83 lines
2.1 KiB
Markdown
83 lines
2.1 KiB
Markdown
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---
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layout: post
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title: "使用 Octave 工具设计巴特沃斯滤波器"
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subtitle: ""
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description: "使用 Octave 工具设计巴特沃斯低通、高通和带阻滤波器。"
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excerpt: "使用 Octave 工具设计巴特沃斯低通、高通和带阻滤波器。"
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date: 2022-09-07 15:44:00
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author: "Rick Chan"
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tags: ["DSP", "Butterworth", "Lowpass", "Highpass", "Bandstop"]
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categories: ["Algorithm"]
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published: true
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---
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- [1. 巴特沃斯低通滤波器](#1-巴特沃斯低通滤波器)
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- [2. 巴特沃斯带阻滤波器](#2-巴特沃斯带阻滤波器)
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- [3. 巴特沃斯高通滤波器](#3-巴特沃斯高通滤波器)
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- [4. 外部参考资料](#4-外部参考资料)
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需要安装和加载 signal 包。
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```m
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>> pkg install -forge signal
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>> pkg load signal
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```
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## 1. 巴特沃斯低通滤波器
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设计一个 6 阶低通滤波器，截至频率为 100Hz，采样频率为 1000Hz。
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```m
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>> fc = 100;
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>> fs = 1000;
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>> [b,a] = butter(6,fc/(fs/2),'low');
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>> freqz(b,a,[],fs)
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>> b
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b =
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0.070115 0.420692 1.051731 1.402308 1.051731 0.420692 0.070115
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>> a
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a =
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1.0000e+00 1.1876e+00 1.3052e+00 6.7433e-01 2.6347e-01 5.1753e-02 5.0225e-03
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dataIn = randn(1000,1);
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dataOut = filter(b,a,dataIn);
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figure(2)
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subplot(1, 2, 1);
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plot(dataIn);
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subplot(1, 2, 2);
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plot(dataOut);
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```
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a、b 即为公式：
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$$y(n)=\sum_{k=0}^{M}b(k)x(n-k)-\sum_{l=1}^{N}a(l)y(n-l)$$
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中的系数。
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a 只需要 6 个系数就可以，a(1) 是为了计算方便，其结果始终为 1.0，并表示为归一化的系数，在实际使用时不会用到 a(1)。
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## 2. 巴特沃斯带阻滤波器
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```m
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>> [b,a] = butter(3,[0.2 0.6],'stop');
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>> freqz(b,a)
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```
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## 3. 巴特沃斯高通滤波器
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```m
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>> [z,p,k] = butter(9,300/500,'high');
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>> sos = zp2sos(z,p,k);
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>> fvtool(sos,'Analysis','freq')
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```
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## 4. 外部参考资料
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1. [Butterworth filter design](https://ww2.mathworks.cn/help/signal/ref/butter.html#bucse3u-ftype)
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