Highpass FIR

Design highpass finite impulse response filter

Description

A highpass filter attenuates the energy of an input signal below a specified frequency threshold. 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 highpass FIR filters:

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

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

• Design Filter Live Editor task — Design a highpass 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 Highpass FIR Filter Using Live Editor Task.

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

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

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

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

Examples

Design Highpass FIR Filter Using designfilt

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

d = designfilt("highpassfir", ...  % Response type
    SampleRate=2000, ...           % Sample rate
    StopbandFrequency=400, ...     % Frequency constraints
    PassbandFrequency=550, ...
    StopbandAttenuation=25, ...    % Magnitude constraints
    PassbandRipple=5, ...
    DesignMethod="kaiserwin", ...  % Design method
    MinOrder="even", ...           % Design method options
    ScalePassband=false);
filterAnalyzer(d)

Design Highpass 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 Highpass FIR.

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

   • Under Specify frequency parameters, specify a stopband frequency of 400 Hz and a passband frequency of 550 Hz.

   • Under Specify magnitude parameters, specify a stopband attenuation of 25 dB and a passband ripple of 5 dB.

   • Under Specify algorithm, select Kaiser window. Under Specify algorithm options, specify the minimum order as Even and clear the box to scale the passband.

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

   

Design Highpass 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 Highpass FIR.

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

   • In Design by, select Specification.

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

   • Under Frequency Specifications, specify a stopband frequency of 400 Hz and a passband frequency of 550 Hz.

   • Under Magnitude Specifications, specify a stopband attenuation of 25 Hz and a passband ripple of 5 dB.

   • Under Algorithm, select Kaiser window. Under Algorithm Options, specify the minimum order as Even and clear the box to scale the passband.

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 = highpassfir1filt
   
   designedFilter = designfilt('highpassfir', ...
       'StopbandFrequency',400,'PassbandFrequency',550, ...
       'StopbandAttenuation',25,'PassbandRipple',5, ...
       'SampleRate',2000,'DesignMethod','kaiserwin', ...
       'MinOrder','Even','ScalePassband',false);
   
   end

Parameters

Design Method

Design Method — Filter design algorithm

equiripple | Kaiser window | maximally flat | window | constrained least squares | least squares | interpolated FIR | 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 Stopband Frequency	Passband Ripple Stopband Attenuation	N/A
N/A	Passband Frequency Stopband Frequency	Passband Ripple Stopband Attenuation	Minimum Order Phase Constraint	✓
N/A	Passband Frequency Stopband Frequency	Passband Ripple Stopband Attenuation	Stopband Shape Stopband Decay	✓
Filter Order	Passband Frequency Stopband Frequency	N/A	Passband Weight Stopband Weight
Filter Order	Passband Frequency Stopband Frequency	N/A	Passband Weight Stopband Weight Phase Constraint	✓
Filter Order	Passband Frequency	Passband Ripple Stopband Attenuation	N/A	✓
Filter Order	Stopband Frequency	Passband Ripple Stopband Attenuation	N/A	✓
Filter Order	Cutoff Frequency	Passband Ripple Stopband Attenuation	N/A	✓
Filter Order	Passband Frequency Stopband Frequency	Passband Ripple	Phase Constraint	✓
Filter Order	Passband Frequency Stopband Frequency	Stopband Attenuation	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 Stopband Frequency	Passband Ripple Stopband Attenuation	Minimum Order Scale Passband

Maximally Flat — Maximally flat algorithm

design method

Design the filter using the maximally flat algorithm. These filters have a smooth monotonic frequency response that is maximally flat in the passband.

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

The maximally flat design method supports these design parameter combinations.

Filter Order	Frequency Specifications	Magnitude Specifications	Design Method Options	DSP System Toolbox License Required
Filter Order	Half-Power Frequency	N/A	N/A

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	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	Passband Ripple Stopband Attenuation	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 Stopband Frequency	N/A	Passband Weight Stopband Weight

Interpolated FIR Filter — Interpolated FIR filter algorithm

design method

Design the filter using the interpolated FIR filter algorithm. 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 design algorithm splits the design problem into two stages:

1. Upsample the filter to achieve the stringent specifications without using many multipliers.

2. Remove the images created when upsampling the previous filter.

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="ifir".	In the Specify algorithm section of the task, set Design method to Interpolated FIR.	In the Algorithm section of the filter parameters panel, set Design method to Interpolated FIR.

The interpolated FIR filter 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 Stopband Frequency	Passband Ripple Stopband Attenuation	Interpolation Factor Joint Optimization SystemObject flag is always true.	✓

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 Stopband Frequency	N/A	Norm Density Factor Initial Norm Initial Numerator Passband Weight Stopband Weight 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 — Passband end frequency

positive scalar

Specify the 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 passband frequency is the lowest frequency for which the magnitude response of the filter is within an interval of width Passband Ripple from the reference value, usually 0 dB.

designfilt Function	Design Filter Live Editor Task	Filter Designer App
Use the PassbandFrequency 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 and enter a positive scalar as the value.	In the Frequency Specifications section of the filter parameters panel, select a set of Frequency Constraints containing Passband frequency and enter a positive scalar as the value.

Stopband Frequency — Stopband end frequency

positive scalar

Specify the 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 stopband frequency is the highest frequency 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 StopbandFrequency 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 and enter a positive scalar as the value.	In the Frequency Specifications section of the filter parameters panel, select a set of Frequency Constraints containing Stopband frequency and enter a positive scalar as the value.

Cutoff Frequency — 6 dB frequency

positive scalar

Specify the 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 cutoff frequency is the 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 CutoffFrequency 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 and enter a positive scalar as the value.	In the Frequency Specifications section of the filter parameters panel, set Frequency Constraints to Cutoff (6dB) Frequency and enter a positive scalar as the value.

Half-Power Frequency — 3 dB frequency

positive scalar

Specify the half-power 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 half-power frequency is the frequency at which the magnitude response of the filter is pow2db(1/2) = 10 log₁₀½ = –3.01 dB below the reference value, usually 0 dB.

designfilt Function	Design Filter Live Editor Task	Filter Designer App
Use the HalfPowerFrequency name-value argument. Input the value as a positive scalar.	In the Specify Frequency Parameters section of the task, set Frequency Constraints to Half power (3dB) frequency and enter a positive scalar as the value.	In the Frequency Specifications section of the filter parameters panel, set Frequency Constraints to Half power (3dB) frequency and enter a positive scalar as the value.

Magnitude Specifications

Passband Ripple — Gain fluctuation in passband

positive scalar

Specify the passband ripple as a positive scalar in decibels.

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

designfilt Function	Design Filter Live Editor Task	Filter Designer App
Use the PassbandRipple 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 (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 Passband ripple (dB) and enter a positive scalar in decibels as the 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.

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 options:

• 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. For example:

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

• 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 — Passband optimization weight

positive scalar

Passband optimization weight for a Least Squares or Equiripple 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 stopband are equally weighted, each with unit weight. By increasing the passband weight, you can increase the passband ripple at the expense of increasing 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 PassbandWeight name-value argument. Input the value as a positive scalar.	In the Specify Algorithm Options section of the task, specify Passband Weight as a positive scalar.	In the Algorithm Options section of the filter parameters panel, specify Passband Weight as a positive scalar.

Scale Passband — Scale passband

true | false

Scale passband when using the Window design method or the Kaiser 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, select the Scale Passband box.	In the Algorithm Options section of the filter parameters panel, select the Scale Passband box.

Stopband Weight — Stopband optimization weight

positive scalar

Stopband optimization weight for a Least Squares or Equiripple 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 stopband are equally weighted, each with unit weight. By increasing the stopband weight, you can increase the stopband attenuation at the expense of increasing the 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 options:

• 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, select the Zero Phase box.	In the Algorithm Options section of the filter parameters panel, select 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 approximate 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

Interpolation Factor — Interpolation factor of interpolated FIR filter

positive integer ≥ 1

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

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

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

Joint Optimization — Enable design speed and filter order optimization

false | true

Enable design speed and filter order optimization for the Interpolated FIR Filter algorithm, specified as true or false. Set this argument to true to enable both design speed and filter order optimization.

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

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

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 on the Equiripple FIR filter, 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.

Stopband Decay — Stopband decay rate

real scalar

Stopband decay rate of an Equiripple filter design, specified as a real scalar. The interpretation of this parameter depends on the value you specify for Stopband Shape:

• If you specify a flat stopband, this parameter is ignored.

• If you specify that the stopband decays linearly, this parameter specifies the slope of the stopband.

• If you specify that the stopband decays as 1/f, this parameter specifies the power to which 1/f is raised. The value is proportional to the slope of the stopband in log space.

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

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

Stopband Shape — Shape of stopband

flat | linear | 1/f

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

• Flat — The filter has a flat stopband.

• Linear — The filter stopband decays linearly with a slope of decay dB/Hz or dB/rad/s, where decay is the Stopband Decay value you specify.

• 1/f — The filter stopband decays as the power law (1/f)^decay or 6 × decay dB per octave, where decay is the Stopband Decay value you specify.

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

designfilt Function	Design Filter Live Editor Task	Filter Designer App
Use the StopbandShape name-value argument. Input the value as "flat", "linear", or "1/f".	In the Specify Algorithm Options section of the task, set Stopband Shape to Flat, Linear, or 1/f.	In the Algorithm Options section of the filter parameters panel, set Stopband Shape to Flat, Linear, or 1/f.

More About

Other Highpass FIR Filter Design Functions

Use one of these functions to design a highpass 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

• fircls1 — Constrained-least-squares linear-phase FIR lowpass and highpass filter design

• firpm — Parks-McClellan optimal FIR filter design

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

• firceqrip — Constrained equiripple FIR filter

• firgr — Generalized Remez FIR filter design

• firlpnorm — Least P-norm optimal FIR filter

• ifir — Interpolated FIR filter design

• designHighpassFIR — Design and implement highpass FIR filter

Use this function to highpass-filter a signal:

• highpass — Highpass-filter signals