Digital Filter Design

FIR, IIR, windowing, equiripple, least squares, Butterworth, Chebyshev, elliptic, pulse shaping

Design digital filters using as a starting point a set of specifications (designfilt) or a design algorithm (butter, fir1). Generate FIR differentiators and Hilbert filters.

Apps

Filter Analyzer	View, analyze, and compare filters (Since R2024a)
Filter Designer	Design filters by choosing algorithm or specifying constraints

Live Editor Tasks

Design Filter

Design a digital filter in the Live Editor (Since R2021b)

Functions

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FIR Filters

`cfirpm`	Complex and nonlinear-phase equiripple FIR filter design
`designfilt`	Design digital filter
`fir1`	Window-based FIR filter design
`fir2`	Frequency sampling-based FIR filter design
`fircls`	Constrained-least-squares FIR multiband filter design
`fircls1`	Constrained-least-squares linear-phase FIR lowpass and highpass filter design
`firls`	Least-squares linear-phase FIR filter design
`firpm`	Parks-McClellan optimal FIR filter design
`firpmord`	Parks-McClellan optimal FIR filter order estimation
`gaussdesign`	Gaussian FIR pulse-shaping filter design
`intfilt`	Interpolation FIR filter design
`kaiserord`	Kaiser window FIR filter design estimation parameters
`maxflat`	Generalized digital Butterworth filter design
`rcosdesign`	Raised cosine FIR pulse-shaping filter design
`sgolay`	Savitzky-Golay filter design

IIR Filters

`butter`	Butterworth filter design
`buttord`	Butterworth filter order and cutoff frequency
`cheby1`	Chebyshev Type I filter design
`cheb1ord`	Chebyshev Type I filter order
`cheby2`	Chebyshev Type II filter design
`cheb2ord`	Chebyshev Type II filter order
`designfilt`	Design digital filter
`ellip`	Elliptic filter design
`ellipord`	Minimum order for elliptic filters
`yulewalk`	Recursive digital filter design

Filter Utilities

`digitalFilter`	Digital filter
`double`	Cast coefficients of digital filter to double precision
`filt2block`	Generate Simulink filter block
`filterAnalyzer`	Analyze filters with Filter Analyzer app (Since R2024a)
`info`	Information about digital filter
`isdouble`	Determine if digital filter coefficients are double precision
`issingle`	Determine if digital filter coefficients are single precision
`polyscale`	Scale roots of polynomial
`polystab`	Stabilize polynomial
`scaleFilterSections`	Scale cascaded transfer functions with scale values (Since R2023b)
`setSampleRate`	Set sample rate of digital filter (Since R2026a)
`single`	Cast coefficients of digital filter to single precision

Filter Responses

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FIR Responses

Lowpass FIR	Design lowpass finite impulse response filter
Highpass FIR	Design highpass finite impulse response filter
Bandpass FIR	Design bandpass finite impulse response filter
Bandstop FIR	Design bandstop finite impulse response filter
Differentiator FIR	Design differentiator finite impulse response filter
Hilbert FIR	Design Hilbert finite impulse response filter
Arbitrary Response FIR	Design finite impulse response filter of arbitrary response

IIR Responses

Lowpass IIR	Design lowpass infinite impulse response filter
Highpass IIR	Design highpass infinite impulse response filter
Bandpass IIR	Design bandpass infinite impulse response filter
Bandstop IIR	Design bandstop infinite impulse response filter

Topics

Use Filter Designer App

Import or create filters, design, inspect, and export filter designs.
- STEP 1: Import or Create Filters
- STEP 2: Design Filters
- STEP 3: Quantize Filters
- STEP 4: Manage and Analyze Filters
- STEP 5: Export and Share Filters
IIR Filter Design
This example compares classical Butterworth, Chebyshev, and elliptic designs; and explores Bessel, Yule-Walker, and generalized Butterworth filters.
FIR Filter Design
This example shows how to use windowing, least squares, or the Parks-McClellan algorithm to design lowpass, highpass, multiband, or arbitrary-response filters, differentiators, or Hilbert transformers.
Filter Implementation
Filter signals using the filter function.
Anti-Causal, Zero-Phase Filter Implementation
Eliminate the phase distortion introduced by an IIR filter.
Compensate for the Delay Introduced by an FIR Filter
Use indexing to counteract the time shifts introduced by filtering.
Compensate for the Delay Introduced by an IIR Filter
Remove delays and distortion introduced by filtering, when it is critical to keep phase information intact.
Take Derivatives of a Signal
Use a differentiator filter to differentiate a signal without amplifying the noise.
Generate Guitar Chords Using the Karplus-Strong Algorithm
Generate realistic guitar chords using the Karplus-Strong algorithm and discrete-time filters.

Related Information

Filter Design in MATLAB

Featured Examples

Practical Introduction to Digital Filter Design

Use the designfilt function to design FIR and IIR filters based on frequency response specifications.

Open Live Script

Practical Introduction to Digital Filtering

Design, analyze, and apply digital filters to remove unwanted content from a signal without distorting the data.

Open Live Script

Filter Design Gallery

Identify a filter response of interest, see how it is designed using the designfilt function, and use it in your own project.

Open Live Script

Teaching Resources

Digital Signal Processing: Signals and Filter Design

Learn the concepts behind analog and digital signals, filters, and filter designs, and apply your learning to build a filtering app.