Bandstop FIR

Design bandstop finite impulse response filter

Description

A bandstop filter attenuates the energy of an input signal within a specified frequency range. A finite impulse response (FIR) filter computes an output signal as a running weighted average of input samples.

Signal Processing Toolbox™ provides different ways to design bandstop FIR filters:

• designfilt function — Design a bandstop FIR filter at the command line or in a script. Use "bandstopfir" as the first argument when you call the function.

  For an example, see Design Bandstop FIR Filter Using designfilt.

• Design Filter Live Editor task — Design a bandstop FIR filter as part of a live script. The task displays code that you can paste into other MATLAB^® programs.

  For an example, see Design Bandstop FIR Filter Using Live Editor Task.

• Filter Designer app — Design a bandstop FIR filter interactively. Export your design to the MATLAB workspace, to Simulink^®, or to a file.

  For an example, see Design Bandstop FIR Filter Using Filter Designer.

All of these methods output digitalFilter objects. If you have a DSP System Toolbox™ license, you can output your design as a filter System object™ and include additional Design Method Options.

For other ways to design bandstop FIR filters using MATLAB, see Other Bandstop FIR Filter Design Functions.

Examples

Design Bandstop FIR Filter Using designfilt

To design the filter at the command line or in a script, use the designfilt function with "bandstopfir" as first argument. Use name-value arguments to specify your design further.

d = designfilt("bandstopfir", ...                           % Filter type
    SampleRate=2000, ...                                    % Sample rate
    FilterOrder=40, ...                                     % Filter order
    PassbandFrequency1=300,StopbandFrequency1=350, ...      % Frequency constraints
    StopbandFrequency2=700,PassbandFrequency2=750, ...
    DesignMethod="ls", ...                                  % Design method
    PassbandWeight1=3,StopbandWeight=15,PassbandWeight2=1); % Design method options
filterAnalyzer(d)

Design Bandstop FIR Filter Using Live Editor Task

To design the filter using the Design Filter Live Editor task:

1. Specify the filter:

   • Under Select filter response, select Bandstop FIR.

   • Under Sample Rate, specify the Frequency units as Hz and the Input sample rate (Hz) as 2000.

   • Under Specify filter order, set Order mode to Specify and enter a value of 40.

   • Under Specify frequency parameters, specify:

     • Passband frequency 1 as 300 Hz

     • Stopband frequency 1 as 350 Hz

     • Stopband frequency 2 as 700 Hz

     • Passband frequency 2 as 750 Hz

   • Under Specify algorithm, select FIR least-squares. Under Specify algorithm options, specify:

     • Passband weight 1 as 3

     • Stopband weight as 15

     • Passband weight 2 as 1

2. The Live Editor task updates the filter automatically by default.

   

Design Bandstop FIR Filter Using Filter Designer

To design the filter using the Filter Designer app:

1. In the Response gallery of the Designer tab in the app toolstrip, select Bandstop FIR.

2. Specify the filter using the options in the Filter Parameters Table:

   • In Design by, select Specification.

   • In Sample Rate, specify the Frequency units as Hz and the Input sample rate (Hz) as 2000.

   • Under Filter Order, set Order mode to Specify and enter a value of 40.

   • Under Frequency Specifications, specify:

     • Passband frequency 1 as 300 Hz

     • Stopband frequency 1 as 350 Hz

     • Stopband frequency 2 as 700 Hz

     • Passband frequency 2 as 750 Hz

   • Under Algorithm, select FIR least-squares. Under Algorithm Options, specify:

     • Passband weight 1 as 3

     • Stopband weight as 15

     • Passband weight 2 as 1

3. In the Filter section of the Designer tab, click Update Filter.

   

4. Export code to create your digital filter. On the toolstrip, click Export and select Generate MATLAB function > Digital Filter Object. The code appears in the Editor.

   function designedFilter = bandstopfir1filt
   
   designedFilter = designfilt('bandstopfir', ...
       'FilterOrder',40,'PassbandFrequency1',300, ...
       'StopbandFrequency1',350,'StopbandFrequency2',700, ...
       'PassbandFrequency2',750,'SampleRate',2000, ...
       'DesignMethod','ls','PassbandWeight1',3, ...
       'StopbandWeight',15);
   
   end

Parameters

Design Method

Design Method — Filter design algorithm

equiripple | Kaiser window | window | constrained least squares | least squares | least Pth-norm

Specify the algorithm to design the filter. The available design methods correlate with the set of design specifications that you choose.

Equiripple — Parks-McClellan algorithm

design method

Design the filter using the Parks-McClellan algorithm. Equiripple filters have a frequency response that minimizes the maximum ripple magnitude over all bands.

designfilt Function	Design Filter Live Editor Task	Filter Designer App
Specify DesignMethod="equiripple".	In the Specify algorithm section of the task, set Design method to Equiripple.	In the Algorithm section of the filter parameters panel, set Design method to Equiripple.

The equiripple design method supports these design parameter combinations.

Filter Order	Frequency Specifications	Magnitude Specifications	Design Method Options	DSP System Toolbox License Required
N/A	Passband Frequency 1 Stopband Frequency 1 Stopband Frequency 2 Passband Frequency 2	Passband Ripple 1 Stopband Attenuation Passband Ripple 2	N/A
N/A	Passband Frequency 1 Stopband Frequency 1 Stopband Frequency 2 Passband Frequency 2	Passband Ripple 1 Stopband Attenuation Passband Ripple 2	Phase Constraint	✓
Filter Order	Passband Frequency 1 Stopband Frequency 1 Stopband Frequency 2 Passband Frequency 2	N/A	Passband Weight 1 Stopband Weight Passband Weight 2
Filter Order	Passband Frequency 1 Stopband Frequency 1 Stopband Frequency 2 Passband Frequency 2	N/A	Passband Weight 1 Stopband Weight Passband Weight 2 Phase Constraint	✓
Filter Order	Passband Frequency 1 Stopband Frequency 1 Stopband Frequency 2 Passband Frequency 2	Passband 1 Constrained Stopband Constrained Passband 2 Constrained	Passband Weight 1 Stopband Weight Passband Weight 2 Phase Constraint	✓

Kaiser Window — Kaiser window algorithm

design method

Design the filter using the Kaiser window algorithm. The method truncates the impulse response of an ideal filter and uses a Kaiser window to attenuate the resulting truncation oscillations.

designfilt Function	Design Filter Live Editor Task	Filter Designer App
Specify DesignMethod="kaiserwin".	In the Specify algorithm section of the task, set Design method to Kaiser window.	In the Algorithm section of the filter parameters panel, set Design method to Kaiser window.

The Kaiser window design method supports these design parameter combinations.

Filter Order	Frequency Specifications	Magnitude Specifications	Design Method Options	DSP System Toolbox License Required
N/A	Passband Frequency 1 Stopband Frequency 1 Stopband Frequency 2 Passband Frequency 2	Passband Ripple 1 Stopband Attenuation Passband Ripple 2	Minimum Order Scale Passband

Window — Window algorithm

design method

Design the filter using the window algorithm. The method uses a least-squares approximation to compute the filter coefficients and then smooths the impulse response with Window.

designfilt Function	Design Filter Live Editor Task	Filter Designer App
Specify DesignMethod="window".	In the Specify algorithm section of the task, set Design method to Window.	In the Algorithm section of the filter parameters panel, set Design method to Window.

The window design method supports these design parameter combinations.

Filter Order	Frequency Specifications	Magnitude Specifications	Design Method Options	DSP System Toolbox License Required
Filter Order	Cutoff Frequency 1 Cutoff Frequency 2	N/A	Window Scale Passband

Constrained Least Squares — Constrained least squares algorithm

design method

Design the filter using the constrained least squares algorithm. The method minimizes the discrepancy between a specified arbitrary piecewise-linear function and the magnitude response of the filter. At the same time, it lets you set constraints on the passband ripple and the stopband attenuation.

designfilt Function	Design Filter Live Editor Task	Filter Designer App
Specify DesignMethod="cls".	In the Specify algorithm section of the task, set Design method to FIR constrained least-squares.	In the Algorithm section of the filter parameters panel, set Design method to FIR constrained least-squares.

The constrained least squares design method supports these design parameter combinations.

Filter Order	Frequency Specifications	Magnitude Specifications	Design Method Options	DSP System Toolbox License Required
Filter Order	Cutoff Frequency 1 Cutoff Frequency 2	Passband Ripple 1 Stopband Attenuation Passband Ripple 2	Passband Offset Zero Phase

Least Squares — Least squares algorithm

design method

Design the filter using the least squares algorithm. The method minimizes the discrepancy between a specified arbitrary piecewise-linear function and the filter’s magnitude response.

designfilt Function	Design Filter Live Editor Task	Filter Designer App
Specify DesignMethod="ls".	In the Specify algorithm section of the task, set Design method to FIR least-squares.	In the Algorithm section of the filter parameters panel, set Design method to FIR least-squares.

The least squares design method supports these design parameter combinations.

Filter Order	Frequency Specifications	Magnitude Specifications	Design Method Options	DSP System Toolbox License Required
Filter Order	Passband Frequency 1 Stopband Frequency 1 Stopband Frequency 2 Passband Frequency 2	N/A	Passband Weight 1 Stopband Weight Passband Weight 2

Least Pth-Norm — Least Pth-norm algorithm

design method

Design the filter using the least Pth-norm unconstrained optimization algorithm.

You must have a DSP System Toolbox license to use this design method.

designfilt Function	Design Filter Live Editor Task	Filter Designer App
Specify DesignMethod="lpnorm".	In the Specify algorithm section of the task, set Design method to FIR least p-norm.	In the Algorithm section of the filter parameters panel, set Design method to FIR least p-norm.

The least Pth-norm method supports these design parameter combinations.

Filter Order	Frequency Specifications	Magnitude Specifications	Design Method Options	DSP System Toolbox License Required
Filter Order	Passband Frequency 1 Stopband Frequency 1 Stopband Frequency 2 Passband Frequency 2	N/A	Norm Density Factor Initial Norm Initial Numerator Passband Weight 1 Stopband Weight Passband Weight 2 Phase Constraint	✓

Sample Rate

Sample Rate — Filter sample rate

positive scalar

Specify the filter sample rate as a positive scalar expressed in hertz.

designfilt Function	Design Filter Live Editor Task	Filter Designer App
To specify a sample rate, use the SampleRate name-value argument and input a value in hertz. To work with normalized frequencies, omit the sample rate.	In the Sample Rate section of the task: To specify a sample rate, set Frequency units to Hz and type a value for Input sample rate (Hz). To work with normalized frequencies, set Frequency units to Normalized.	In the Sample Rate section of the filter parameters panel: To specify a sample rate, set Frequency units to Hz and type a value for Input sample rate (Hz). To work with normalized frequencies, set Frequency units to Normalized.

Filter Order

Filter Order — Highest power in transfer function (filter length – 1)

positive integer

Specify the filter order N as a positive integer. Some design methods let you specify the order. Others generate minimum-order designs, which are the shortest filters that satisfy the specified constraints.

designfilt Function	Design Filter Live Editor Task	Filter Designer App
To specify a filter order, use the FilterOrder name-value argument and input a positive integer. To use a minimum-order design, specify frequency and magnitude constraints accordingly.	In the Specify Filter Order section of the task: To specify a filter order, set Order mode to Specify and enter a value for Order. To use a minimum-order design, set Order mode to Minimum.	In the Filter Order section of the filter parameters panel: To specify a filter order, set Order mode to Specify and enter a value for Order. To use a minimum-order design, set Order mode to Minimum.

Frequency Specifications

Passband Frequency 1 — Lower passband-end frequency

positive scalar

Specify the lower passband frequency as a positive scalar smaller than the Nyquist frequency. If you work with normalized frequencies, the Nyquist frequency is 1. If you specify a sample rate F_s , the Nyquist frequency is F_s/2.

The lower passband frequency is the highest frequency in the lower passband for which the magnitude response of the filter is within an interval of width Passband Ripple 1 about the reference value, usually 0 dB.

designfilt Function	Design Filter Live Editor Task	Filter Designer App
Use the PassbandFrequency1 name-value argument. Input the value as a positive scalar.	In the Specify Frequency Parameters section of the task, select a set of Frequency Constraints containing Passband frequency 1 and enter a positive scalar as value.	In the Frequency Specifications section of the filter parameters panel, select a set of Frequency Constraints containing Passband frequency 1 and enter a positive scalar as value.

Cutoff Frequency 1 — Lower 6 dB frequency

positive scalar

Specify the lower cutoff frequency as a positive scalar smaller than the Nyquist frequency. If you work with normalized frequencies, the Nyquist frequency is 1. If you specify a sample rate F_s, the Nyquist frequency is F_s/2.

The lower cutoff frequency is the lowest frequency at which the magnitude response of the filter is mag2db(1/2)= 20 log₁₀½ = –6.02 dB below the reference value, usually 0 dB.

designfilt Function	Design Filter Live Editor Task	Filter Designer App
Use the CutoffFrequency1 name-value argument. Input the value as a positive scalar.	In the Specify Frequency Parameters section of the task, set Frequency Constraints to Cutoff (6dB) frequency 1 and enter a positive scalar as value.	In the Frequency Specifications section of the filter parameters panel, set Frequency Constraints to Cutoff (6dB) Frequency 1 and enter a positive scalar as value.

Stopband Frequency 1 — Lower stopband-end frequency

positive scalar

Specify the lower stopband frequency as a positive scalar smaller than the Nyquist frequency. If you work with normalized frequencies, the Nyquist frequency is 1. If you specify a sample rate F_s, the Nyquist frequency is F_s/2.

The lower stopband frequency is the lowest frequency in the stopband for which the magnitude response of the filter is at least Stopband Attenuation dB lower than the reference value, usually 0 dB.

designfilt Function	Design Filter Live Editor Task	Filter Designer App
Use the StopbandFrequency1 name-value argument. Input the value as a positive scalar.	In the Specify Frequency Parameters section of the task, select a set of Frequency Constraints containing Stopband frequency 1 and enter a positive scalar as value.	In the Frequency Specifications section of the filter parameters panel, select a set of Frequency Constraints containing Stopband frequency 1 and enter a positive scalar as value.

Stopband Frequency 2 — Higher stopband-end frequency

positive scalar

Specify the higher stopband frequency as a positive scalar smaller than the Nyquist frequency. If you work with normalized frequencies, the Nyquist frequency is 1. If you specify a sample rate F_s, the Nyquist frequency is F_s/2.

The higher stopband frequency is the highest frequency in the stopband for which the magnitude response of the filter is at least Stopband Attenuation dB lower than the reference value, usually 0 dB.

designfilt Function	Design Filter Live Editor Task	Filter Designer App
Use the StopbandFrequency2 name-value argument. Input the value as a positive scalar.	In the Specify Frequency Parameters section of the task, select a set of Frequency Constraints containing Stopband frequency 2 and enter a positive scalar as value.	In the Frequency Specifications section of the filter parameters panel, select a set of Frequency Constraints containing Stopband frequency 2 and enter a positive scalar as value.

Cutoff Frequency 2 — Higher 6 dB frequency

positive scalar

Specify the higher cutoff frequency as a positive scalar smaller than the Nyquist frequency. If you work with normalized frequencies, the Nyquist frequency is 1. If you specify a sample rate F_s, the Nyquist frequency is F_s/2.

The higher cutoff frequency is the highest frequency at which the magnitude response of the filter is mag2db(1/2)= 20 log₁₀½ = –6.02 dB below the reference value, usually 0 dB.

designfilt Function	Design Filter Live Editor Task	Filter Designer App
Use the CutoffFrequency2 name-value argument. Input the value as a positive scalar.	In the Specify Frequency Parameters section of the task, set Frequency Constraints to Cutoff (6dB) frequency 2 and enter a positive scalar as value.	In the Frequency Specifications section of the filter parameters panel, set Frequency Constraints to Cutoff (6dB) Frequency 2 and enter a positive scalar as value.

Passband Frequency 2 — Higher passband-end frequency

positive scalar

Specify the higher passband frequency as a positive scalar smaller than the Nyquist frequency. If you work with normalized frequencies, the Nyquist frequency is 1. If you specify a sample rate F _s , the Nyquist frequency is F _s/2.

The higher passband frequency is the lowest frequency in the higher passband for which the magnitude response of the filter is within an interval of width Passband Ripple 2 about the reference value, usually 0 dB.

designfilt Function	Design Filter Live Editor Task	Filter Designer App
Use the PassbandFrequency2 name-value argument. Input the value as a positive scalar.	In the Specify Frequency Parameters section of the task, select a set of Frequency Constraints containing Passband frequency 2 and enter a positive scalar as value.	In the Frequency Specifications section of the filter parameters panel, select a set of Frequency Constraints containing Passband frequency 2 and enter a positive scalar as value.

Magnitude Specifications

Passband Ripple 1 — Gain fluctuation in lower passband

positive scalar

Specify the lower passband ripple as a positive scalar in decibels.

The lower passband ripple measures the fluctuation of the gain of the filter in the lower passband about the reference value, usually 0 dB.

designfilt Function	Design Filter Live Editor Task	Filter Designer App
Use the PassbandRipple1 name-value argument. Input the value as a positive scalar in decibels.	In the Specify Magnitude Parameters section of the task, select a set of Magnitude Constraints containing Passband ripple 1 (dB) and enter a positive scalar in decibels as value.	In the Magnitude Specifications section of the filter parameters panel, select a set of Magnitude Constraints containing Passband ripple 1 (dB) and enter a positive scalar in decibels as value.

Stopband Attenuation — Gain decrease in stopband

positive scalar

Specify the stopband attenuation as a positive scalar in decibels.

The stopband attenuation measures the extent by which the filter gain in the stopband is decreased in comparison to the reference value, usually 0 dB.

designfilt Function	Design Filter Live Editor Task	Filter Designer App
Use the StopbandAttenuation name-value argument. Input the value as a positive scalar in decibels.	In the Specify Magnitude Parameters section of the task, select a set of Magnitude Constraints containing Stopband attenuation (dB) and enter a positive scalar in decibels as the value.	In the Magnitude Specifications section of the filter parameters panel, select a set of Magnitude Constraints containing Stopband attenuation (dB) and enter a positive scalar in decibels as the value.

Passband Ripple 2 — Gain fluctuation in higher passband

positive scalar

Specify the higher passband ripple as a positive scalar in decibels.

The higher passband ripple measures the fluctuation of the gain of the filter in the higher passband about the reference value, usually 0 dB.

designfilt Function	Design Filter Live Editor Task	Filter Designer App
Use the PassbandRipple2 name-value argument. Input the value as a positive scalar in decibels.	In the Specify Magnitude Parameters section of the task, select a set of Magnitude Constraints containing Passband ripple 2 (dB) and enter a positive scalar in decibels as value.	In the Magnitude Specifications section of the filter parameters panel, select a set of Magnitude Constraints containing Passband ripple 2 (dB) and enter a positive scalar in decibels as value.

Passband 1 Constrained — Option to constrain lower passband ripple

logical value

Use this argument to constrain the ripple in the lower passband for an Equiripple design.

designfilt Function	Design Filter Live Editor Task	Filter Designer App
Use the Passband1Constrained name-value argument. Input the value as true.	In the Specify magnitude parameters section of the task, set Magnitude Constraints to Constrained bands and check Constrained first passband ripple.	In the Magnitude Specifications section of the filter parameters panel, set Magnitude constraints to Constrained bands and check Constrained first passband ripple.

Stopband Constrained — Option to constrain stopband attenuation

logical value

Use this argument to constrain the attenuation of the stopband for an Equiripple design.

designfilt Function	Design Filter Live Editor Task	Filter Designer App
Use the StopbandConstrained name-value argument. Input the value as true.	In the Specify magnitude parameters section of the task, set Magnitude Constraints to Constrained bands and check Constrained stopband attenuation.	In the Magnitude Specifications section of the filter parameters panel, set Magnitude constraints to Constrained bands and check Constrained stopband attenuation.

Passband 2 Constrained — Option to constrain higher passband ripple

logical value

Use this argument to constrain the ripple in the higher passband for an Equiripple design.

designfilt Function	Design Filter Live Editor Task	Filter Designer App
Use the Passband2Constrained name-value argument. Input the value as true.	In the Specify magnitude parameters section of the task, set Magnitude Constraints to Constrained bands and check Constrained second passband ripple.	In the Magnitude Specifications section of the filter parameters panel, set Magnitude constraints to Constrained bands and check Constrained second passband ripple.

Design Method Options

Basic Options

Minimum Order — Minimum order parity

any | even | odd

Minimum order parity of a Kaiser Window design or an Equiripple design, specified as one of these:

• Any — The returned filter can have even or odd order, whichever is smaller.

• Even — The returned filter has the smallest possible even order.

• Odd — The returned filter has the smallest possible odd order. This option is available only for equiripple designs.

You must have a DSP System Toolbox license to use this option with the equiripple method.

designfilt Function	Design Filter Live Editor Task	Filter Designer App
Use the MinOrder name-value argument. Input the value as "any", "even", or "odd".	In the Specify Algorithm Options section of the task, set Minimum Order to Any or Even.	In the Algorithm Options section of the filter parameters panel, set Minimum Order to Any or Even.

Passband Offset — Passband offset

positive scalar

Passband offset for a Constrained Least Squares design, specified as a positive scalar in decibels. This parameter specifies the filter gain in the passband.

Example: Setting this parameter to 0 results in a filter with unit gain in the passband.

Example: Setting this parameter to 2 results in a filter with a passband gain of 2 dB or 1.259.

designfilt Function	Design Filter Live Editor Task	Filter Designer App
Use the PassbandOffset name-value argument. Input the value as a positive scalar.	In the Specify Algorithm Options section of the task, specify Passband Offset as a positive scalar.	In the Algorithm Options section of the filter parameters panel, specify Passband Offset as a positive scalar.

Passband Weight 1 — Lower passband optimization weight

positive scalar

Lower passband optimization weight for an Equiripple, Least Squares, or Least Pth-Norm design, specified as a positive scalar.

Weights are a way of specifying the relative importance of the passband ripple and the stopband attenuation in a filter design. By default, the passband and the stopbands are equally weighted, each with unit weight. By increasing a passband weight, you can decrease the passband ripple at the expense of decreasing the stopband attenuation.

You must have a DSP System Toolbox license to use this option with some syntaxes.

designfilt Function	Design Filter Live Editor Task	Filter Designer App
Use the PassbandWeight1 name-value argument. Input the value as a positive scalar.	In the Specify Algorithm Options section of the task, specify Passband Weight 1 as a positive scalar.	In the Algorithm Options section of the filter parameters panel, specify Passband Weight 1 as a positive scalar.

Passband Weight 2 — Higher passband optimization weight

positive scalar

Higher passband optimization weight for an Equiripple, Least Squares, or Least Pth-Norm design, specified as a positive scalar.

Weights are a way of specifying the relative importance of the passband ripple and the stopband attenuation in a filter design. By default, the passband and the stopbands are equally weighted, each with unit weight. By increasing a passband weight, you can decrease the passband ripple at the expense of decreasing the stopband attenuation.

You must have a DSP System Toolbox license to use this option with some syntaxes.

designfilt Function	Design Filter Live Editor Task	Filter Designer App
Use the PassbandWeight2 name-value argument. Input the value as a positive scalar.	In the Specify Algorithm Options section of the task, specify Passband Weight 2 as a positive scalar.	In the Algorithm Options section of the filter parameters panel, specify Passband Weight 2 as a positive scalar.

Scale Passband — Scale passband

true | false

Scale passband when using the Kaiser Window design method or the Window design method, specified as a logical scalar. When you set this parameter to true, the passband is scaled, after windowing, so that the filter has unit gain at zero frequency.

designfilt Function	Design Filter Live Editor Task	Filter Designer App
Use the ScalePassband name-value argument. Input the value as true or false.	In the Specify Algorithm Options section of the task, check the Scale Passband box.	In the Algorithm Options section of the filter parameters panel, check the Scale Passband box.

Stopband Weight — Stopband optimization weight

positive scalar

Stopband optimization weight for an Equiripple, Least Squares, or Least Pth-Norm design, specified as a positive scalar.

Weights are a way of specifying the relative importance of the passband ripple and the stopband attenuation in a filter design. By default, the passband and the stopbands are equally weighted, each with unit weight. By increasing the stopband weight, you can increase the attenuation of the stopband at the expense of increasing passband ripple.

You must have a DSP System Toolbox license to use this option with some syntaxes.

designfilt Function	Design Filter Live Editor Task	Filter Designer App
Use the StopbandWeight name-value argument. Input the value as a positive scalar.	In the Specify Algorithm Options section of the task, specify Stopband Weight as a positive scalar.	In the Algorithm Options section of the filter parameters panel, specify Stopband Weight as a positive scalar.

Window — Window

numeric vector | window name | function handle | cell array

Window used by the Window algorithm, specified as one of these:

• Hamming (@hamming)

• Hann (@hann)

• Kaiser (@kaiser) — Specify the shape factor as a positive real scalar.

• Rectangular (@rectwin)

• Chebyshev (@chebwin) — Specify the sidelobe magnitude factor as a positive scalar in decibels.

• Bartlett (@bartlett)

• Blackman (@blackman)

• Flat top (@flattopwin)

• Gaussian (@gausswin) — To use a Gaussian window with a width factor α ≠ 2.5 in the Filter Designer app or the Design Filter Live Editor task, specify it as a custom window.

• Nuttall (@nuttallwin)

• Triangular (@triang)

• Custom — Specify a custom window as a vector of length N + 1, where N is the Filter Order. You can also specify the custom window as a function name or a function handle with N + 1 as first input. Additional inputs can be passed by specifying a cell array.

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

Example: "hamming" specifies a Hamming window of the required order.

Example: @hann specifies a Hann window of the required order.

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

designfilt Function	Design Filter Live Editor Task	Filter Designer App
Use the Window name-value argument. Input the value as a numeric vector, a window name, a function handle, or a cell array if you need to specify additional window parameter values.	In the Specify Algorithm Options section of the task, specify a value from the Window drop-down list and enter additional window parameter values if needed.	In the Algorithm Options section of the filter parameters panel, specify a value from the Window drop-down list and enter additional window parameter values if needed.

Zero Phase — Zero phase

false | true

Zero phase for a Constrained Least Squares design, specified as logical scalar. When you set this parameter to true, the zero-phase response of the filter is always positive, enabling you to perform spectral factorization on the result and obtain a minimum-phase filter from it.

designfilt Function	Design Filter Live Editor Task	Filter Designer App
Use the ZeroPhase name-value argument. Input the value as true or false.	In the Specify Algorithm Options section of the task, check the Zero Phase box.	In the Algorithm Options section of the filter parameters panel, check the Zero Phase box.

Advanced Options

Density Factor — Density of frequency grid

positive scalar ≥ 10

Density of the frequency grid used by the Least Pth-Norm algorithm, specified as a positive scalar ≥ 10. The frequency grid has roughly (Density Factor × Filter Order)/(2 × Passband Frequency) frequency points. Increasing the density factor results in filters that more closely match an equiripple filter but take longer to compute.

You must have a DSP System Toolbox license to use this option. This parameter is available only in the designfilt function.

designfilt Function	Design Filter Live Editor Task	Filter Designer App
Use the DensityFactor name-value argument. Input the value as a positive scalar greater than 10.	N/A	N/A

Initial Norm — Initial Pth norm

positive scalar

Initial Pth norm used by the Least Pth-Norm 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.

You must have a DSP System Toolbox license to use this option. This parameter is available only in the designfilt function.

designfilt Function	Design Filter Live Editor Task	Filter Designer App
Use the InitialNorm name-value argument. Input the value as a positive scalar.	N/A	N/A

Initial Numerator — Initial estimate of filter numerator coefficients

vector of size (N+1)-by-1

Initial estimate of the filter numerator coefficients for the Least Pth-Norm algorithm, specified as a vector of size (N+1)-by-1, where N is the Filter Order that you specify.

You must have a DSP System Toolbox license to use this option. This parameter is available only in the designfilt function.

designfilt Function	Design Filter Live Editor Task	Filter Designer App
Use the InitialNumerator name-value argument. Input the value as a vector of size (N+1)-by-1, where N is the filter order.	N/A	N/A

Norm — L-infinity norm

positive scalar

L-infinity norm used by the Least Pth-Norm algorithm, specified as a positive scalar.

You must have a DSP System Toolbox license to use this option.

designfilt Function	Design Filter Live Editor Task	Filter Designer App
Use the Norm name-value argument. Input the value as a positive scalar.	In the Specify Algorithm Options section of the task, specify Norm as a positive scalar.	In the Algorithm Options section of the filter parameters panel, specify Norm as a positive scalar.

Phase Constraint — Phase constraint

linear | minimum | maximum

Phase constraint for an Equiripple or Least Pth-Norm design, specified as one of these options:

• Linear — Design a linear-phase equiripple FIR filter.

• Minimum — Design a minimum-phase equiripple FIR filter.

• Maximum — Design a maximum-phase equiripple FIR filter.

You must have a DSP System Toolbox license to use this option.

designfilt Function	Design Filter Live Editor Task	Filter Designer App
Use the PhaseConstraint name-value argument. Input the value as "linear", "minimum", or "maximum".	In the Specify Algorithm Options section of the task, set Phase Constraint to Linear, Minimum, or Maximum.	In the Algorithm Options section of the filter parameters panel, set Phase Constraint to Linear, Minimum, or Maximum.

More About

Other Bandstop FIR Filter Design Functions

Use one these functions to design a bandstop FIR filter:

• fir1 — Window-based FIR filter design

• fir2 — Frequency sampling-based FIR filter design

• firls — Least-squares linear-phase FIR filter design

• fircls — Constrained-least-squares FIR multiband filter design

• firpm — Parks-McClellan optimal FIR filter design

• cfirpm — Complex and nonlinear-phase equiripple FIR filter design

• firgr — Generalized Remez FIR filter design

• firlpnorm — Least P-norm optimal FIR filter

• designBandstopFIR — Design and implement bandstop FIR filter

Use this function to bandstop-filter a signal:

• bandstop — Bandstop-filter signals