1、 探究心电信号的初步分析。心电信号（频率一般在0.05Hz〜100Hz范围）是一种 基本的人体生理信号，体表检测人体心电信号中常带有工频干扰（50HZ)、基线漂移（频率低于0.5Hz)和肌电干扰等各种噪声。
2、 为了得到不失真的原始心电信号，需要滤波预处理。设计数字低通滤波器、高通滤波器、带阻滤波器，用MATLAB软件对含噪心电信号分别进行高通、带阻和低通滤波等处理，将心电信号中的低频基线漂移、50Hz工频高频和高频杂波进行滤除。
3、 通过观察对含噪心电图信号的滤波作用，获得数字滤波的感性知识。
题目
给定一组干净心电信号数据，数据文件存于Ecg.txt。采样频率fs=500Hzf_s = 500Hzfs=500Hz。
Ecg.txt 内容如下：（实际上就是1800采样点的一维数组）
10111314151518212325252525262728292928262524252525231918171717161513121196300-1-2-3-5-6-9-13-15-16-18-19-20-20-21-21-20-19-19-21-22-23-22-21-20-20-21-22-24-25-25-24-23-22-20-20-21-21-20-18-17-17-18-18-16-16-16-15-15-16-17-17-16-15-14-13-14-13-11-9-7-6-5-7-8-7-6-5-4-3-2-200000000101210000110000011113556653445431000133212333441000001002345457910101085589910966710111313131413121214141212121213161717181817192840526679909910611011010491673711-3-13-18-21-22-22-21-21-20-18-16-13-10-6-4-6-5-2-10022222111000000001210000011101112346644556810101011131315171824262728282830313233312828313334343432302929282624211918181716137420-1-3-6-10-11-12-14-16-17-18-21-21-20-20-21-21-21-23-24-23-22-21-22-22-23-24-24-22-22-23-23-23-23-22-20-17-15-15-16-16-15-15-14-12-11-12-11-9-8-7-7-7-8-8-8-8-8-7-7-6-6-5-5-5-5-3-3-3-2-1000-1-2-10012212333455666663222343214566767788898678999965544420000000-3-4-3-3-2-3-4-6-3-2-2-3-3-4-30123343335776579991098913121111131210101213121212141719212127395264768796106114118117108896336140-7-10-12-14-14-14-12-11-10-9-10-10-8-7-7-5-4-2-1-100000023334224545433468874320001000112223569111415161824242425283032353533323234363737373737373635333129272422141184200-3-5-7-10-13-16-18-21-23-24-25-27-27-26-28-29-28-26-26-25-25-26-27-28-28-28-28-28-28-28-27-27-25-23-21-22-22-20-19-19-19-18-16-16-15-14-13-12-13-12-12-11-11-11-9-8-8-8-6-4-3-3-1-1-2-1000000-1-10120-100000100011100001121013443323442221000000-1000132111223333444442100000-1-100-1-2-2-5-6-6-5-4-4-5-7-7-6-5-4-2-1-3-20000-1-2-2-100012223333112455654468101213141517182435476072849610511311511310489643511-4-12-16-18-19-20-21-21-20-18-17-15-15-14-15-15-12-9-8-6-5-6-6-5-3-1-10-2-2-2-10032101233223344545556676678889991010131415151619212324272828303233343635333232333332313029292826231816141210500-1-4-7-11-15-18-20-22-23-24-26-29-31-31-32-34-34-35-37-40-41-40-39-38-37-37-38-39-38-36-36-37-38-38-36-36-36-36-36-37-40-39-37-36-35-34-33-33-32-33-31-29-29-30-30-29-27-25-22-21-21-23-23-21-19-20-19-19-20-20-19-18-17-16-15-15-14-12-11-9-8-8-9-8-6-4-4-4-5-6-6-6-6-6-6-6-8-6-4-4-2-1-2-3-3-3-4-4-4-3-4-5-5-4-4-5-7-8-7-6-5-4-4-4-6-6-4-3-3-3-3-4-3-1-1-1-1-1-2-1000210000-1-1-2-4-4-4-3-3-3-2-2-2-4-3-3-3-4-5-3-3-3-5-6-6-7-7-6-6-6-6-6-7-7-7-6-6-7-7-8-6-5-6-6-6-4-5-6-3-1-1000-100233223446891114171716202841556780911001051071071008455230-15-22-26-28-28-27-27-26-23-20-17-14-12-11-11-9-7-4-1000122220-1000000-2-200000000011000233444555665691112141618182322232324262830323537383838383736343029282726262523222114106420-1-4-8-12-14-16-17-18-19-22-25-27-27-27-28-30-31-32-32-33-32-32-32-33-34-32-32-32-32-30-29-30-29-28-26-26-26-26-27-27-27-26-25-24-24-24-24-21-20-19-19-19-21-20-19-17-17-19-20-22-22-18-15-13-13-13-14-14-13-11-10-9-8-10-10-10-9-10-10-9-9-9-9-9-9-8-8-8-7-6-5-6-5-6-7-6-5-5-5-6-6-7-7-6-6-6-6-6-7-6-6-6-5-4-6-8-7-6-5-5-5-5-6-4-4-3-3-3-2-4-2-2-3-5-6-7-8-8-5-4-4-3-3-4-3-2-2-100-2-2-2-2000-3-4-3-3-3-3-2-4-5-5-4-3-3-4-5-5-5-5-5-5-6-6-4-3-4-4-5-5-6-4-4-3-2-3-3-4-4-4-3-2-1-1-2-2002343333212211110025910111211791829404957647076818177633812-6-17-22-25-25-27-27-23-19-16-14-12-11-11-10-8-6-4-2-2-3-20000-2-4-3-1000-1-2-101331000012000222221234332234677556777991011131616151314151817171716161614131312117520-2-5-8-12-15-18-22-23-26-28-30-33-37-41-42-44-46-46-46-46-47-47-47-47-47-49-51-51-50-48-46-46-45-45-47-46-44-44-43-42-41-41-40-39-37-36-35-35-36-35-34-32-31-30-31-32-31-29-27-26-26-26-25-23-23-21-20-19-19-19-18-17-16-15-14-15-16-14-12-11-10-9-7-8-7-7-6-6-5-5-6-5-4-200-2-5-6-5-4-3-10-1-10122102101210000000000002210001100-10001000000000000110000001100010000000122000001100233332235666555568755678111516171819191718253544525964666767666148274-13-24-29-31-32-32-31-31-31-30-29-27-24-23-22-21-19-19-19-19-17-16-15-14-13-12-10-8-9-10-9-8-7-7-7-7-8-7-6-6-5-5-7-8-8-7-7-8-9-11-13-12-10-8-7-6-6-8-7-7-7-6-4-3-3-1-10000024678881113141719171719212222242422222324232218171717151211987410-2-4-7-9-11-12-14-16-16-16-16-16-17-20-21-20-19-20-20-21-23-24-23-21-21-22-21-21-23-24-23-22-20-19-19-19-17-17-17-15-15-15-16-15-13-12-11-10-9-9-8-7-6-6-6-6-6-5-4-4-2-1-3-3-3-2-3-3-2-1-2-101444345710111088889111088898899910111213111011121212121199101112121211111110111211111212111113139881010975444443223444200002221122355567911121311101111121314141414151514131211121111111098912131517181921242424283747586776838992928982694826100-3-4-4-4-5-5-5-3-3-200000333434665455334689877668111091112121212111091010121110101010101112111112141618242628292929303133353736343435353637383635353433313027262523131097510-3-6-8-9-10-12-14-16-18-19-19-19-21-21-23-25-24-24-25-24-24-25-26-25-25-25-25-23-23-23-24-23-22-23-23-23-24-22-19-20-21-21-22-24-24-22-19-19-19-19-20-20-19-17-16-14-14-14-13-11-10-9-6-6-7-6-5-3-3-3-4-6-6-4-4-4-4-5-6-5-4-3-3-4-3-5-5-3-1-1-2-1-2-2-10000-2-2-10001001234654555442234421000000-1-4-3-200-1-2-3-3-3-4-4-4-4-5-5-5-4-2000000000001378999101110108655789111199101112131416192221192334465665758390959793846742160-10-16-19-20-19-19-16-13-12-11-9-8-7-5-4-2000-100100114557766567891089910111110910101010108810121312121212121313131314131517161719212224272829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1️⃣产生模拟高斯白噪声信号，与干净心电混合，设计一个IIR低通滤波器和一个FIR低通滤波器分别滤除心电信号中的白噪声干扰，调整白噪声信噪比大小，对滤波前后的心电信号的频谱进行分析比较。
其中数字低通滤波器指标要求：
通带截止频率Wp=0.lπ\piπ阻带截止频率Ws=0.16π\piπ阻带衰减不小于15 dB通带衰减不大于1 dB
总体要求：
编写一个IIR低通滤波器和一个FIR低通滤波器仿真程序，在屏幕上打印出数
字滤波器的频率区间[0，π\piπ]上的幅频响应特性由线(∣H(ejω)∣|H(e^{j\omega})|∣H(ejω)∣)计算其对含噪心电信号的低通滤波响应序列，并在屏幕上打印出干净心电信号波形，含工频干扰的心电信号波形以及IIR低通滤波和FIR低通后的信号波形，并进行比较同时对滤波前后的心电信号的频谱进行分析比较，并在屏幕上打印出滤波前后的心电信号的频谱，观察其变化。
题目要求设计两个低通滤波器，一个使用FIR，一个使用IIR
FIR低通滤波器设计：
wp2=0.1*pi;ws2=0.16*pi;wdelta=ws2-wp2;N=ceil(8*pi/wdelta);Wn=(0.1+0.16)*pi/2;b2=fir1(N-1,Wn/pi);[H2,W2]=freqz(b2,1,512);figure;subplot(2,1,1);plot(W2/pi,20*log10(abs(H2)),'r','linewidth',2);title({ '$$ FIR-LP-Frequency-Response-Curve $$' },'Interpreter','latex');xlabel({ '$$ Frequency(\Omega/\pi) $$' },'Interpreter','latex');ylabel({ '$$ Amplitude(dB) $$' },'Interpreter','latex');
FIR滤波效果对比图
IIR低通滤波器
% 通带截止频率 0.1 pi 阻带截止频率 0.16 pi% 阻带衰减15db 通带衰减1dbclose all;Rp=0.99;Rs=16;Fs=1;Ts=1/Fs;wpz=0.1/Fs;wsz=0.16/Fs;wp=2*Fs*tan(wpz*pi/2);ws=2*Fs*tan(wsz*pi/2);[N,Wn]=buttord(wp,ws,Rp,Rs,'s');[Z,P,K]=buttap(N);[Bap,Aap]=zp2tf(Z,P,K);[b,a]=lp2lp(Bap,Aap,Wn);[bz,az]=bilinear(b,a,Fs);[H,W]=freqz(bz,az);%plot(W*Fs/pi,20*log10(abs(H)));plot(W*Fs/pi,20*log10(abs(H)),'r','linewidth',2);grid on;title({ '$$ IIR-LP-Frequency-Response-Curve $$' },'Interpreter','latex');xlabel({ '$$ Frequency(\Omega/\pi) $$' },'Interpreter','latex');ylabel({ '$$ Amplitude(dB) $$' },'Interpreter','latex');
IIR滤波效果对比图
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