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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; d1 = designfilt("lowpassfir", ... PassbandFrequency=Fpass, ... StopbandFrequency=Fstop, ... PassbandRipple=Apass, ... StopbandAttenuation=Astop, ... DesignMethod="equiripple", ... SampleRate=Fs); filterAnalyzer(d1)
Lowpass IIR Filters
Maximally Flat Design
Fpass = 100; Fstop = 150; Apass = 0.5; Astop = 65; Fs = 1e3; d2 = designfilt("lowpassiir", ... PassbandFrequency=Fpass, ... StopbandFrequency=Fstop, ... PassbandRipple=Apass, ... StopbandAttenuation=Astop, ... DesignMethod="butter", ... SampleRate=Fs); filterAnalyzer(d2)
Ripple in Passband and Stopband
N = 8; Fpass = 100; Apass = 0.5; Astop = 65; Fs = 1e3; d3 = designfilt("lowpassiir", ... FilterOrder=N, ... PassbandFrequency=Fpass, ... PassbandRipple=Apass, ... StopbandAttenuation=Astop, ... SampleRate=Fs); filterAnalyzer(d3)
Highpass FIR Filters
Equiripple Design
Fstop = 350; Fpass = 400; Astop = 65; Apass = 0.5; Fs = 1e3; d4 = designfilt("highpassfir", ... StopbandFrequency=Fstop, ... PassbandFrequency=Fpass, ... StopbandAttenuation=Astop, ... PassbandRipple=Apass, ... DesignMethod="equiripple", ... SampleRate=Fs); filterAnalyzer(d4)
Highpass IIR Filters
Maximally Flat Design
Fstop = 350; Fpass = 400; Astop = 65; Apass = 0.5; Fs = 1e3; d5 = designfilt("highpassiir", ... StopbandFrequency=Fstop ,... PassbandFrequency=Fpass, ... StopbandAttenuation=Astop, ... PassbandRipple=Apass, ... DesignMethod="butter", ... SampleRate=Fs); filterAnalyzer(d5)
Ripple in Passband and Stopband
N = 8; Fpass = 400; Astop = 65; Apass = 0.5; Fs = 1e3; d6 = designfilt("highpassiir", ... FilterOrder=N, ... PassbandFrequency=Fpass, ... StopbandAttenuation=Astop, ... PassbandRipple=Apass, ... SampleRate=Fs); filterAnalyzer(d6)
Bandpass FIR Filters
Equiripple Design
Fstop1 = 150; Fpass1 = 200; Fpass2 = 300; Fstop2 = 350; Astop1 = 65; Apass = 0.5; Astop2 = 65; Fs = 1e3; d7 = designfilt("bandpassfir", ... StopbandFrequency1=Fstop1, ... PassbandFrequency1=Fpass1, ... PassbandFrequency2=Fpass2, ... StopbandFrequency2=Fstop2, ... StopbandAttenuation1=Astop1, ... PassbandRipple=Apass, ... StopbandAttenuation2=Astop2, ... DesignMethod="equiripple", ... SampleRate=Fs); filterAnalyzer(d7)
Asymmetric Band Attenuations
N = 50; Fstop1 = 150; Fpass1 = 200; Fpass2 = 300; Fstop2 = 350; Wstop1 = 3; Wstop2 = 100; Fs = 1e3; d8 = designfilt("bandpassfir", ... FilterOrder=N, ... StopbandFrequency1=Fstop1, ... PassbandFrequency1=Fpass1, ... PassbandFrequency2=Fpass2, ... StopbandFrequency2=Fstop2, ... StopbandWeight1=Wstop1,StopbandWeight2=Wstop2, ... DesignMethod="equiripple",SampleRate=Fs); filterAnalyzer(d8)
Bandpass IIR Filters
Maximally Flat Design
Fstop1 = 150; Fpass1 = 200; Fpass2 = 300; Fstop2 = 350; Astop1 = 65; Apass = 0.5; Astop2 = 65; Fs = 1e3; d9 = designfilt("bandpassiir", ... StopbandFrequency1=Fstop1, ... PassbandFrequency1=Fpass1, ... PassbandFrequency2=Fpass2, ... StopbandFrequency2=Fstop2, ... StopbandAttenuation1=Astop1, ... PassbandRipple=Apass, ... StopbandAttenuation2=Astop2, ... DesignMethod="butter", ... SampleRate=Fs); filterAnalyzer(d9)
Ripple in Passband and Stopband
N = 8; Fpass1 = 200; Fpass2 = 300; Astop1 = 65; Apass = 0.5; Astop2 = 65; Fs = 1e3; d10 = designfilt("bandpassiir", ... FilterOrder=N, ... PassbandFrequency1=Fpass1, ... PassbandFrequency2=Fpass2, ... StopbandAttenuation1=Astop1, ... PassbandRipple=Apass, ... StopbandAttenuation2=Astop2, ... SampleRate=Fs); filterAnalyzer(d10)
Bandstop FIR Filters
Equiripple Design
Fpass1 = 100; Fstop1 = 150; Fstop2 = 350; Fpass2 = 400; Apass1 = 0.5; Astop = 65; Apass2 = 0.5; Fs = 1e3; d11 = designfilt("bandstopfir", ... PassbandFrequency1=Fpass1, ... StopbandFrequency1=Fstop1, ... StopbandFrequency2=Fstop2, ... PassbandFrequency2=Fpass2, ... PassbandRipple1=Apass1, ... StopbandAttenuation=Astop, ... PassbandRipple2=Apass2, ... DesignMethod="equiripple", ... SampleRate=Fs); filterAnalyzer(d11)
Asymmetric Passband Ripples
N = 30; Fpass1 = 100; Fstop1 = 150; Fstop2 = 350; Fpass2 = 400; Wpass1 = 1; Wpass2 = 10; Fs = 1e3; d12 = designfilt("bandstopfir", ... FilterOrder=N, ... PassbandFrequency1=Fpass1, ... StopbandFrequency1=Fstop1, ... StopbandFrequency2=Fstop2, ... PassbandFrequency2=Fpass2, ... PassbandWeight1=Wpass1, ... PassbandWeight2=Wpass2, ... DesignMethod="equiripple", ... SampleRate=Fs); filterAnalyzer(d12)
Bandstop IIR Filters
Maximally Flat Design
Fpass1 = 100; Fstop1 = 150; Fstop2 = 350; Fpass2 = 400; Apass1 = 0.5; Astop = 65; Apass2 = 0.5; Fs = 1e3; d13 = designfilt("bandstopiir", ... PassbandFrequency1=Fpass1, ... StopbandFrequency1=Fstop1, ... StopbandFrequency2=Fstop2, ... PassbandFrequency2=Fpass2, ... PassbandRipple1=Apass1, ... StopbandAttenuation=Astop, ... PassbandRipple2=Apass2, ... DesignMethod="butter", ... SampleRate=Fs); filterAnalyzer(d13)
Ripple in Passband and Stopband
N = 8; Fpass1 = 125; Fpass2 = 375; Apass = 0.5; Astop = 65; Fs = 1e3; d14 = designfilt("bandstopiir", ... FilterOrder=N, ... PassbandFrequency1=Fpass1, ... PassbandFrequency2=Fpass2, ... PassbandRipple=Apass, ... StopbandAttenuation=Astop, ... SampleRate=Fs); filterAnalyzer(d14)
Arbitrary Magnitude FIR Filters
Single-Band Arbitrary Magnitude Design
N = 300; % Frequencies are in normalized units F1 = 0:0.01:0.18; F2 = [0.2 0.38 0.4 0.55 0.562 0.585 0.6 0.78]; F3 = 0.79:0.01:1; FreqVect = [F1 F2 F3]; % vector of frequencies % Define desired response using linear units A1 = 0.5+sin(2*pi*7.5*F1)/4; % Sinusoidal section A2 = [0.5 2.3 1 1 -0.2 -0.2 1 1]; % Piece-wise linear section A3 = 0.2+18*(1-F3).^2; % Quadratic section AmpVect = [A1 A2 A3]; d15 = designfilt("arbmagfir",... FilterOrder=N, ... Amplitudes=AmpVect, ... Frequencies=FreqVect,... DesignMethod="freqsamp"); filterAnalyzer(d15,MagnitudeMode="zerophase")
Multiband Lowpass Design with Stepped Attenuation Levels on Stopband
N = 150; B = 2; % Number of bands % Frequencies are in normalized units F1 = [0 0.25]; % Passband F2 = [0.3 0.4 0.401 0.5 0.501 0.6 0.601 0.7 0.701 0.8 0.801 0.9 0.901 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 d16 = designfilt("arbmagfir", ... FilterOrder=N, ... NumBands=B, ... BandFrequencies1=F1, ... BandAmplitudes1=A1, ... BandFrequencies2=F2, ... BandAmplitudes2=A2, ... BandWeights1=W1, ... BandWeights2=W2); filterAnalyzer(d16)
Differentiator FIR Filters
Full Band Design
N = 41; Fs = 1e3; d17 = designfilt("differentiatorfir", ... FilterOrder=N, ... DesignMethod="equiripple", ... SampleRate=Fs); filterAnalyzer(d17,MagnitudeMode="zerophase",OverlayAnalysis="phase")
Partial Band Design
N = 40; Fpass = 100; Fstop = 150; Fs = 1e3; d18 = designfilt("differentiatorfir", ... FilterOrder=N, ... PassbandFrequency=Fpass, ... StopbandFrequency=Fstop, ... DesignMethod="equiripple", ... SampleRate=Fs); filterAnalyzer(d18,MagnitudeMode="zerophase",OverlayAnalysis="phase")
Hilbert FIR Filters
Equiripple Design
N = 40; Tw = 50; Fs = 1e3; d19 = designfilt("hilbertfir", ... FilterOrder=N, ... TransitionWidth=Tw, ... DesignMethod="equiripple", ... SampleRate=Fs); filterAnalyzer(d19,MagnitudeMode="zerophase",OverlayAnalysis="phase")
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