数字信号仿真实验——实验三无限冲激响应数字滤波器的设计

小灰灰 2023-10-05 13:41 2阅读 0赞

## 1.实验目的![在这里插入图片描述][20201115160032636.bmp_pic_center] ##

## 2.实验原理 ##

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQyMDc4OTM0_size_16_color_FFFFFF_t_70_pic_center]  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQyMDc4OTM0_size_16_color_FFFFFF_t_70_pic_center 1]  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQyMDc4OTM0_size_16_color_FFFFFF_t_70_pic_center 2]  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQyMDc4OTM0_size_16_color_FFFFFF_t_70_pic_center 3]  
![在这里插入图片描述][20201115160337744.bmp_pic_center]

## 3.实验内容 ##

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQyMDc4OTM0_size_16_color_FFFFFF_t_70_pic_center 4]  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQyMDc4OTM0_size_16_color_FFFFFF_t_70_pic_center 5]

## 4.实验报告要求 ##

（1）在实验报告中简述实验目的和实验原理要点  
（2）记录在实验内容中所设计的滤波器的传递函数H(Z)及对应的幅频特性曲线，定性分析它们的性能，判断设计是否满足要求。  
（3）对比滤波前后的心电图信号波形，说明数字滤波器的滤波过程与滤波作用。  
（4）总结试验中的主要结论。

## Matlab程序1： ##

Problem1
    FS=1;%采样频率
    t=1/FS;
    fp=0.3;
    fs=0.2;
    wp=2*pi*fp/FS;%数字
    ws=2*pi*fs/FS;
    omegap=2*FS*tan(wp/2);%频率预畸变
    omegas=2*FS*tan(ws/2);
    [n,wn]=cheb1ord(omegap,omegas,0.8,20,'s');%切比雪夫（Wp，WS，Rp，Rs）通带和阻带的截止频率，通带和阻带的波纹系数
    [b,a]=cheby1(n,0.8,wn,'high','s');%切比雪夫1型，n阶，Rp=0.8指定允许的波纹，wn固有频率
    [bz,az]=bilinear(b,a,FS)%双线性变换
    freqz(bz,az,512,FS)%计算离散系统频响特性
    title('Made by LEI')

## 运行结果1： ##

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQyMDc4OTM0_size_16_color_FFFFFF_t_70_pic_center 6]

## 实验分析1： ##

实验分析：az=1.0000 1.5289 1.6537 0.9452 0.2796  
bz=0.0262 -0.1047 0.1570 -0.1047 0.0262  
观察图像，其通带衰减即fp=0.3HZ时通带衰减小于0.8dB ；其阻带衰减即fs=0.2HZ时阻带衰减大于20dB故满足设计要求。

## Matlab程序2\_1： ##

Problem2_1
    FS=1;%采样频率
    t=1/FS;
    fp=0.2;
    fs=0.3;
    wp=2*pi*fp/FS;%数字角频率
    ws=2*pi*fs/FS;
    omegap=2*FS*tan(wp/2);%频率预畸变
    omegas=2*FS*tan(ws/2);
    [n,wn]=cheb1ord(omegap,omegas,1,25,'s')%模拟低通的阶次n和截止频率Wn
    [b,a]=cheby1(n,1,wn,'s');%模拟低通滤波器设计
    [bz,az]=bilinear(b,a,FS)%双线性变换法设计数字低通滤波器
    freqz(bz,az,512,FS)
    title('Made by LEI')

## 运行结果2\_1： ##

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQyMDc4OTM0_size_16_color_FFFFFF_t_70_pic_center 7]

## Matlab程序2\_2： ##

Problem2_2
    FS=1;
    t=1/FS;
    fp=0.2;
    fs=0.3;
    wp=2*pi*fp/FS;%数字角频率
    ws=2*pi*fs/FS;
    omegap=2*FS*tan(wp/2);%频率预畸变
    omegas=2*FS*tan(ws/2);
    [n,wn]=buttord(omegap,omegas,1,25,'s');%模拟低通的阶次n和截止频率Wn
    [b,a]=butter(n,wn,'s');%模拟低通滤波器设计
    [bz,az]=bilinear(b,a,FS);%双线性变换法设计数字低通滤波器
    freqz(bz,az,512,FS)
    title('Made by LEI')

## 运行结果2\_2： ##

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQyMDc4OTM0_size_16_color_FFFFFF_t_70_pic_center 8]

## 实验分析2： ##

实验分析：az=1.000 -1.5977 1.7459 -1.0200 0.3074  
bz=0.0243 0.0970 0.1456 0.0970 0.0243  
比较Butterworth低通滤波器与Chebyshev低通滤波器的幅频特性曲线，可发现Butterworth滤波器阻带衰减更快，逐渐趋于理想滤波器的幅频特性。

## Matlab程序3： ##

Problem3
    FS=1*10^5;
    t=1/FS;
    fp=[20000 30000];	
    fs=[15000 35000];
    wp=2*pi*fp/FS;
    ws=2*pi*fs/FS;
    omegap=2*FS*tan(wp/2);
    omegas=2*FS*tan(ws/2);
    [n,wn]=buttord(omegap,omegas,1,40,'s');
    [b,a]=butter(n,wn,'s');
    [bz,az]=bilinear(b,a,FS);
    freqz(bz,az,512,FS)
    title('Made by LEI')
    bz
    Az

## 运行结果3： ##

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQyMDc4OTM0_size_16_color_FFFFFF_t_70_pic_center 9]

## 实验分析3： ##

实验分析：观察其幅频特性曲线，其上下边带1dB处的通带临界频率分别为20KHZ和30KHZ，当频率低于15KHZ时，衰减大于40dB，故满足设计要求。

## Matlab程序4\_1： ##

Problem4_1
    clear
    FS=1500;
    t=1/FS;
    fp=80;
    fs=100;
    wp=2*pi*fp/FS;
    ws=2*pi*fs/FS;
    omegap=2*FS*tan(wp/2);
    omegas=2*FS*tan(ws/2);
    [n,wn]=buttord(omegap,omegas,1.4,1.6,'s');%通带衰减rp=1.4，阻带衰减rs=1.6
    [b,a]=butter(n,wn,'s');
    [bz,az]=bilinear(b,a,FS);
    figure(1)
    freqz(bz,az,512,FS)
    title('Made by LEI')
    x=[-4 2 0 -4 -6 -4 -2 -6 -6 -4 -4 -6 -6 -2 6 12 8 0 -16 -38 -60 -84 -90 -66 -32 -4 -2 -4 8 12 12 10 6 6 6 4 0 0 0 0 0 -2 -4 0 0 0 -2 -2 0 0 -2 -2 -2 -2 0];
    figure(2)
    subplot(211)
    plot(x)
    title('Made by LEI')
    y=filter(bz,az,x);
    subplot(212)
    plot(y)
    figure(3)
    subplot(211)
    N=100
    n=0:N-1;
    mf=fft(x,N);
    stem(n,abs(mf));
    title('Made by LEI')
    y=filter(bz,az,x);
    mfa=fft(y,N);
    subplot(212)
    stem(n,abs(mfa));
    Problem4_2
    Clear
    FS=1500;%采样频率
    t=1/FS;
    fp=80;
    fs=100;
    wp=2*pi*fp/FS;%数字
    ws=2*pi*fs/FS;
    omegap=2*FS*tan(wp/2);%频率预畸变
    omegas=2*FS*tan(ws/2);
    [n,wn]=cheb1ord(omegap,omegas,1.4,1.6,'s')
    [b,a]=cheby1(n,1,wn,'s');
    [bz,az]=bilinear(b,a,FS)
    figure(1)
    freqz(bz,az,512,FS)
    title('Made by LEI')
    x=[-4 2 0 -4 -6 -4 -2 -6 -6 -4 -4 -6 -6 -2 6 12 8 0 -16 -38 -60 -84 -90 -66 -32 -4 -2 -4 8 12 12 10 6 6 6 4 0 0 0 0 0 -2 -4 0 0 0 -2 -2 0 0 -2 -2 -2 -2 0];
    figure(2)
    subplot(211)
    plot(x)
    title('Made by LEI')
    y=filter(bz,az,x);
    subplot(212)
    plot(y)
    figure(3)
    subplot(211)
    N=100
    n=0:N-1;
    mf=fft(x,N);
    stem(n,abs(mf));
    title('Made by LEI')
    y=filter(bz,az,x);
    mfa=fft(y,N);
    subplot(212)
    stem(n,abs(mfa));

## 运行结果4： ##

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQyMDc4OTM0_size_16_color_FFFFFF_t_70_pic_center 10]  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQyMDc4OTM0_size_16_color_FFFFFF_t_70_pic_center 11]  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQyMDc4OTM0_size_16_color_FFFFFF_t_70_pic_center 12]  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQyMDc4OTM0_size_16_color_FFFFFF_t_70_pic_center 12]  
**本人能力有限，解释尚不清楚明了，如遇任何问题，大家可留言或私信。后续将程序文件打包上传，供大家学习使用。**

**本文希望对大家有帮助，当然上文若有不妥之处，欢迎指正。**

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