Filter Design

Design and analyze FIR and IIR filters

You can design and analyze a variety of digital FIR and IIR filters using DSP System Toolbox™ functions, apps, and blocks. Some of these filters include advanced filters such as Nyquist filters, halfband filters, CIC filters, advanced equiripple filters, and quasi-linear phase IIR filters.

The design techniques compute the filter coefficients based on the filter design specifications. Certain blocks such as Tunable Bandpass IIR Filter and Tunable Bandstop IIR Filter have tunable filter specifications, so you can change the filter specifications and redesign the filter while the simulation is running.

Apps

Filter Builder Design filters starting with frequency and magnitude specifications (filterBuilder)

Live Editor Tasks

Design Filter

Design a digital filter or implement a System object in the Live Editor (Since R2021b)

Functions

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Filter Design and Visualization Tools

`filterDesigner`	Open Filter Designer app
`filterBuilder`	Interactive filter design
`fvtool`	Visualize frequency response of DSP filters
`designfilt`	Design a digital filter or implement a System object

fdesign Methods

`butter`	Butterworth IIR digital filter design
`cheby1`	Chebyshev Type I filter using specification object
`cheby2`	Chebyshev Type II filter using specification object
`design`	Apply design method to filter specification object
`designmethods`	Methods available for designing filter from specification object
`designoptions`	Show all options available for specified design
`designopts`	Valid input arguments and values for specification object and method
`ellip`	Elliptic filter using specification object
`equiripple`	Equiripple single-rate FIR filter from specification object
`freqsamp`	Real or complex frequency-sampled FIR filter from specification object
`help`	Help for design method with filter specification
`setspecs`	Specifications for filter specification object
`validstructures`	Structures for specification object with design method

fdesign Objects

`fdesign`	Filter design specification object
`fdesign.bandpass`	Bandpass filter design specification object
`fdesign.bandstop`	Bandstop filter design specification object
`fdesign.highpass`	Highpass filter specification object
`fdesign.lowpass`	Lowpass filter specification
`fdesign.decimator`	Decimator filter specification object
`fdesign.interpolator`	Interpolator filter specification
`fdesign.rsrc`	Rational-factor sample-rate converter specification
`fdesign.arbgrpdelay`	Arbitrary group delay filter specification object
`fdesign.arbmag`	Arbitrary response magnitude filter specification object
`fdesign.arbmagnphase`	Arbitrary response magnitude and phase filter specification object
`fdesign.ciccomp`	CIC compensator filter specification object
`fdesign.comb`	IIR comb filter specification object
`fdesign.differentiator`	Differentiator filter specification object
`fdesign.fracdelay`	Fractional delay filter specification object
`fdesign.halfband`	Halfband filter specification object
`fdesign.hilbert`	Hilbert filter specification object
`fdesign.isinchp`	Inverse sinc highpass filter specification
`fdesign.isinclp`	Inverse sinc lowpass filter specification
`fdesign.notch`	Notch filter specification
`fdesign.nyquist`	Nyquist filter specification
`fdesign.peak`	Peak filter specification
`fdesign.polysrc`	Construct polynomial sample-rate converter (POLYSRC) filter designer

Design and Implement FIR Filters

`designLowpassFIR`	Design and implement lowpass FIR filter (Since R2023b)
`designHighpassFIR`	Design and implement highpass FIR filter (Since R2023b)
`designBandpassFIR`	Design and implement bandpass FIR filter (Since R2023b)
`designBandstopFIR`	Design and implement bandstop FIR filter (Since R2023b)
`designHalfbandFIR`	Design and implement halfband FIR filter (Since R2023b)
`designMultirateFIR`	Multirate FIR filter design
`designMultistageDecimator`	Multistage decimator design
`designMultistageInterpolator`	Multistage interpolator design

Design FIR Filters

`designFracDelayFIR`	Design band-limited fractional delay FIR filter (Since R2021a)
`fircband`	Constrained-band equiripple FIR filter
`firceqrip`	Constrained equiripple FIR filter
`fireqint`	Equiripple FIR interpolators
`firgr`	Parks-McClellan FIR filter
`firhalfband`	Halfband FIR filter design
`firlpnorm`	Least P-norm optimal FIR filter
`firls`	Least-square linear-phase FIR filter design
`firminphase`	Minimum-phase FIR spectral factor
`firnyquist`	Lowpass Nyquist (Lth-band) FIR filter
`firpr2chfb`	Two-channel FIR filter bank for perfect reconstruction
`ifir`	Interpolated FIR filter design
`normalizefreq`	Switch filter specification between normalized frequency and absolute frequency

Design IIR Filters

`designLowpassIIR`	Design and implement lowpass IIR filter (Since R2023b)
`designHighpassIIR`	Design and implement highpass IIR filter (Since R2023b)
`designBandpassIIR`	Design and implement bandpass IIR filter (Since R2023b)
`designBandstopIIR`	Design and implement bandstop IIR filter (Since R2023b)
`designHalfbandIIR`	Design and implement halfband IIR filter in the form of a coupled allpass filter (Since R2023b)
`designNotchPeakIIR`	Design and implement high-order Butterworth notch or peak IIR filter (Since R2023b)
`ca2tf`	Convert coupled allpass filter to transfer function form
`cl2tf`	Convert coupled allpass lattice to transfer function form
`iircomb`	IIR comb notch or peak filter
`iirgrpdelay`	Optimal IIR filter with prescribed group-delay
`iirlpnorm`	Least P-norm optimal IIR filter
`iirlpnormc`	Constrained least Pth-norm optimal IIR filter
`iirnotch`	Second-order IIR notch filter
`iirpeak`	Second-order IIR peak or resonator filter
`normalizefreq`	Switch filter specification between normalized frequency and absolute frequency

Objects

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Single-rate

`dsp.Differentiator`	Direct form FIR fullband differentiator filter
`dsp.HampelFilter`	Filter outliers using Hampel identifier
`dsp.HighpassFilter`	FIR or IIR highpass filter
`dsp.LowpassFilter`	FIR or IIR lowpass filter
`dsp.MedianFilter`	Median filter
`dsp.NotchPeakFilter`	Second-order tunable notching and peaking IIR filter
`dsp.VariableBandwidthFIRFilter`	Variable bandwidth FIR filter
`dsp.VariableBandwidthIIRFilter`	Variable bandwidth IIR filter

Multirate

`dsp.CICCompensationDecimator`	Compensate for CIC decimation filter using FIR decimator
`dsp.CICCompensationInterpolator`	Compensate for CIC interpolation filter using FIR interpolator
`dsp.FIRHalfbandDecimator`	Halfband decimator
`dsp.FIRHalfbandInterpolator`	Halfband interpolator
`dsp.IIRHalfbandDecimator`	Decimate by factor of two using polyphase IIR
`dsp.IIRHalfbandInterpolator`	Interpolate by a factor of two using polyphase IIR

Blocks

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Filter Design and Visualization Tools

Analog Filter Design	Design and implement analog filters
Digital Filter Design	Design and implement digital FIR and IIR filters
Filter Realization Wizard	Construct filter realizations using digital filter blocks or Sum, Gain, and Delay blocks

Filter Design Sources

Tunable Lowpass FIR Filter	Design lowpass FIR filter with tunable filter specifications (Since R2023b)
Tunable Lowpass IIR Filter	Design lowpass IIR filter with tunable filter specifications (Since R2023b)
Tunable Highpass FIR Filter	Design highpass FIR filter with tunable filter specifications (Since R2023b)
Tunable Highpass IIR Filter	Design highpass IIR filter with tunable filter specifications (Since R2023b)
Tunable Bandpass FIR Filter	Design bandpass FIR filter with tunable filter specifications (Since R2023b)
Tunable Bandpass IIR Filter	Design bandpass IIR filter with tunable filter specifications (Since R2023a)
Tunable Bandstop FIR Filter	Design bandstop FIR filter with tunable filter specifications (Since R2023b)
Tunable Bandstop IIR Filter	Design bandstop IIR filter with tunable filter specifications (Since R2023a)

Singlerate

Arbitrary Response Filter	Design arbitrary response filter
Bandpass Filter	Design bandpass filter
Bandstop Filter	Design bandstop filter
Comb Filter	Design comb Filter
Differentiator Filter	Direct form FIR fullband differentiator filter
Hampel Filter	Filter outliers using Hampel identifier
Highpass Filter	Design FIR or IIR highpass filter
Hilbert Filter	Design Hilbert filter
Inverse Sinc Filter	Design inverse sinc filter
Lowpass Filter	Design FIR or IIR lowpass filter
Median Filter	Median filter
Notch-Peak Filter	Design second-order tunable notching and peaking IIR filter
Variable Bandwidth FIR Filter	Design tunable bandwidth FIR filter
Variable Bandwidth IIR Filter	Design tunable bandwidth IIR filter

Multirate

CIC Filter	Design Cascaded Integrator-Comb (CIC) Filter
Nyquist Filter	Design Nyquist filter

Topics

Using Filter Designer
Use Filter Designer as a powerful yet convenient graphical tool to design and analyze filters.
Design a Filter in Fdesign — Process Overview
Learn how to analyze, design, and implement filters in MATLAB^® and Simulink^®.
Filter Builder Design Process
filterBuilder GUI.
Use Filter Designer with DSP System Toolbox Software
Presents a detailed reference covering the fixed-point, multirate, and scaling pages of the Filter Designer App.
Lowpass FIR Filter Design
This example shows how to design a lowpass FIR filter using fdesign.
Lowpass Filter Design in MATLAB
This example shows how to design lowpass filters.
Controlling Design Specifications in Lowpass FIR Design
This example shows how to control the filter order, passband ripple, stopband attenuation, and transition region width of a lowpass FIR filter.
Minimax FIR Filter Design
This example shows how to use some of the key features of the generalized Remez FIR filter design function.
Designing Filters with Non-Equiripple Stopband
This example shows how to design lowpass filters with stopbands that are not equiripple.
Design and Implement a Filter
Design a digital lowpass filter and incorporate it into your model to simulate the presence of low frequency noise.
Minimizing Lowpass FIR Filter Length
This example shows how to minimize the number coefficients, by designing minimum-phase or minimum-order filters.
References — Advanced Filters
Suggested reading and sources for advanced filter design topics.

Featured Examples

IIR Halfband Stages in Multistage Filter Design

Discusses IIR halfband stages in multistage decimators and interpolators.

Open Live Script

Classic IIR Filter Design

Design classic IIR filters. The example initially focuses on the scenario where critical design parameter is the cutoff frequency at which the power of the filter decays to half (–3 dB) the nominal passband value.

Open Live Script

Design Peak and Notch Filters

Design peak and notch filters. Filters that peak or notch at a certain frequency retain or eliminate a particular frequency component of a signal. The design parameters that you can set for such filters are the frequency at which you want the peak or notch and the 3-dB bandwidth or the Q factor. Using these specifications and by increasing the filter order, you can design filters that more closely approximate an ideal filter.

Open Live Script

Arbitrary Magnitude and Phase Filter Design

Design filters with customized magnitude and phase specifications. Many filter design problems focus on the magnitude response only, while assuming a linear phase response through symmetry. In some cases, however, the desired filter needs to satisfy constraints on both magnitude and phase.

Open Live Script

Least Pth-Norm Optimal FIR Filter Design

Design least Pth-norm FIR filters with the firlpnorm function. This function uses a least-Pth unconstrained optimization algorithm to design FIR filters with arbitrary magnitude response.

Open Live Script

Least Pth-Norm Optimal IIR Filter Design

Design optimal IIR filters with arbitrary magnitude response using the least-Pth unconstrained optimization algorithm.

Open Live Script

FIR Nyquist (L-th band) Filter Design

Design lowpass FIR Nyquist filters. It also compares these filters with raised cosine and square root raised cosine filters. These filters are widely used in pulse-shaping for digital transmission systems. They also find application in interpolation/decimation and filter banks.

Open Live Script

Design of Decimators and Interpolators

Design filters for decimation and interpolation of discrete sequences.

Open Script

IIR Filter Design Given a Prescribed Group Delay

Design arbitrary group delay filters using the fdesign.arbgrpdelay filter designer. This designer uses a least-Pth constrained optimization algorithm to design allpass IIR filters that meet a prescribed group delay.

Open Live Script

Fractional Delay Filters Using Farrow Structures

Use Farrow structures to design digital fractional delay filters. Digital fractional delay filters are useful tools to fine-tune the sampling instants of signals. They are typically found in the synchronization of digital modems where the delay parameter varies over time. This example illustrates why the Farrow structure is a popular method for implementing time-varying FIR fractional delay filters.

Open Live Script

Design Fractional Delay FIR Filters

Design an implementation of fractional delay FIR filters.

Open Live Script