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1、IIR滤波器matlab源程序（1）IIR一阶低通滤波器 clear;fi=1;fs=10;Gc2=0.9;wc=2*pi*fi/fs; omegac=tan(wc/2);alpha=(sqrt(Gc2)/sqrt(1-Gc2)*omegac;a=(1-alpha)/(1+alpha);b=(1-a)/2;w=0:pi/300:pi; Hw2=alpha2./(alpha2+(tan(w/2).2);plot(w/pi,Hw2);grid;hold on;（2）一阶高通滤波器 clear;fi=1;fs=10;Gc2=0.5;wc=2*pi*fi/fs;omegac=tan(wc/2);alp
2、ha=(sqrt(1-Gc2)/(sqrt(Gc2)*omegac;a=(1-alpha)/(1+alpha);b=(1+a)/2;w=0:pi/300:pi;Hw2=(tan(w/2).2)./(alpha2+(tan(w/2).2);plot(w/pi,Hw2);grid;hold on;（3）Notch 嵌波滤波器clear;Gb2=0.5;w0=0.35*pi;deltaw=0.1*pi;b=1/(1+tan(deltaw/2)*(sqrt(1-Gb2)/sqrt(Gb2);B=1 -2*cos(w0) 1.*b;A=1 -2*b*cos(w0) (2*b-1);w=0:pi/500:
3、pi;H=freqz(B,A,w);plot(w/pi,abs(H);grid;（4）Peak 滤波器clear;Ac=3;Gb2=10(-Ac/10);w0=0.35*pi;deltaw=0.1*pi;b=1/(1+tan(deltaw/2)*(sqrt(Gb2)/sqrt(1-Gb2);B=1 0 -1.*(1-b);A=1 -2*b*cos(w0) (2*b-1);w=0:pi/500:pi;H=freqz(B,A,w);plot(w/pi,abs(H);grid;（5）IIR低通滤波（Butterworth）% IIR Lowpass Use Butterworthclear;fs=2
4、0;fpass=4;fstop=5;Ap=0.5;As=10;wp=2*pi*fpass/fs;ws=2*pi*fstop/fs;omegap=tan(wp/2);omegas=tan(ws/2);ep=sqrt(10(Ap/10)-1);es=sqrt(10(As/10)-1);N=ceil(log(es/ep)/log(omegas/omegap);omega0=omegap/ep(1/N);K=floor(N/2);for i=1:K theta(i)=pi*(N-1+2*i)/(2*N);endfor i=1:K G(i)=omega02/(1-2*omega0*cos(theta(i
5、)+omega02);endfor i=1:K a1(i)=2*(omega02-1)/(1-2*omega0*cos(theta(i)+omega02);endfor i=1:K a2(i)=(1+2*omega0*cos(theta(i)+omega02)/(1-2*omega0*cos(theta(i)+omega02);endif K(N/2) G0=omega0/(omega0+1);a0=(omega0-1)/(omega0+1);endw=0:pi/300:pi;Hw2=1./(1+(tan(w/2)/omega0).(2*N);plot(w/pi,Hw2);grid;（6）II
6、R高通滤波（Butterworth）% IIR Hightpass Use Butterworthclear;fs=20;fpass=5;fstop=4;Ap=0.5;As=10;wp=2*pi*fpass/fs;ws=2*pi*fstop/fs;omegap=cot(wp/2);omegas=cot(ws/2);ep=sqrt(10(Ap/10)-1);es=sqrt(10(As/10)-1);N=ceil(log(es/ep)/log(omegas/omegap);omega0=omegap/ep(1/N);K=floor(N/2);for i=1:K theta(i)=pi*(N-1+2
7、*i)/(2*N);endfor i=1:K G(i)=omega02/(1-2*omega0*cos(theta(i)+omega02);endfor i=1:K a1(i)=-2*(omega02-1)/(1-2*omega0*cos(theta(i)+omega02);endfor i=1:K a2(i)=(1+2*omega0*cos(theta(i)+omega02)/(1-2*omega0*cos(theta(i)+omega02);endif K(N/2) G0=omega0/(omega0+1);a0=-(omega0-1)/(omega0+1);endw=(0+eps):pi
8、/300:pi;Hw2=1./(1+(cot(w/2)/omega0).(2*N);plot(w/pi,Hw2);grid;（7）IIR带通滤波（Butterworth）% IIR Bandpass Use Butterworthclear;fs=20;fpa=2;fpb=4;fsa=1.5;fsb=4.5;Ap=0.0877;As=16.9897;wpa=2*pi*fpa/fs;wpb=2*pi*fpb/fs;wsa=2*pi*fsa/fs;wsb=2*pi*fsb/fs;c=sin(wpa+wpb)/(sin(wpa)+sin(wpb);omegap=abs(c-cos(wpb)/sin(
9、wpb);omegasa=(c-cos(wsa)/sin(wsa);omegasb=(c-cos(wsb)/sin(wsb);omegas=min(abs(omegasa),abs(omegasb);ep=sqrt(10(Ap/10)-1);es=sqrt(10(As/10)-1);N=ceil(log(es/ep)/log(omegas/omegap);omega0=omegap/ep(1/N);K=floor(N/2);for i=1:K theta(i)=pi*(N-1+2*i)/(2*N);endfor i=1:K G(i)=omega02/(1-2*omega0*cos(theta(
10、i)+omega02);endfor i=1:K a1(i)=4*c*(omega0*cos(theta(i)-1)/(1-2*omega0*cos(theta(i)+omega02);endfor i=1:K a2(i)=2*(2*c2+1-omega02)/(1-2*omega0*cos(theta(i)+omega02);endfor i=1:K a3(i)=-(4*c*(omega0*cos(theta(i)+1)/(1-2*omega0*cos(theta(i)+omega02);endfor i=1:K a4(i)=(1+2*omega0*cos(theta(i)+omega02)
11、/(1-2*omega0*cos(theta(i)+omega02);endif K(N/2) G0=omega0/(1+omega0);a0(1)=-2*c/(1+omega0);a0(2)=(1-omega0)/(1+omega0);endw=(0+eps):pi/300:pi;Hw2=1./(1+(c-cos(w)./(omega0*sin(w).(2*N);plot(w/pi,Hw2);grid;（8）IIR带阻滤波（Butterworth）% IIR Bandstop Use Butterworthclear;fs=20;fpa=1.5;fpb=4.5;fsa=2;fsb=4;Ap=
12、0.5;As=10;wpa=2*pi*fpa/fs;wpb=2*pi*fpb/fs;wsa=2*pi*fsa/fs;wsb=2*pi*fsb/fs;c=sin(wpa+wpb)/(sin(wpa)+sin(wpb);omegap=abs(sin(wpb)/(c-cos(wpb);omegasa=sin(wsa)/(cos(wsa)-c);omegasb=sin(wsb)/(cos(wsb)-c);omegas=min(abs(omegasa),abs(omegasb);ep=sqrt(10(Ap/10)-1);es=sqrt(10(As/10)-1);N=ceil(log(es/ep)/log
13、(omegas/omegap);omega0=omegap/ep(1/N);K=floor(N/2);theta=zeros(1,K);for i=1:K theta(i)=pi*(N-1+2*i)/(2*N);endG=zeros(1,K);a1=zeros(1,K);a2=zeros(1,K);for i=1:K G(i)=omega02/(1-2*omega0*cos(theta(i)+omega02);endfor i=1:K a1(i)=2*(omega02-1)/(1-2*omega0*cos(theta(i)+omega02);endfor i=1:K a2(i)=(1+2*om
14、ega0*cos(theta(i)+omega02)/(1-2*omega0*cos(theta(i)+omega02);endif K(N/2) G0=omega0/(omega0+1);a0=(omega0-1)/(omega0+1);endw=(0+eps):pi/300:pi;Hw2=1./(1+(sin(w)./(omega0*(c-cos(w).(2*N);plot(w/pi,Hw2);grid;（9）IIR低通滤波（chebyshev 1）% IIR Lowpass Use Chebyshev Type 1clear;fs=20;fpass=4;fstop=5;Ap=0.5;As=10;wp=2*pi*fpass/fs;ws=2*pi*fstop/fs;omegap=tan(wp/2);omegas=tan(ws/2);ep=sqrt(10(Ap/10)-1);es=sqrt(10(As/10)-1);e=es/ep;w=omegas/omegap;N=ceil(log(e+sqrt(e2-1)/log(w+sqrt(w2-1);
