Main Content

このページの内容は最新ではありません。最新版の英語を参照するには、ここをクリックします。

フィルター設計ギャラリー

この例では、Signal Processing Toolbox® 製品の関数 designfilt を使用する、さまざまな FIR および IIR デジタル フィルターの設計法を説明します。

ギャラリーは、対象となるフィルター応答を特定し、コードを表示して独自のプロジェクトで使用できるように設計されています。ここには designfilt が提供する利用可能なフィルター応答のそれぞれについての例が含まれています。ただし、これらは、各応答タイプに対応するフィルターを設計する方法として可能なもののごく一部であることを留意してください。仕様セットを網羅したリストについては、Signal Processing Toolbox のドキュメンテーションを参照してください。

この例では、特に注意書きがなければ、周波数の単位はいずれも Hz で、すべてのリップルと減衰の値の単位はデシベルです。

ローパス FIR フィルター

等リップル設計

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 Figure 1: Magnitude Response (dB) contains an axes object. The axes object with title Magnitude Response (dB), xlabel Frequency (Hz), ylabel Magnitude (dB) contains 2 objects of type line.

ローパス IIR フィルター

最大フラット設計

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 Figure 2: Magnitude Response (dB) contains an axes object. The axes object with title Magnitude Response (dB), xlabel Frequency (Hz), ylabel Magnitude (dB) contains 2 objects of type line.

通過帯域および阻止帯域のリップル

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 Figure 3: Magnitude Response (dB) contains an axes object. The axes object with title Magnitude Response (dB), xlabel Frequency (Hz), ylabel Magnitude (dB) contains 2 objects of type line.

ハイパス FIR フィルター

等リップル設計

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 Figure 4: Magnitude Response (dB) contains an axes object. The axes object with title Magnitude Response (dB), xlabel Frequency (Hz), ylabel Magnitude (dB) contains 2 objects of type line.

ハイパス IIR フィルター

最大フラット設計

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 Figure 5: Magnitude Response (dB) contains an axes object. The axes object with title Magnitude Response (dB), xlabel Frequency (Hz), ylabel Magnitude (dB) contains 2 objects of type line.

通過帯域および阻止帯域のリップル

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 Figure 6: Magnitude Response (dB) contains an axes object. The axes object with title Magnitude Response (dB), xlabel Frequency (Hz), ylabel Magnitude (dB) contains 2 objects of type line.

バンドパス FIR フィルター

等リップル設計

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 Figure 7: Magnitude Response (dB) contains an axes object. The axes object with title Magnitude Response (dB), xlabel Frequency (Hz), ylabel Magnitude (dB) contains 2 objects of type line.

非対称バンド減衰

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 Figure 8: Magnitude Response (dB) contains an axes object. The axes object with title Magnitude Response (dB), xlabel Frequency (Hz), ylabel Magnitude (dB) contains 2 objects of type line.

バンドパス IIR フィルター

最大フラット設計

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 Figure 9: Magnitude Response (dB) contains an axes object. The axes object with title Magnitude Response (dB), xlabel Frequency (Hz), ylabel Magnitude (dB) contains 2 objects of type line.

通過帯域および阻止帯域のリップル

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 Figure 10: Magnitude Response (dB) contains an axes object. The axes object with title Magnitude Response (dB), xlabel Frequency (Hz), ylabel Magnitude (dB) contains 2 objects of type line.

バンドストップ FIR フィルター

等リップル設計

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 Figure 11: Magnitude Response (dB) contains an axes object. The axes object with title Magnitude Response (dB), xlabel Frequency (Hz), ylabel Magnitude (dB) contains 2 objects of type line.

非対称通過帯域リップル

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 Figure 12: Magnitude Response (dB) contains an axes object. The axes object with title Magnitude Response (dB), xlabel Frequency (Hz), ylabel Magnitude (dB) contains 2 objects of type line.

バンドストップ IIR フィルター

最大フラット設計

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 Figure 13: Magnitude Response (dB) contains an axes object. The axes object with title Magnitude Response (dB), xlabel Frequency (Hz), ylabel Magnitude (dB) contains 2 objects of type line.

通過帯域および阻止帯域のリップル

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 Figure 14: Magnitude Response (dB) contains an axes object. The axes object with title Magnitude Response (dB), xlabel Frequency (Hz), ylabel Magnitude (dB) contains 2 objects of type line.

任意振幅 FIR フィルター

シングルバンド任意振幅設計

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 Figure 15: Zero-phase Response contains an axes object. The axes object with title Zero-phase Response, xlabel Normalized Frequency ( times pi blank rad/sample), ylabel Amplitude contains 2 objects of type line.

阻止帯域で階段状に減衰するマルチバンド ローパス設計

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 Figure 16: Magnitude Response (dB) contains an axes object. The axes object with title Magnitude Response (dB), xlabel Normalized Frequency ( times pi blank rad/sample), ylabel Magnitude (dB) contains 2 objects of type line.

微分器 FIR フィルター

フル バンド設計

N = 41;
Fs = 1e3;

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

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

Figure Figure 17: Zero-phase Response and Phase Response contains an axes object. The axes object with title Zero-phase Response and Phase Response, xlabel Frequency (Hz), ylabel Amplitude contains an object of type line.

部分バンド設計

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 Figure 18: Zero-phase Response and Phase Response contains an axes object. The axes object with title Zero-phase Response and Phase Response, xlabel Frequency (Hz), ylabel Amplitude contains an object of type line.

ヒルベルト FIR フィルター

等リップル設計

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 Figure 19: Zero-phase Response and Phase Response contains an axes object. The axes object with title Zero-phase Response and Phase Response, xlabel Frequency (Hz), ylabel Amplitude contains an object of type line.

参考

|