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Filter Design Gallery

This example shows how to design a variety of FIR and IIR digital filters with the designfilt function in the Signal Processing Toolbox® product.

The gallery is designed for you to identify a filter response of interest, view the code, and use it in your own project. It contains examples for each of the available filter responses offered by designfilt. Note, however, that these are only a few of the possible ways in which you can design filters for each response type. For an exhaustive list of specification sets, see the Signal Processing Toolbox documentation.

Except when noted otherwise, in this example all frequency units are in hertz, and all ripple and attenuation values are in decibels.

Lowpass FIR Filters

Equiripple Design

Fpass = 100;
Fstop = 150;
Apass = 1;
Astop = 65;
Fs = 1e3;

d = designfilt('lowpassfir', ...
  'PassbandFrequency',Fpass,'StopbandFrequency',Fstop, ...
  'PassbandRipple',Apass,'StopbandAttenuation',Astop, ...
  'DesignMethod','equiripple','SampleRate',Fs);

fvtool(d)

Figure Filter Visualization Tool - Magnitude Response (dB) contains an axes and other objects of type uitoolbar, uimenu. The axes with title Magnitude Response (dB) contains 2 objects of type line.

Lowpass IIR Filters

Maximally Flat Design

Fpass = 100;
Fstop = 150;
Apass = 0.5;
Astop = 65;
Fs = 1e3;

d = designfilt('lowpassiir', ...
  'PassbandFrequency',Fpass,'StopbandFrequency',Fstop, ...
  'PassbandRipple',Apass,'StopbandAttenuation',Astop, ...
  'DesignMethod','butter','SampleRate',Fs);

fvtool(d)

Figure Filter Visualization Tool - Magnitude Response (dB) contains an axes and other objects of type uitoolbar, uimenu. The axes with title Magnitude Response (dB) contains 2 objects of type line.

Ripple in Passband and Stopband

N = 8;
Fpass = 100;
Apass = 0.5;
Astop = 65;
Fs = 1e3;

d = designfilt('lowpassiir', ...
  'FilterOrder',N, ...  
  'PassbandFrequency',Fpass, ...
  'PassbandRipple',Apass,'StopbandAttenuation',Astop, ...
  'SampleRate',Fs);

fvtool(d)

Figure Filter Visualization Tool - Magnitude Response (dB) contains an axes and other objects of type uitoolbar, uimenu. The axes with title Magnitude Response (dB) contains 2 objects of type line.

Highpass FIR Filters

Equiripple Design

Fstop = 350;
Fpass = 400;
Astop = 65;
Apass = 0.5;
Fs = 1e3;

d = designfilt('highpassfir','StopbandFrequency',Fstop, ...
  'PassbandFrequency',Fpass,'StopbandAttenuation',Astop, ...
  'PassbandRipple',Apass,'SampleRate',Fs,'DesignMethod','equiripple');

fvtool(d)

Figure Filter Visualization Tool - Magnitude Response (dB) contains an axes and other objects of type uitoolbar, uimenu. The axes with title Magnitude Response (dB) contains 2 objects of type line.

Highpass IIR Filters

Maximally Flat Design

Fstop = 350;
Fpass = 400;
Astop = 65;
Apass = 0.5;
Fs = 1e3;

d = designfilt('highpassiir','StopbandFrequency',Fstop ,...
  'PassbandFrequency',Fpass,'StopbandAttenuation',Astop, ...
  'PassbandRipple',Apass,'SampleRate',Fs,'DesignMethod','butter');

fvtool(d)

Figure Filter Visualization Tool - Magnitude Response (dB) contains an axes and other objects of type uitoolbar, uimenu. The axes with title Magnitude Response (dB) contains 2 objects of type line.

Ripple in Passband and Stopband

N = 8;
Fpass = 400;
Astop = 65;
Apass = 0.5;
Fs = 1e3;

d = designfilt('highpassiir', ...
  'FilterOrder',N, ...  
  'PassbandFrequency',Fpass, ...
  'StopbandAttenuation',Astop,'PassbandRipple',Apass, ...
  'SampleRate',Fs);

fvtool(d)

Figure Filter Visualization Tool - Magnitude Response (dB) contains an axes and other objects of type uitoolbar, uimenu. The axes with title Magnitude Response (dB) contains 2 objects of type line.

Bandpass FIR Filters

Equiripple Design

Fstop1 = 150;
Fpass1 = 200;
Fpass2 = 300;
Fstop2 = 350;
Astop1 = 65;
Apass  = 0.5;
Astop2 = 65;
Fs = 1e3;

d = designfilt('bandpassfir', ...
  'StopbandFrequency1',Fstop1,'PassbandFrequency1', Fpass1, ...
  'PassbandFrequency2',Fpass2,'StopbandFrequency2', Fstop2, ...
  'StopbandAttenuation1',Astop1,'PassbandRipple', Apass, ...
  'StopbandAttenuation2',Astop2, ...
  'DesignMethod','equiripple','SampleRate',Fs);

fvtool(d)

Figure Filter Visualization Tool - Magnitude Response (dB) contains an axes and other objects of type uitoolbar, uimenu. The axes with title Magnitude Response (dB) contains 2 objects of type line.

Asymmetric Band Attenuations

N = 50;
Fstop1 = 150;
Fpass1 = 200;
Fpass2 = 300;
Fstop2 = 350;
Wstop1 = 3;
Wstop2 = 100;
Fs = 1e3;

d = designfilt('bandpassfir', ...
  'FilterOrder',N, ...
  'StopbandFrequency1',Fstop1,'PassbandFrequency1', Fpass1, ...
  'PassbandFrequency2',Fpass2,'StopbandFrequency2', Fstop2, ...
  'StopbandWeight1',Wstop1,'StopbandWeight2',Wstop2, ...
   'DesignMethod','equiripple','SampleRate',Fs);
  
fvtool(d)

Figure Filter Visualization Tool - Magnitude Response (dB) contains an axes and other objects of type uitoolbar, uimenu. The axes with title Magnitude Response (dB) contains 2 objects of type line.

Bandpass IIR Filters

Maximally Flat Design

Fstop1 = 150;
Fpass1 = 200;
Fpass2 = 300;
Fstop2 = 350;
Astop1 = 65;
Apass  = 0.5;
Astop2 = 65;
Fs = 1e3;

d = designfilt('bandpassiir', ...
  'StopbandFrequency1',Fstop1,'PassbandFrequency1', Fpass1, ...
  'PassbandFrequency2',Fpass2,'StopbandFrequency2', Fstop2, ...
  'StopbandAttenuation1',Astop1,'PassbandRipple', Apass, ...
  'StopbandAttenuation2',Astop2, ...
  'DesignMethod','butter','SampleRate', Fs);

fvtool(d)

Figure Filter Visualization Tool - Magnitude Response (dB) contains an axes and other objects of type uitoolbar, uimenu. The axes with title Magnitude Response (dB) contains 2 objects of type line.

Ripple in Passband and Stopband

N = 8;
Fpass1 = 200;
Fpass2 = 300;
Astop1 = 65;
Apass  = 0.5;
Astop2 = 65;
Fs = 1e3;

d = designfilt('bandpassiir', ...
  'FilterOrder',N, ...
  'PassbandFrequency1', Fpass1,'PassbandFrequency2', Fpass2, ...
  'StopbandAttenuation1', Astop1, 'PassbandRipple', Apass, ...
  'StopbandAttenuation2', Astop2, ...
  'SampleRate', Fs);

fvtool(d)

Figure Filter Visualization Tool - Magnitude Response (dB) contains an axes and other objects of type uitoolbar, uimenu. The axes with title Magnitude Response (dB) contains 2 objects of type line.

Bandstop FIR Filters

Equiripple Design

Fpass1 = 100;
Fstop1 = 150;
Fstop2 = 350;
Fpass2 = 400;
Apass1 = 0.5;
Astop  = 65;
Apass2 = 0.5;
Fs = 1e3;

d = designfilt('bandstopfir', ...
  'PassbandFrequency1',Fpass1,'StopbandFrequency1',Fstop1, ...
  'StopbandFrequency2',Fstop2,'PassbandFrequency2',Fpass2, ...
  'PassbandRipple1',Apass1,'StopbandAttenuation',Astop, ...
  'PassbandRipple2', Apass2, ...
  'DesignMethod','equiripple','SampleRate', Fs);

fvtool(d)

Figure Filter Visualization Tool - Magnitude Response (dB) contains an axes and other objects of type uitoolbar, uimenu. The axes with title Magnitude Response (dB) contains 2 objects of type line.

Asymmetric Passband Ripples

N = 30;
Fpass1 = 100;
Fstop1 = 150;
Fstop2 = 350;
Fpass2 = 400;
Wpass1 = 1;
Wpass2  = 10;
Fs = 1e3;

d = designfilt('bandstopfir', ...
  'FilterOrder',N, ...
  'PassbandFrequency1',Fpass1,'StopbandFrequency1',Fstop1, ...
  'StopbandFrequency2',Fstop2,'PassbandFrequency2',Fpass2, ...
  'PassbandWeight1',Wpass1,'PassbandWeight2',Wpass2, ...
  'DesignMethod','equiripple','SampleRate', Fs);

fvtool(d)

Figure Filter Visualization Tool - Magnitude Response (dB) contains an axes and other objects of type uitoolbar, uimenu. The axes with title Magnitude Response (dB) contains 2 objects of type line.

Bandstop IIR Filters

Maximally Flat Design

Fpass1 = 100;
Fstop1 = 150;
Fstop2 = 350;
Fpass2 = 400;
Apass1 = 0.5;
Astop  = 65;
Apass2 = 0.5;
Fs = 1e3;

d = designfilt('bandstopiir', ...
  'PassbandFrequency1',Fpass1,'StopbandFrequency1',Fstop1, ...
  'StopbandFrequency2',Fstop2,'PassbandFrequency2',Fpass2, ...
  'PassbandRipple1',Apass1,'StopbandAttenuation',Astop, ...
  'PassbandRipple2', Apass2, ...
  'DesignMethod','butter','SampleRate', Fs);

fvtool(d)

Figure Filter Visualization Tool - Magnitude Response (dB) contains an axes and other objects of type uitoolbar, uimenu. The axes with title Magnitude Response (dB) contains 2 objects of type line.

Ripple in Passband and Stopband

N = 8;
Fpass1 = 125;
Fpass2 = 375;
Apass = 0.5;
Astop  = 65;
Fs = 1e3;

d = designfilt('bandstopiir', ...
  'FilterOrder',N, ...
  'PassbandFrequency1',Fpass1,'PassbandFrequency2',Fpass2, ...
  'PassbandRipple',Apass,'StopbandAttenuation', Astop, ...
  'SampleRate',Fs);

fvtool(d)

Figure Filter Visualization Tool - Magnitude Response (dB) contains an axes and other objects of type uitoolbar, uimenu. The axes with title Magnitude Response (dB) contains 2 objects of type line.

Arbitrary Magnitude FIR Filters

Single-Band Arbitrary Magnitude Design

N = 300;

% Frequencies are in normalized units
F1 = 0:0.01:0.18;
F2 = [.2 .38 .4 .55 .562 .585 .6 .78];
F3 = 0.79:0.01:1;
FreqVect = [F1 F2 F3]; % vector of frequencies

% Define desired response using linear units
A1 = .5+sin(2*pi*7.5*F1)/4;    % Sinusoidal section
A2 = [.5 2.3 1 1 -.2 -.2 1 1]; % Piecewise linear section
A3 = .2+18*(1-F3).^2;          % Quadratic section

AmpVect = [A1 A2 A3];

d = designfilt('arbmagfir',...
  'FilterOrder',N,'Amplitudes',AmpVect,'Frequencies',FreqVect,...
  'DesignMethod','freqsamp');

fvtool(d,'MagnitudeDisplay','Zero-phase')

Figure Filter Visualization Tool - Zero-phase Response contains an axes and other objects of type uitoolbar, uimenu. The axes with title Zero-phase Response contains 2 objects of type line.

Multiband Lowpass Design with Stepped Attenuation Levels on Stopband

N = 150;
B = 2; % Number of bands
% Frequencies are in normalized units
F1 = [0 .25]; % Passband
F2 = [.3 .4 .401 .5 .501 .6 .601 .7 .701 .8 .801 .9 .901 1]; % Stopband
A1 = ones(size(F1));  % Desired amplitudes for band 1 in linear units
A2 = zeros(size(F2)); % Desired amplitudes for band 2 in linear units
% Vector of weights
W = 10.^([0 0 5 5 10 10 15 15 20 20 25 25 30 30 35 35]/20);
W1 = W(1:2);   % Weights for band 1
W2 = W(3:end); % Weights for band 2

d = designfilt('arbmagfir', ...
  'FilterOrder',N,'NumBands',B, ...
  'BandFrequencies1',F1,'BandAmplitudes1',A1, ...
  'BandFrequencies2',F2,'BandAmplitudes2',A2, ...
  'BandWeights1',W1,'BandWeights2', W2);

fvtool(d)

Figure Filter Visualization Tool - Magnitude Response (dB) contains an axes and other objects of type uitoolbar, uimenu. The axes with title Magnitude Response (dB) contains 2 objects of type line.

Differentiator FIR Filters

Full Band Design

N = 41;
Fs = 1e3;

d = designfilt('differentiatorfir', ...
'FilterOrder',N, 'DesignMethod','equiripple','SampleRate',Fs);

fvtool(d,'MagnitudeDisplay','zero-phase','OverlayedAnalysis','phase')

Figure Filter Visualization Tool - Zero-phase Response and Phase Response contains an axes and other objects of type uitoolbar, uimenu. The axes with title Zero-phase Response and Phase Response contains an object of type line.

Partial Band Design

N = 40;
Fpass = 100;
Fstop = 150;
Fs = 1e3;

d = designfilt('differentiatorfir', ...
'FilterOrder',N, ...
'PassbandFrequency',Fpass,'StopbandFrequency',Fstop, ...
'DesignMethod','equiripple','SampleRate',Fs);

fvtool(d,'MagnitudeDisplay','zero-phase','OverlayedAnalysis','phase')

Figure Filter Visualization Tool - Zero-phase Response and Phase Response contains an axes and other objects of type uitoolbar, uimenu. The axes with title Zero-phase Response and Phase Response contains an object of type line.

Hilbert FIR Filters

Equiripple Design

N = 40;
Tw = 50;
Fs = 1e3;

d = designfilt('hilbertfir', ...
'FilterOrder',N,'TransitionWidth',Tw, ...
'DesignMethod','equiripple','SampleRate',Fs);

fvtool(d,'MagnitudeDisplay','Zero-phase','OverlayedAnalysis','phase')

Figure Filter Visualization Tool - Zero-phase Response and Phase Response contains an axes and other objects of type uitoolbar, uimenu. The axes with title Zero-phase Response and Phase Response contains an object of type line.

See Also

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