbandWeight'

'StopbandWeight2'

'ls'

'StopbandWeight1'

'PassbandWeight'

'StopbandWeight2'

If you have a DSP System Toolbox license, the designfilt function supports these additional design specifications. (since R2024a)

Filter Order Argument NamesFrequency Constraint Argument NamesMagnitude Constraint Argument Names'DesignMethod' Argument ValuesDesign Option Argument Names

N/A (Minimum-order design)

'StopbandFrequency1'

'PassbandFrequency1'

'PassbandFrequency2'

'StopbandFrequency2'

'StopbandAttenuation1'

'PassbandRipple'

'StopbandAttenuation2'

'equiripple'

'MinOrder'

'PhaseConstraint'

'FilterOrder'

'StopbandFrequency1'

'PassbandFrequency1'

'PassbandFrequency2'

'StopbandFrequency2'

N/A

'equiripple'

'StopbandWeight1'

'PassbandWeight'

'StopbandWeight2'

'PhaseConstraint'

'FilterOrder' (since R2025a)

'StopbandFrequency1'

'PassbandFrequency1'

'PassbandFrequency2'

'StopbandFrequency2'

N/A

'lpnorm'

'Norm'

'DensityFactor'

'InitialNorm'

'InitialNumerator'

'PassbandWeight'

'StopbandWeight1'

'StopbandWeight2'

'PhaseConstraint'

'FilterOrder'

'StopbandFrequency1'

'PassbandFrequency1'

'PassbandFrequency2'

'StopbandFrequency2'

Stopband1Constrained

PassbandConstrained

Stopband2Constrained

'equiripple'

'StopbandWeight1'

'PassbandWeight'

'StopbandWeight2'

'PhaseConstraint'

Select this option to design an infinite impulse response (IIR) bandpass filter. This example uses the first specification set from the table.

d = designfilt('bandpassiir', ...       % Response type
       'StopbandFrequency1',400, ...    % Frequency constraints
       'PassbandFrequency1',450, ...
       'PassbandFrequency2',600, ...
       'StopbandFrequency2',650, ...
       'StopbandAttenuation1',40, ...   % Magnitude constraints
       'PassbandRipple',1, ...
       'StopbandAttenuation2',50, ...
       'DesignMethod','ellip', ...      % Design method
       'MatchExactly','passband', ...   % Design method options
       'SampleRate',2000)               % Sample rate

  • If you omit 'FilterOrder' (when required), or any of the frequency constraints, designfilt generates an error.

  • If you omit the magnitude constraints, designfilt uses default values.

  • If you omit 'DesignMethod', designfilt uses the default design method for the specification set.

  • If you omit the design method options, designfilt uses the default values for the design method that you have selected.

  • If you omit 'SampleRate', designfilt sets it to 2 Hz.

Filter Order Argument NamesFrequency Constraint Argument NamesMagnitude Constraint Argument Names'DesignMethod' Argument ValuesDesign Option Argument Names

N/A (Minimum-order design)

'StopbandFrequency1'

'PassbandFrequency1'

'PassbandFrequency2'

'StopbandFrequency2'

'StopbandAttenuation1'

'PassbandRipple'

'StopbandAttenuation2'

'butter' (default)

'MatchExactly'

'cheby1'

'MatchExactly'

'cheby2'

'MatchExactly'

'ellip'

'MatchExactly'

'FilterOrder'

'HalfPowerFrequency1'

'HalfPowerFrequency2'

N/A

'butter'

N/A

'FilterOrder'

'PassbandFrequency1'

'PassbandFrequency2'

'PassbandRipple'

'cheby1'

N/A

'FilterOrder'

'PassbandFrequency1'

'PassbandFrequency2'

'StopbandAttenuation1'

'PassbandRipple'

'StopbandAttenuation2'

'ellip'

N/A

'FilterOrder'

'StopbandFrequency1'

'StopbandFrequency2'

'StopbandAttenuation'

'cheby2'

N/A

If you have a DSP System Toolbox license, the designfilt function supports these additional design specifications. (since R2024a)

Filter Order Argument NamesFrequency Constraint Argument NamesMagnitude Constraint Argument Names'DesignMethod' Argument ValuesDesign Option Argument Names

'FilterOrder' (since R2025a)

'StopbandFrequency1'

'PassbandFrequency1'

'PassbandFrequency2'

'StopbandFrequency2'

N/A

'lpnorm'

'Norm'

'DensityFactor'

'MaxPoleRadius'

'InitialNorm'

'InitialNumerator'

'InitialDenominator'

'StopbandWeight1'

'PassbandWeight'

'StopbandWeight2'

'FilterOrder'

'StopbandFrequency1'

'PassbandFrequency1'

'PassbandFrequency2'

'StopbandFrequency2'

'PassbandRipple'

'ellip'

N/A

'FilterOrder'

'HalfPowerFrequency1'

'HalfPowerFrequency2'

'PassbandRipple'

'cheby1'

N/A

'FilterOrder'

'HalfPowerFrequency1'

'HalfPowerFrequency2'

'StopbandAttenuation'

'cheby2'

N/A

'FilterOrder'

'HalfPowerFrequency1'

'HalfPowerFrequency2'

'StopbandAttenuation1'

'PassbandRipple'

'StopbandAttenuation2'

'ellip'

N/A

'FilterOrder'

'HalfPowerFrequency1'

'HalfPowerFrequency2'

'PassbandBandwidth'

N/A

'cheby1'

N/A

'FilterOrder'

'HalfPowerFrequency1'

'HalfPowerFrequency2'

'StopbandBandwidth'

N/A

'cheby2'

N/A

Select this option to design a finite impulse response (FIR) bandstop filter. This example uses the fourth specification set from the table.

d = designfilt('bandstopfir', ...       % Response type
       'FilterOrder',32, ...            % Filter order
       'PassbandFrequency1',400, ...    % Frequency constraints
       'StopbandFrequency1',500, ...
       'StopbandFrequency2',700, ...
       'PassbandFrequency2',850, ...
       'DesignMethod','ls', ...         % Design method
       'PassbandWeight1',1, ...         % Design method options
       'StopbandWeight', 3, ...
       'PassbandWeight2',5, ...
       'SampleRate',2000)               % Sample rate

  • If you omit 'FilterOrder' (when required), or any of the frequency constraints, designfilt generates an error.

  • If you omit the magnitude constraints, designfilt uses default values.

  • If you omit 'DesignMethod', designfilt uses the default design method for the specification set.

  • If you omit the design method options, designfilt uses the default values for the design method that you have selected.

  • If you omit 'SampleRate', designfilt sets it to 2 Hz.

Filter Order Argument NamesFrequency Constraint Argument NamesMagnitude Constraint Argument Names'DesignMethod' Argument ValuesDesign Option Argument Names

N/A (Minimum-order design)

'PassbandFrequency1'

'StopbandFrequency1'

'StopbandFrequency2'

'PassbandFrequency2'

'PassbandRipple1'

'StopbandAttenuation'

'PassbandRipple2'

'equiripple' (default)

N/A

'kaiserwin'

'MinOrder'

'ScalePassband'

'FilterOrder'

'CutoffFrequency1'

'CutoffFrequency2'

N/A

'window'

'Window'

'ScalePassband'

'FilterOrder'

'CutoffFrequency1'

'CutoffFrequency2'

'PassbandRipple1'

'StopbandAttenuation'

'PassbandRipple2'

'cls'

'PassbandOffset'

'ZeroPhase'

'FilterOrder'

'PassbandFrequency1'

'StopbandFrequency1'

'StopbandFrequency2'

'PassbandFrequency2'

N/A

'equiripple' (default)

'PassbandWeight1'

'StopbandWeight'

'PassbandWeight2'

'ls'

'PassbandWeight1'

'StopbandWeight'

'PassbandWeight2'

If you have a DSP System Toolbox license, the designfilt function supports these additional design specifications. (since R2024a)

Filter Order Argument NamesFrequency Constraint Argument NamesMagnitude Constraint Argument Names'DesignMethod' Argument ValuesDesign Option Argument Names

N/A (Minimum-order design)

'PassbandFrequency1'

'StopbandFrequency1'

'StopbandFrequency2'

'PassbandFrequency2'

'PassbandRipple1'

'StopbandAttenuation'

'PassbandRipple2'

'equiripple'

'PhaseConstraint'

'FilterOrder'

'PassbandFrequency1'

'StopbandFrequency1'

'StopbandFrequency2'

'PassbandFrequency2'

N/A

'equiripple'

'PassbandWeight1'

'StopbandWeight'

'PassbandWeight2'

'PhaseConstraint'

'FilterOrder' (since R2025a)

'PassbandFrequency1'

'StopbandFrequency1'

'StopbandFrequency2'

'PassbandFrequency2'

N/A

'lpnorm'

'Norm'

'DensityFactor'

'InitialNorm'

'InitialNumerator'

'PassbandWeight1'

'StopbandWeight'

'PassbandWeight2'

'PhaseConstraint'

'FilterOrder'

'PassbandFrequency1'

'StopbandFrequency1'

'StopbandFrequency2'

'PassbandFrequency2'

Passband1Constrained

StopbandConstrained

Passband2Constrained

'equiripple'

'PassbandWeight1'

'StopbandWeight'

'PassbandWeight2'

'PhaseConstraint'

Select this option to design an infinite impulse response (IIR) bandstop filter. This example uses the first specification set from the table.

d = designfilt('bandstopiir', ...       % Response type
       'PassbandFrequency1',400, ...    % Frequency constraints
       'StopbandFrequency1',500, ...
       'StopbandFrequency2',700, ...
       'PassbandFrequency2',850, ...
       'PassbandRipple1',1, ...         % Magnitude constraints
       'StopbandAttenuation',55, ...
       'PassbandRipple2',1, ...
       'DesignMethod','ellip', ...      % Design method
       'MatchExactly','both', ...       % Design method options
       'SampleRate',2000)               % Sample rate

  • If you omit 'FilterOrder' (when required), or any of the frequency constraints, designfilt generates an error.

  • If you omit the magnitude constraints, designfilt uses default values.

  • If you omit 'DesignMethod', designfilt uses the default design method for the specification set.

  • If you omit the design method options, designfilt uses the default values for the design method that you have selected.

  • If you omit 'SampleRate', designfilt sets it to 2 Hz.

Filter Order Argument NamesFrequency Constraint Argument NamesMagnitude Constraint Argument Names'DesignMethod' Argument ValuesDesign Option Argument Names

N/A (Minimum-order design)

'PassbandFrequency1'

'StopbandFrequency1'

'StopbandFrequency2'

'PassbandFrequency2'

'PassbandRipple1'

'StopbandAttenuation'

'PassbandRipple2'

'butter' (default)

'MatchExactly'

'cheby1'

'MatchExactly'

'cheby2'

'MatchExactly'

'ellip'

'MatchExactly'

'FilterOrder'

'HalfPowerFrequency1'

'HalfPowerFrequency2'

N/A

'butter'

N/A

'FilterOrder'

'PassbandFrequency1'

'PassbandFrequency2'

'PassbandRipple'

'cheby1'

N/A

'FilterOrder'

'PassbandFrequency1'

'PassbandFrequency2'

'PassbandRipple'

'StopbandAttenuation'

'ellip'

N/A

'FilterOrder'

'StopbandFrequency1'

'StopbandFrequency2'

'StopbandAttenuation'

'cheby2'

N/A

If you have a DSP System Toolbox license, the designfilt function supports these additional design specifications. (since R2024a)

Filter Order Argument NamesFrequency Constraint Argument NamesMagnitude Constraint Argument Names'DesignMethod' Argument ValuesDesign Option Argument Names

'FilterOrder' (since R2025a)

'PassbandFrequency1'

'StopbandFrequency1'

'StopbandFrequency2'

'PassbandFrequency2'

N/A

'lpnorm'

'Norm'

'DensityFactor'

'MaxPoleRadius'

'InitialNorm'

'InitialNumerator'

'InitialDenominator'

'PassbandWeight1'

'StopbandWeight'

'PassbandWeight2'

'FilterOrder'

'PassbandFrequency1'

'StopbandFrequency1'

'StopbandFrequency2'

'PassbandFrequency2'

'PassbandRipple'

'ellip'

N/A

'FilterOrder'

'HalfPowerFrequency1'

'HalfPowerFrequency2'

'PassbandRipple'

'cheby1'

N/A

'FilterOrder'

'HalfPowerFrequency1'

'HalfPowerFrequency2'

'StopbandAttenuation'

'cheby2'

N/A

'FilterOrder'

'HalfPowerFrequency1'

'HalfPowerFrequency2'

'PassbandRipple'

'StopbandAttenuation'

'ellip'

N/A

'FilterOrder'

'HalfPowerFrequency1'

'HalfPowerFrequency2'

'StopbandBandwidth'

N/A

'cheby2'

N/A

'FilterOrder'

'HalfPowerFrequency1'

'HalfPowerFrequency2'

PassbandBandwidth

N/A

'cheby1'

N/A

Since R2025a

Select this option to design a multi-notch IIR filter. This example uses the second specification set from the table.

d = designfilt('notchiir', ...
    'FilterOrder',[6 6],'CenterFrequency',[2.5 7.5], ...
    'QualityFactor',[2.5 7.5],'PassbandRipple',1, ...
    'SampleRate',20,'SystemObject',true);

Here is an example that designs a notching comb filter.

d = designfilt('notchiir', ...
    'NumNotches',10,'NotchLocations','Harmonic',...
    'Bandwidth',0.125,'BandwidthGain',-3,...
    'ShelvingFilterOrder',1,'SystemObject',true);

  • If you omit 'FilterOrder' (when applicable), or any of the frequency or magnitude constraints, designfilt generates an error.

  • If you omit 'DesignMethod', designfilt uses the default design method for the specification set.

  • If you omit 'SampleRate', designfilt sets it to 2 Hz.

  • To generate a filter System object, set the 'SystemObject' argument to true.

Filter Order Argument NamesFrequency Constraint Argument NamesMagnitude Constraint Argument Names'DesignMethod' Argument Values

'FilterOrder'

'CenterFrequency'

'QualityFactor'

'NotchLocations' set to "Specify"

N/A

'butter'

'FilterOrder'

'CenterFrequency'

'QualityFactor'

'NotchLocations' set to "Specify"

'PassbandRipple'

'cheby1'

'FilterOrder'

'CenterFrequency'

'QualityFactor'

'NotchLocations' set to "Specify"

'StopbandAttenuation'

'cheby2'

'FilterOrder'

'CenterFrequency'

'QualityFactor'

'NotchLocations' set to "Specify"

'PassbandRipple'

'StopbandAttenuation'

'ellip'

'FilterOrder'

'CenterFrequency'

'Bandwidth'

'NotchLocations' set to "Specify"

N/A

'butter'

'FilterOrder'

'CenterFrequency'

'Bandwidth'

'NotchLocations' set to "Specify"

'PassbandRipple'

'cheby1'

'FilterOrder'

'CenterFrequency'

'Bandwidth'

'NotchLocations' set to "Specify"

'StopbandAttenuation'

'cheby2'

'FilterOrder'

'CenterFrequency'

'Bandwidth'

'NotchLocations' set to "Specify"

'PassbandRipple'

'StopbandAttenuation'

'ellip'

'NumNotches'

'ShelvingFilterOrder'

'Bandwidth'

'NotchLocations' set to "Harmonic"

'BandwidthGain'

'butter'

Since R2025a

Select this option to design a multi-peak IIR filter. This example uses the second specification set from the table.

d = designfilt('peakiir', ...
    'FilterOrder',[6 6],'CenterFrequency',[2.5 7.5], ...
    'QualityFactor',[2.5 7.5],'PassbandRipple',1, ...
    'SampleRate',20,'SystemObject',true);

Here is an example that designs a peaking comb filter.

d = designfilt('peakiir', ...
    'NumPeaks',10,'PeakLocations','Harmonic',...
    'Bandwidth',0.125,'BandwidthGain',-3,...
    'ShelvingFilterOrder',1,'SystemObject',true);

  • If you omit 'FilterOrder' (when applicable), or any of the frequency or magnitude constraints, designfilt generates an error.

  • If you omit 'DesignMethod', designfilt uses the default design method for the specification set.

  • If you omit 'SampleRate', designfilt sets it to 2 Hz.

  • To generate a filter System object, set the 'SystemObject' argument to true.

Filter Order Argument NamesFrequency Constraint Argument NamesMagnitude Constraint Argument Names'DesignMethod' Argument Values

'FilterOrder'

'CenterFrequency'

'QualityFactor'

'PeakLocations' set to "Specify"

N/A

'butter'

'FilterOrder'

'CenterFrequency'

'QualityFactor'

'PeakLocations' set to "Specify"

'PassbandRipple'

'cheby1'

'FilterOrder'

'CenterFrequency'

'QualityFactor'

'PeakLocations' set to "Specify"

'StopbandAttenuation'

'cheby2'

'FilterOrder'

'CenterFrequency'

'QualityFactor'

'PeakLocations' set to "Specify"

'PassbandRipple'

'StopbandAttenuation'

'ellip'

'FilterOrder'

'CenterFrequency'

'Bandwidth'

'PeakLocations' set to "Specify"

N/A

'butter'

'FilterOrder'

'CenterFrequency'

'Bandwidth'

'PeakLocations' set to "Specify"

'PassbandRipple'

'cheby1'

'FilterOrder'

'CenterFrequency'

'Bandwidth'

'PeakLocations' set to "Specify"

'StopbandAttenuation'

'cheby2'

'FilterOrder'

'CenterFrequency'

'Bandwidth'

'PeakLocations' set to "Specify"

'PassbandRipple'

'StopbandAttenuation'

'ellip'

'NumPeaks'

'ShelvingFilterOrder'

'Bandwidth'

'PeakLocations' set to "Harmonic"

'BandwidthGain'

'butter'

Select this option to design a finite impulse response (FIR) differentiator filter. This example uses the second specification set from the table.

d = designfilt('differentiatorfir', ... % Response type
       'FilterOrder',42, ...            % Filter order
       'PassbandFrequency',400, ...     % Frequency constraints
       'StopbandFrequency',500, ...
       'DesignMethod','equiripple', ... % Design method
       'PassbandWeight',1, ...          % Design method options
       'StopbandWeight',4, ...
       'SampleRate',2000)               % Sample rate

  • If you omit 'FilterOrder' (when required), or any of the frequency constraints when designing a partial-band differentiator, designfilt generates an error.

  • If you omit 'DesignMethod', designfilt uses the default design method for the specification set.

  • If you omit the design method options, designfilt uses the default values for the design method that you have selected.

  • If you omit 'SampleRate', designfilt sets it to 2 Hz.

Filter Order Argument NamesFrequency Constraint Argument NamesMagnitude Constraint Argument Names'DesignMethod' Argument ValuesDesign Option Argument Names

'FilterOrder'

N/A

N/A

'equiripple' (default)

N/A

'ls'

N/A

'FilterOrder'

'PassbandFrequency'

'StopbandFrequency'

N/A

'equiripple' (default)

'PassbandWeight'

'StopbandWeight'

'ls'

N/A

If you have a DSP System Toolbox license, the designfilt function supports these additional design specifications. (since R2025a)

Filter Order Argument NamesFrequency Constraint Argument NamesMagnitude Constraint Argument Names'DesignMethod' Argument ValuesDesign Option Argument Names

N/A (Minimum-order design)

'PassbandFrequency'

'StopbandFrequency'

'PassbandRipple'

'StopbandAttenuation'

'equiripple'

'DensityFactor'

Select this option to design a finite impulse response (FIR) Hilbert transformer filter. This example uses the specification set from the table.

d = designfilt('hilbertfir', ...        % Response type
       'FilterOrder',12, ...            % Filter order
       'TransitionWidth',400, ...       % Frequency constraints
       'DesignMethod','ls', ...         % Design method
       'SampleRate',2000)               % Sample rate

  • If you omit 'FilterOrder' (when required) or 'TransitionWidth', designfilt generates an error.

  • If you omit 'DesignMethod', designfilt uses the default design method for Hilbert transformers.

  • If you omit 'SampleRate', designfilt sets it to 2 Hz.

Filter Order Argument NamesFrequency Constraint Argument NamesMagnitude Constraint Argument Names'DesignMethod' Argument ValuesDesign Option Argument Names

'FilterOrder'

'TransitionWidth'

N/A

'equiripple' (default)

N/A

'ls'

N/A

If you have a DSP System Toolbox license, the designfilt function supports these additional design specifications. (since R2025a)

Filter Order Argument NamesFrequency Constraint Argument NamesMagnitude Constraint Argument Names'DesignMethod' Argument ValuesDesign Option Argument Names

N/A (Minimum-order design)

'TransitionWidth'

'PassbandRipple'

'equiripple'

'DensityFactor'

'FIRType'

Select this option to design a finite impulse response (FIR) filter of arbitrary magnitude response. This example uses the second specification set from the table.

d = designfilt('arbmagfir', ...         % Response type
       'FilterOrder',88, ...            % Filter order
       'NumBands',4, ...                % Frequency constraints
       'BandFrequencies1',[0 20], ...
       'BandFrequencies2',[25 40], ...
       'BandFrequencies3',[45 65], ...
       'BandFrequencies4',[70 100], ...
       'BandAmplitudes1',[2 2], ...     % Magnitude constraints
       'BandAmplitudes2',[0 0], ...
       'BandAmplitudes3',[1 1], ...
       'BandAmplitudes4',[0 0], ...
       'DesignMethod','ls', ...         % Design method
       'BandWeights1',[1 1]/10, ...     % Design method options
       'BandWeights2',[3 1], ...
       'BandWeights3',[2 4], ...
       'BandWeights4',[5 1], ...
       'SampleRate',200)                % Sample rate

  • If you omit 'FilterOrder', or any of the frequency or magnitude constraints, designfilt generates an error.

  • If you omit 'DesignMethod', designfilt uses the default design method for the specification set.

  • If you omit the design method options, designfilt uses the default values for the design method that you have selected.

  • If you omit 'SampleRate', designfilt sets it to 2 Hz.

Filter Order Argument NamesFrequency Constraint Argument NamesMagnitude Constraint Argument Names'DesignMethod' Argument ValuesDesign Option Argument Names

'FilterOrder'

'Frequencies'

'Amplitudes'

'freqsamp' (default)

'Window'

'equiripple'

'Weights'

'ls'

'Weights'

'FilterOrder'

'NumBands'

'BandFrequencies1'

…

'BandFrequenciesN'

'BandAmplitudes1'

…

'BandAmplitudesN'

'equiripple' (default)

'BandWeights1'

…

'BandWeightsN'

'ls'

'BandWeights1'

…

'BandWeightsN'

If you have a DSP System Toolbox license, the designfilt function supports these additional design specifications. (since R2025a)

Filter Order Argument NamesFrequency Constraint Argument NamesMagnitude Constraint Argument Names'DesignMethod' Argument ValuesDesign Option Argument Names

'FilterOrder'

'Frequencies'

'Amplitudes'

'lpnorm'

'Weights'

'FilterOrder'

'NumBands'

'BandFrequencies1'

…

'BandFrequenciesN'

'BandAmplitudes1'

…

'BandAmplitudesN'

'lpnorm'

'BandWeights1'

…

'BandWeightsN'

'FilterOrder'

'NumBands'

'BandFrequencies1'

…

'BandFrequenciesN'

'BandAmplitudes1'

…

'BandAmplitudesN'

'BandConstrained1'

…

'BandConstrainedN'

'BandRipple1'

…

'BandRippleN'

'equiripple'

'DensityFactor'

'PhaseConstraint'

'BandWeights1'

…

'BandWeightsN'

'BandForcedFrequencyPoints1'

…

'BandForcedFrequencyPointsN'

'UniformGrid'

N/A (Minimum-order design)

'Frequencies'

'Amplitudes'

'equiripple'

'Weights'

'MinOrder'

'InitialOrder'

'PhaseConstraint'

N/A (Minimum-order design)

'NumBands'

'BandFrequencies1'

…

'BandFrequenciesN'

'BandAmplitudes1'

…

'BandAmplitudesN'

'BandRipple1'

…

'BandRippleN'

'equiripple'

'DensityFactor'

'BandWeights1'

…

'BandWeightsN'

'MinOrder'

'InitialOrder'

'PhaseConstraint'

Since R2025a

Select this option to design an infinite impulse response (IIR) filter of arbitrary magnitude response. This example uses the first specification set from the table.

d = designfilt('arbmagiir', ...
    'FilterOrder',20,'Frequencies',linspace(0,1,30),...
    'Amplitudes',[ones(1,7) zeros(1,8) ones(1,8) zeros(1,7)],...
    'SystemObject',true);

  • If you omit 'FilterOrder', or any of the frequency or magnitude constraints, designfilt generates an error.

  • If you omit 'DesignMethod', designfilt uses the default design method for the specification set.

  • If you omit the design method options, designfilt uses the default values for the design method that you have selected.

  • If you omit 'SampleRate', designfilt sets it to 2 Hz.

  • To generate a filter System object, set the 'SystemObject' argument to true.

Filter Order Argument NamesFrequency Constraint Argument NamesMagnitude Constraint Argument Names'DesignMethod' Argument ValuesDesign Option Argument Names

'FilterOrder'

'Frequencies'

'Amplitudes'

'lpnorm'

'DensityFactor'

'Norm'

'MaxPoleRadius'

'InitialNorm'

'InitialNumerator'

'InitialDenominator'

'Weights'

'FilterOrder'

'NumBands'

'BandFrequencies1'

…

'BandFrequenciesN'

'BandAmplitudes1'

…

'BandAmplitudesN'

'lpnorm'

'BandWeights1'

…

'BandWeightsN'

'DensityFactor'

'Norm'

'MaxPoleRadius'

'InitialNorm'

'InitialNumerator'

'InitialDenominator'

Since R2025a

Select this option to design a finite impulse response (FIR) filter of arbitrary magnitude and phase responses. This example uses the second specification set from the table.

d = designfilt('arbmagnphasefir', ...
        'FilterOrder',20,'NumBands',2, ...
        'BandFrequencies1',[0 0.25],...
        'BandFrequencyResponse1',exp(-12*j*pi*linspace(0,...
        1,2)),'BandFrequencies2',[0.5 0.75], ...
        'BandFrequencyResponse2',exp(-12*j*pi*linspace(0,1,2)), ...
        'SystemObject',true);

  • If you omit 'FilterOrder', or any of the frequency or magnitude constraints, designfilt generates an error.

  • If you omit 'DesignMethod', designfilt uses the default design method for the specification set.

  • If you omit the design method options, designfilt uses the default values for the design method that you have selected.

  • If you omit 'SampleRate', designfilt sets it to 2 Hz.

  • To generate a filter System object, set the 'SystemObject' argument to true.

Filter Order Argument NamesFrequency Constraint Argument NamesMagnitude Constraint Argument Names'DesignMethod' Argument ValuesDesign Option Argument Names

'FilterOrder'

'Frequencies'

'FrequencyResponse''equiripple'

'DensityFactor'

'Weights'

'FilterOrder'

'Frequencies'

'FrequencyResponse''ls'

'DensityFactor'

'Weights'

'FilterOrder'

'Frequencies'

'FrequencyResponse''freqsamp'

'DensityFactor'

'Weights'

'FilterOrder'

'NumBands'

'BandFrequencies1'

…

'BandFrequenciesN'

'BandFrequencyResponse1'

…

'BandFrequencyResponseN'

'equiripple'

'DensityFactor'

'BandWeights1'

…

'BandWeightsN'

'FilterOrder'

'NumBands'

'BandFrequencies1'

…

'BandFrequenciesN'

'BandFrequencyResponse1'

…

'BandFrequencyResponseN'

'ls'

'DensityFactor'

'BandWeights1'

…

'BandWeightsN'

Since R2025a

Select this option to design an infinite impulse response (IIR) filter of arbitrary magnitude and phase responses. This example uses the specification set from the table.

d = designfilt('arbmagnphaseiir', ...
        'FilterOrder',20,...
        'Frequencies',[0 0.25 1],...
        'FrequencyResponse',[complex(1,2) complex(3,4) complex(5,6)],...
        'DesignMethod','ls',...
        'SystemObject',true)

  • If you omit 'FilterOrder', or any of the frequency or magnitude constraints, designfilt generates an error.

  • If you omit 'DesignMethod', designfilt uses the default design method for the specification set.

  • If you omit the design method options, designfilt uses the default values for the design method that you have selected.

  • If you omit 'SampleRate', designfilt sets it to 2 Hz.

  • To generate a filter System object, set the 'SystemObject' argument to true.

Filter Order Argument NamesFrequency Constraint Argument NamesMagnitude Constraint Argument Names'DesignMethod' Argument ValuesDesign Option Argument Names

'FilterOrder'

'Frequencies'

'FrequencyResponse'

'ls'

'Weights'

'NumeratorOrder'

'DenominatorOrder'

'Frequencies'

'FrequencyResponse'

'ls'

'Weights'

Since R2025a

Select this option to design an infinite impulse response (IIR) filter of arbitrary group delay. This example uses the first specification set from the table.

d = designfilt('arbgrpdelayiir', ...
    'FilterOrder',20,'Frequencies',linspace(0,1,30),...
    'GroupDelayResponse',[10*ones(1,15) linspace(10,1,15)],...
    'SystemObject',true);

  • If you omit 'FilterOrder', or any of the frequency or magnitude constraints, designfilt generates an error.

  • If you omit 'DesignMethod', designfilt uses the default design method for the specification set.

  • If you omit the design method options, designfilt uses the default values for the design method that you have selected.

  • If you omit 'SampleRate', designfilt sets it to 2 Hz.

  • To generate a filter System object, set the 'SystemObject' argument to true.

Filter Order Argument NamesFrequency Constraint Argument NamesMagnitude Constraint Argument Names'DesignMethod' Argument ValuesDesign Option Argument Names

'FilterOrder'

'Frequencies'

'GroupDelayResponse'

'lpnorm'

'DensityFactor'

'Norm'

'MaxPoleRadius'

'InitialNorm'

'InitialDenominator'

'Weights'

'FilterOrder'

'NumBands'

'BandFrequencies1'

…

'BandFrequenciesN'

'BandGroupDelayResponse1'

…

'BandGroupDelayResponseN'

'lpnorm'

'BandWeights1'

…

'BandWeightsN'

'DensityFactor'

'Norm'

'MaxPoleRadius'

'InitialNorm'

'InitialDenominator'

Since R2025a

Select this option to design a fractional delay FIR filter.

d = designfilt('fracdelayfir', ...
    'FilterOrder',45,'FractionalDelay',0.6,...
    'SampleRate',20,'SystemObject',true);

  • You must specify 'FilterOrder' or 'Bandwidth', but not both. If you specify both the arguments, the designfilt function generates an error.

  • If you omit 'SampleRate', designfilt sets it to 2 Hz.

Filter Order Argument NamesFrequency Constraint Argument NamesMagnitude Constraint Argument Names'DesignMethod' Argument ValuesDesign Option Argument Names

'FilterOrder'

N/A

N/A

N/A

'FractionalDelay'

N/A

'Bandwidth'

N/A

N/A

'FractionalDelay'

Data Types: char | string

Digital filter, specified as a digitalFilter object generated by designfilt. Use this input to change the specifications of an existing digitalFilter.

Name-Value Arguments

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Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Example: FilterOrder=20,CutoffFrequency=0.4 suffices to specify a lowpass FIR filter.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: 'FilterOrder',20,'CutoffFrequency',0.4 suffices to specify a lowpass FIR filter.

Not all name-value combinations are valid. The valid combinations depend on the filter response that you need and on the frequency and magnitude constraints of your design.

Sample Rate

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Sample rate, specified as a positive scalar expressed in hertz. To work with normalized frequencies, set 'SampleRate' to 2, or simply omit it.

Data Types: double

Filter Order

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Filter order, N, specified as a positive integer.

Data Types: double

Numerator order for IIR filters, specified as a positive integer.

Data Types: double

Denominator order for IIR filters, specified as a positive integer.

Data Types: double

Since R2025a

Source of notch frequencies, specified as one of these:

  • 'Specify' –– Specify the notch center frequencies using the CenterFrequency property.

  • 'Harmonic' –– Attenuate a set of harmonically related frequencies using a comb filter. Specify the number of harmonics using the NumNotches property.

Dependencies

This property applies only when you set the filter response to 'notchiir'.

Data Types: double

Since R2025a

Number of harmonic notches in the two-sided spectrum, specified as a positive integer. The function uses this value to determine the number of harmonically related notch frequencies in the comb filter.

Dependencies

This property applies only when you set the filter response to 'notchiir' and NotchLocations to 'Harmonic'.

Data Types: double

Since R2025a

Source of peak frequencies, specified as one of these:

  • 'Specify' –– Specify the peak center frequencies using the CenterFrequency property.

  • 'Harmonic' –– Amplify a set of harmonically related frequencies using a comb filter. Specify the number of harmonics using the NumPeaks property.

Dependencies

This property applies only when you set the filter response to 'peakiir'.

Data Types: double

Since R2025a

Number of harmonic peaks in the two-sided spectrum, specified as a positive integer. The function uses this value to determine the number of harmonically related peak frequencies in the comb filter.

Dependencies

This property applies only when you set the filter response to 'peakiir' and PeakLocations to 'Harmonic'.

Data Types: double

Since R2025a

Shelving filter order Nsh, specified as a positive integer. The shelving filter order determines the sharpness of the peaks or notches. The greater the value of the shelving filter order, the steeper the slope of the peak or notch. The order of the notching or peaking filter is given by L×Nsh, where L is the number of notches or peaks you specify using NumNotches or NumPeaks.

Dependencies

This property applies only when you set:

  • Filter response to 'notchiir' or 'peakiir'.

  • NotchLocations or PeakLocations to 'Harmonic'.

Data Types: double

Frequency Constraints

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Passband frequency, specified as a positive scalar. The frequency value must be within the Nyquist range.

'PassbandFrequency1' is the lower passband frequency for a bandpass or bandstop design.

'PassbandFrequency2' is the higher passband frequency for a bandpass or bandstop design.

Data Types: double

Stopband frequency, specified as a positive scalar. The frequency value must be within the Nyquist range.

'StopbandFrequency1' is the lower stopband frequency for a bandpass or bandstop design.

'StopbandFrequency2' is the higher stopband frequency for a bandpass or bandstop design.

Data Types: double

6-dB frequency, specified as a positive scalar. The frequency value must be within the Nyquist range.

'CutoffFrequency1' is the lower 6-dB frequency for a bandpass or bandstop design.

'CutoffFrequency2' is the higher 6-dB frequency for a bandpass or bandstop design.

Data Types: double

3-dB frequency, specified as a positive scalar. The frequency value must be within the Nyquist range.

'HalfPowerFrequency1' is the lower 3-dB frequency for a bandpass or bandstop design.

'HalfPowerFrequency2' is the higher 3-dB frequency for a bandpass or bandstop design.

Data Types: double

Bandwidth of the filter passband in normalized frequency units, specified as a positive scalar less than the difference between 'HalfPowerFrequency2' and 'HalfPowerFrequency1'.

Dependencies

This property applies only if you set the filter response to 'bandpassiir' or 'bandstopiir'.

Data Types: double

Frequency width between the two stopband frequencies, specified as a positive scalar.

Dependencies

This property applies only if you set the filter response to 'bandpassiir' or 'bandstopiir'.

Data Types: double

Width of the transition region between passband and stopband for a Hilbert transformer, specified as a positive scalar.

Data Types: double

Response frequencies, specified as a vector. Use this variable to list the frequencies at which a filter of arbitrary magnitude and phase responses has desired amplitudes and phase values. The frequencies must be monotonically increasing and lie within the Nyquist range. The first element of the vector must be either 0 or –fs/2, where fs is the sample rate, and its last element must be fs/2. If you do not specify a sample rate, designfilt uses the default value of 2 Hz.

Data Types: double

Since R2025a

Frequency response values, specified as a vector. Use this variable to specify the arbitrary magnitude and phase response values at the frequencies you specify in the 'Frequencies' argument. The length of this vector must equal the length of the 'Frequencies' vector.

Data Types: double
Complex Number Support: Yes

Since R2025a

Group delay response values, specified as a vector. Use this variable to specify the group delay response values at the frequencies you specify in the 'Frequencies' argument. The length of this vector must equal the length of the 'Frequencies' vector.

Data Types: double

Number of bands in a multiband design, specified as a positive integer scalar not greater than 10.

Data Types: double

Multiband response frequencies, specified as numeric vectors. 'BandFrequenciesi', where i runs from 1 through 'NumBands', is a vector containing the frequencies at which the ith band of a multiband design has the desired values, 'BandAmplitudesi', 'BandFrequencyResponsei', 'BandGroupDelayResponsei'. 'NumBands' can be at most 10. The frequencies must lie within the Nyquist range and must be specified in monotonically increasing order. Adjacent frequency bands must have the same amplitude at their junction.

Data Types: double

Since R2025a

Multiband frequency response values, specified as numeric vectors. 'BandFrequencyResponsei', where i runs from 1 through 'NumBands', is a vector containing the frequency response values in the ith band specified at the frequency values given by 'BandFrequenciesi'. 'NumBands' can be at most 10.

Data Types: double
Complex Number Support: Yes

Since R2025a

Multiband group delay response values, specified as numeric vectors. 'BandGroupDelayResponsei', where i runs from 1 through 'NumBands', is a vector containing the group delay response values in the ith band specified at the frequency values given by 'BandFrequenciesi'. 'NumBands' can be at most 10.

Data Types: double

Since R2025a

Center frequency f0 of the notch or peak IIR filter, specified as a scalar or a vector. The center frequency values must be in the range 0 < f0 < fs/2.

When specified as a vector, the length of this argument must be equal to the length of the FilterOrder and QualityFactor arguments. If you specify the input sample rate through the SampleRate property, then specify the value of the center frequency in Hz.

Dependencies

This property applies only when you set the filter response to 'notchiir' or 'peakiir'.

Data Types: double

Since R2025a

Quality factor q of the notch or peak IIR filter, specified as a positive scalar or a vector. When specified as a vector, the length of this argument must be equal to the length of the CenterFrequency argument.

Quality factor of the filter is defined as the ratio of the lowest center frequency of the peak or notch f0 (not including DC) to the 3 dB bandwidth BW calculated at the −3 dB point, and is given by q = f0/BW.

Dependencies

This property applies only when you set the filter response to 'notchiir' or 'peakiir'.

Data Types: double

Since R2025a

3-dB bandwidth BW of the notch or peak IIR filter, specified as a scalar or a vector.

When you set NotchLocations or PeakLocations to:

  • 'Specify' –– The bandwidth must be a numeric scalar or a vector of length equal to the length of the NumNotches or NumPeaks property. The bandwidth value must be in the range 0 < BW < fs/2.

  • 'Harmonic' –– The bandwidth must be a numeric scalar in the range 0 < BW < fs/(2 × NumNotches or NumPeaks).

By default, the function calculates the bandwidth at the point –3 dB from the center frequency of the peak or notch. For example, setting BW to 0.01 specifies that the –3 dB point will be +/− 0.005 (in normalized frequency) from the center of the notch or peak.

Dependencies

This property applies only when you set the filter response to 'notchiir' or 'peakiir'.

Data Types: double

Since R2025a

Target combined bandwidth, specified as a positive scalar less than 0.999×fs/2, where fs is the input sample rate. This is the value of the combined bandwidth that the design must satisfy. Combined bandwidth is defined as the minimum of the gain bandwidth and the group delay bandwidth.

Specifying both filter length and target combined bandwidth results in an overdetermined design. The filter design does not support specifying both values. When you specify the target combined bandwidth, the algorithm determines the corresponding filter length and designs the filter accordingly.

Specify a higher target combined bandwidth for a longer filter. For example, setting the bandwidth to 0.9 × fs/2 yields a filter of length of 52, while increasing the bandwidth to 0.99 × fs/2 yields a length of 724, which is more than 10 times longer. As bandwidth tends towards fs/2, the filter length theoretically tends towards infinity.

Dependencies

This property applies only when you set the filter response to 'fracdelayfir'.

Data Types: double

Magnitude Constraints

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Passband ripple, specified as a positive scalar expressed in decibels.

'PassbandRipple1' is the lower-band passband ripple for a bandstop design.

'PassbandRipple2' is the higher-band passband ripple for a bandstop design.

Data Types: double

Stopband attenuation, specified as a positive scalar expressed in decibels.

'StopbandAttenuation1' is the lower-band stopband attenuation for a bandpass design.

'StopbandAttenuation2' is the higher-band stopband attenuation for a bandpass design.

Data Types: double

Since R2024a

Option to constrain passband ripple, specified as a logical value.

Set 'Passband1Constrained' to true to constrain the first passband ripple in the bandstop FIR filter.

Set 'Passband2Constrained' to true to constrain the second passband ripple in the bandstop FIR filter.

Set 'PassbandConstrained' to true to constrain the passband ripple in the bandpass FIR filter.

Data Types: logical

Since R2024a

Option to constrain stopband attenuation, specified as a logical value.

Set 'Stopband1Constrained' to true to constrain the first stopband attenuation in the bandpass FIR filter.

Set 'Stopband2Constrained' to true to constrain the second stopband attenuation in the bandpass FIR filter.

Set 'StopbandConstrained' to true to constrain the stopband attenuation in the bandstop FIR filter.

Data Types: logical

Desired response amplitudes of an arbitrary magnitude response filter, specified as a vector. Express the amplitudes in linear units. The vector must have the same length as 'Frequencies'.

Data Types: double

Multiband response amplitudes, specified as numeric vectors. 'BandAmplitudesi', where i runs from 1 through 'NumBands', is a vector containing the desired amplitudes in the ith band of a multiband design. 'NumBands' can be at most 10. Express the amplitudes in linear units. 'BandAmplitudesi' must have the same length as 'BandFrequenciesi'. Adjacent frequency bands must have the same amplitude at their junction.

Data Types: double

Since R2025a

Multiband constrained flag, specified as logical vectors. This property enables you to constrain the passband ripple in your multiband design. You cannot constrain the passband ripple in all bands simultaneously. 'BandConstrainedi', where i runs from 1 through 'NumBands', is a vector that specifies if the corresponding ith band of a multiband design is constrained or not. 'NumBands' can be at most 10. 'BandConstrainedi' must have the same length as 'BandAmplitudesi' and 'BandFrequenciesi'.

Data Types: logical

Since R2025a

Multiband response passband ripples, specified as sets of positive scalars or of vectors. 'BandRipplei', where i runs from 1 through 'NumBands', is a scalar or vector containing the desired passband ripple of the ith band of a multiband design. 'NumBands' can be at most 10. If specified as a vector, 'BandRipplei' must have the same length as 'BandAmplitudesi' and 'BandFrequenciesi'.

Data Types: double

Since R2025a

Gain at which the bandwidth is measured, specified as a scalar. This property allows you specify the bandwidth of the notch or peak at a gain different from the –3 dB default.

Dependencies

This property applies only when you set:

  • The filter response to 'notchiir' or 'peakiir'.

  • The NotchLocations or PeakLocations to 'Harmonic'.

Data Types: double

Design Method

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Design method, specified as a character vector or string scalar. The choice of design method depends on the set of frequency and magnitude constraints that you specify.

  • 'butter' designs a Butterworth IIR filter. Butterworth filters have a smooth monotonic frequency response that is maximally flat in the passband. They sacrifice rolloff steepness for flatness.

  • 'cheby1' designs a Chebyshev type I IIR filter. Chebyshev type I filters have a frequency response that is equiripple in the passband and maximally flat in the stopband. Their passband ripple increases with increasing rolloff steepness.

  • 'cheby2' designs a Chebyshev type II IIR filter. Chebyshev type II filters have a frequency response that is maximally flat in the passband and equiripple in the stopband.

  • 'cls' designs an FIR filter using constrained least squares. The method minimizes the discrepancy between a specified arbitrary piecewise-linear function and the filter’s magnitude response. At the same time, it lets you set constraints on the passband ripple and stopband attenuation.

  • 'ellip' designs an elliptic IIR filter. Elliptic filters have a frequency response that is equiripple in both passband and stopband.

  • 'equiripple' designs an equiripple FIR filter using the Parks-McClellan algorithm. Equiripple filters have a frequency response that minimizes the maximum ripple magnitude over all bands.

  • 'freqsamp' designs an FIR filter of arbitrary magnitude response by sampling the frequency response uniformly and taking the inverse Fourier transform.

  • 'kaiserwin' designs an FIR filter using the Kaiser window method. The method truncates the impulse response of an ideal filter and uses a Kaiser window to attenuate the resulting truncation oscillations.

  • 'lpnorm' designs a least Pth-norm optimal IIR filter using the least-Pth unconstrained optimization algorithm. For more information, see Least Pth-Norm Optimal IIR Filter Design. (since R2023b)

  • 'ls' designs an FIR filter using least squares. The method minimizes the discrepancy between a specified arbitrary piecewise-linear function and the filter’s magnitude response.

  • 'maxflat' designs a maximally flat FIR filter. These filters have a smooth monotonic frequency response that is maximally flat in the passband.

  • 'window' uses a least-squares approximation to compute the filter coefficients and then smooths the impulse response with 'Window'.

  • 'ifir' designs an interpolated FIR filter. Interpolated FIR filters are narrowband FIR filters with relatively lower filter orders. To achieve an efficient design that reduces the total number of required multipliers, the 'ifir' design algorithm splits the design problem into two stages. In the first stage, the filter is upsampled to achieve the stringent specifications without using many multipliers. In the second stage, the filter removes the images created when upsampling the previous filter. (since R2025a)

Data Types: char | string

Design Method Options

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Since R2025a

Type of the linear-phase FIR filter, specified as one of these:

  • '1' –– Even-order and symmetric FIR filter

  • '2' –– Odd-order and symmetric FIR filter

  • '3' –– Even-order and antisymmetric FIR filter

  • '4' –– Odd-order and antisymmetric FIR filter

Dependencies

This property applies only when you set the filter response to 'hilbertfir'.

Data Types: char | string

Minimum order parity of a 'kaiserwin' design or an 'equiripple' design, specified as 'any', 'even', or 'odd'.

When you set 'MinOrder' to:

  • 'any' –– The returned filter can have even or odd order, whichever is smaller.

  • 'even' –– designfilt returns a minimum-order filter with even order.

  • 'odd' –– designfilt returns a minimum-order filter with odd order.

Data Types: char | string

Window, specified as a vector of length N + 1, where N is the filter order. 'Window' can also be paired with a window name or function handle that specifies the function used to generate the window. Any such function must take N + 1 as first input. Additional inputs can be passed by specifying a cell array. By default, 'Window' is an empty vector for the 'freqsamp' design method and @hamming for the 'window' design method.

For a list of available windows, see Windows.

Example: 'Window',hann(N+1) and 'Window',(1-cos(2*pi*(0:N)'/N))/2 both specify a Hann window to use with a filter of order N.

Example: 'Window','hamming' specifies a Hamming window of the required order.

Example: 'Window',@mywindow lets you define your own window function.

Example: 'Window',{@kaiser,0.5} specifies a Kaiser window of the required order with shape parameter 0.5.

Data Types: double | char | string | function_handle | cell

Band to match exactly, specified as 'stopband', 'passband', or 'both'. 'both' is available only for the elliptic design method, where it is the default. 'stopband' is the default for the 'butter' and 'cheby2' methods. 'passband' is the default for 'cheby1'.

Data Types: char | string

Since R2023b

L-infinity norm, specified as a positive scalar.

Dependencies

This property applies only when you set DesignMethod to 'lpnorm'.

Data Types: double

Since R2025a

Density of the frequency grid, specified as a positive scalar ≥ 10. The frequency grid has roughly (DensityFactor × FilterOrder)/(2 × Passbandfrequency) frequency points. Increasing the density factor results in filters that more exactly match an equiripple filter, but that take longer to compute.

Data Types: double

Since R2025a

Maximum pole radius, specified as a scalar in the range (0,1]. This value indicates the maximum radius of each pole in the pole/zero plot of the designed filter.

Dependencies

This property applies only when you set DesignMethod to 'lpnorm'.

Data Types: double

Since R2025a

Initial Pth norm used by the 'lpnorm' algorithm, specified as a positive scalar. Starting the optimization with a smaller initial value aids in the convergence of the algorithm. For more information, see Least Pth-Norm Optimal IIR Filter Design.

Dependencies

This property applies only when you set DesignMethod to 'lpnorm'.

Data Types: double

Since R2025a

Initial estimate of the filter order, specified as a positive integer.

Dependencies

This property applies only when you specify the filter response to 'arbmagfir'.

Data Types: double

Since R2025a

Initial estimate of the filter numerator coefficients, specified as a vector of size (N+1)-by-1, where N is the filter order that you specify in the FilterOrder argument.

Dependencies

This property applies only when you set DesignMethod to 'lpnorm'.

Data Types: double

Since R2025a

Initial estimate of the filter denominator coefficients, specified as a vector of size (N+1)-by-1, where N is the filter order that you specify in the FilterOrder argument.

Dependencies

This property applies only when you set DesignMethod to 'lpnorm'.

Data Types: double

Since R2025a

Interpolation factor used by the interpolated FIR filter design algorithm, specified as a positive integer ≥ 1.

Dependencies

This property applies only when you set DesignMethod to 'ifir'.

Data Types: double

Since R2025a

Set this property to true to enable both design speed and filter order optimization.

Dependencies

This property applies only when you set DesignMethod to 'ifir'.

Data Types: logical

Passband offset, specified as a positive scalar expressed in decibels. 'PassbandOffset' specifies the filter gain in the passband.

Example: 'PassbandOffset',0 results in a filter with unit gain in the passband.

Example: 'PassbandOffset',2 results in a filter with a passband gain of 2 dB or 1.259.

Data Types: double

Scale passband, specified as a logical scalar. When you set 'ScalePassband' to true, the passband is scaled, after windowing, so that the filter has unit gain at zero frequency.

Example: 'Window',{@kaiser,0.1},'ScalePassband',true help specify a filter whose magnitude response at zero frequency is exactly 0 dB. This is not the case when you specify 'ScalePassband',false. To verify, visualize the filter with Filter Analyzer and zoom in.

Data Types: logical

Zero phase, specified as logical scalar. When you set 'ZeroPhase' to true, the zero-phase response of the resulting filter is always positive. This lets you perform spectral factorization on the result and obtain a minimum-phase filter from it.

Data Types: logical

Since R2025a

Shape of the stopband of the equiripple FIR filter, specified as one of these options:

  • 'flat' –– Stopband shape is flat.

  • 'linear' –– Stopband decays with a slope of decay dB/rad/s.

  • '1/f' –– Stopband decays as (1/f)decay or 6 × decay dB per octave.

decay is the value you specify in the StopbandDecay property.

Data Types: char | string

Since R2025a

Stopband decay, specified as a real scalar. When the StopbandShape property is set to one of these options:

  • '1/f' –– The stopband decay value specifies the power that 1/f is raised.

  • 'linear' –– The stopband decay value specifies the slope of the stopband.

  • 'flat' –– The stopband decay value has no impact on the stopband shape.

Data Types: double

Since R2025a

Sinc frequency factor, specified as a positive scalar. The magnitude response of the equiripple FIR filter has the shape of an inverse sinc function, 1/sinc(C × π × F)P.

  • C is the value you specify in SincFrequencyFactor.

  • P is the value you specify in SincPower.

  • F is the normalized frequency.

The inverse sinc shape compensates for the sinc-like responses in the frequency domain such as the effect of the zero-order hold in a D/A converter. The amount of compensation in the passband is controlled by the C and P arguments.

Data Types: double

Since R2025a

Sinc power P, specified as a positive scalar. This value specifies the power to which the inverse sinc function is raised.

The magnitude response of the equiripple FIR filter is given by 1/sinc(C × π × F)P

where,

  • C is the value you specify in SincFrequencyFactor.

  • P is the value you specify in SincPower.

  • F is the normalized frequency.

Data Types: double

Since R2024a

Phase constraint on the equiripple FIR filter, specified as one of these options:

  • 'Minimum' –– Design a minimum-phase equiripple FIR filter.

  • 'Maximum' –– Design a maximum-phase equiripple FIR filter.

  • 'Linear' –– Design a linear-phase equiripple FIR filter.

Data Types: char | string

Passband optimization weight, specified as a positive scalar.

'PassbandWeight1' is the lower-band passband optimization weight for a bandstop FIR design.

'PassbandWeight2' is the higher-band passband optimization weight for a bandstop FIR design.

Data Types: double

Stopband optimization weight, specified as a positive scalar.

'StopbandWeight1' is the lower-band stopband optimization weight for a bandpass FIR design.

'StopbandWeight2' is the higher-band stopband optimization weight for a bandpass FIR design.

Data Types: double

Optimization weights, specified as a positive scalar or a vector of the same length as 'Amplitudes'.

Data Types: double

Multiband weights, specified as sets of positive scalars or of vectors. 'BandWeightsi', where i runs from 1 through 'NumBands', is a scalar or vector containing the optimization weights of the ith band of a multiband design. If specified as a vector, 'BandWeightsi' must have the same length as 'BandAmplitudesi'.

Data Types: double

Since R2025a

Force the magnitude response at specified frequencies in the multiband design to 0 dB, specified as sets of positive scalars or vectors. 'BandForcedFrequencyPointsi', where i runs from 1 through 'NumBands', is a scalar or a vector containing the frequencies in each band at which to force the magnitude response to 0 dB. If specified as a vector, 'BandForcedFrequencyPointsi' must have the same length as 'BandWeightsi'.

Data Types: double

Since R2025a

Option to specify the frequency grid as uniform in the equiripple filter design, specified as a logical scalar. When you set this property to true, the function spaces the frequency grid points uniformly in the frequency bands of interest. The density of the uniform grid is controlled by the DensityFactor argument

Data Types: logical

Since R2025a

Fractional delay of the filter in samples, specified as a real scalar in the range [0,1].

When you set FractionalDelay to 0 or 1, the designed filter has a full bandwidth.

Dependencies

This property applies only when you set the filter response to 'fracdelayfir'.

Data Types: double

Implementation

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Since R2023b

When you set this property to:

  • true –– The designfilt function generates one of the filter System objects depending on the filter response and the design method you choose.

  • false –– The designfilt function generates a digitalFilter object.

Data Types: logical

Output Arguments

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Digital filter, returned as one of these:

More About

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Version History

Introduced in R2014a

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See Also

Live Editor Tasks

Functions

Apps

Objects

Topics