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滤波器设计库

此示例说明如何使用 Signal Processing Toolbox® 产品中的 designfilt 函数设计各种 FIR 和 IIR 数字滤波器。

该库旨在帮助您识别感兴趣的滤波器响应,查看代码,并在您自己的工程中使用它。它包含 designfilt 提供的每个可用滤波器响应的示例。但请注意,这些只是为每种响应类型设计滤波器的几种可能方式。有关设定集的详尽列表,请参阅 Signal Processing Toolbox 文档。

除非另有说明,否则在此示例中,所有频率均以赫兹为单位,所有波纹和衰减值均以分贝为单位。

低通 FIR 滤波器

等波纹设计

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.

低通 IIR 滤波器

最平坦设计

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.

通带和阻带中的波纹

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.

高通 FIR 滤波器

等波纹设计

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.

高通 IIR 滤波器

最平坦设计

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.

通带和阻带中的波纹

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.

带通 FIR 滤波器

等波纹设计

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.

不对称频带衰减

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.

带通 IIR 滤波器

最平坦设计

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.

通带和阻带中的波纹

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.

带阻 FIR 滤波器

等波纹设计

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.

不对称通带波纹

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.

带阻 IIR 滤波器

最平坦设计

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.

通带和阻带中的波纹

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.

任意幅值 FIR 滤波器

单频带任意幅值设计

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.

多频带低通设计,阻带具有阶梯式衰减电平

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.

FIR 微分滤波器

全频带设计

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.

部分频带设计

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 滤波器

等波纹设计

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.

另请参阅

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