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（1）IIR一階低通濾波器 P576
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=alpha^2./(alpha^2+(tan(w/2)).^2);
plot(w/pi,Hw2);
grid;
hold on;
?（2）一階高通濾波器 P581
clear;
fi=1;fs=10;Gc2=0.5;
wc=2*pi*fi/fs;
omegac=tan(wc/2);
alpha=(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)./(alpha^2+(tan(w/2)).^2);
plot(w/pi,Hw2);
grid;
hold on;
（3）Notch 嵌波濾波器
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:pi;
H=freqz(B,A,w);
plot(w/pi,abs(H));
grid;
（4）Peak 濾波器
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;
% IIR Lowpass Use Butterworth
% copyright by Etual
clear;
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);
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);
end
for i=1:K
??? G(i)=omega0^2/(1-2*omega0*cos(theta(i))+omega0^2);
end
for i=1:K
??? a1(i)=2*(omega0^2-1)/(1-2*omega0*cos(theta(i))+omega0^2);
end
for i=1:K
??? a2(i)=(1+2*omega0*cos(theta(i))+omega0^2)/(1-2*omega0*cos(theta(i))+omega0^2);
end
if K<(N/2)
??? G0=omega0/(omega0+1);a0=(omega0-1)/(omega0+1);
end
w=0:pi/300:pi;
Hw2=1./(1+(tan(w/2)/omega0).^(2*N));
plot(w/pi,Hw2);
grid;
（6）IIR高通濾波（Butterworth）
% IIR Hightpass Use Butterworth
% copyright by Etual
clear;
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*i)/(2*N);
end
for i=1:K
??? G(i)=omega0^2/(1-2*omega0*cos(theta(i))+omega0^2);
end
for i=1:K
??? a1(i)=-2*(omega0^2-1)/(1-2*omega0*cos(theta(i))+omega0^2);
end
for i=1:K
??? a2(i)=(1+2*omega0*cos(theta(i))+omega0^2)/(1-2*omega0*cos(theta(i))+omega0^2);
end
if K<(N/2)
??? G0=omega0/(omega0+1);a0=-(omega0-1)/(omega0+1);
end
w=(0+eps):pi/300:pi;
Hw2=1./(1+(cot(w/2)/omega0).^(2*N));
plot(w/pi,Hw2);
grid;
（7）IIR帶通濾波（Butterworth）
% IIR Bandpass Use Butterworth
% copyright by Etual
clear;
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(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);
end
for i=1:K
??? G(i)=omega0^2/(1-2*omega0*cos(theta(i))+omega0^2);
end
for i=1:K
??? a1(i)=4*c*(omega0*cos(theta(i))-1)/(1-2*omega0*cos(theta(i))+omega0^2);
end
for i=1:K
??? a2(i)=2*(2*c^2+1-omega0^2)/(1-2*omega0*cos(theta(i))+omega0^2);
end
for i=1:K
??? a3(i)=-(4*c*(omega0*cos(theta(i))+1))/(1-2*omega0*cos(theta(i))+omega0^2);
end
for i=1:K
??? a4(i)=(1+2*omega0*cos(theta(i))+omega0^2)/(1-2*omega0*cos(theta(i))+omega0^2);
end
if K<(N/2)
??? G0=omega0/(1+omega0);a0(1)=-2*c/(1+omega0);a0(2)=(1-omega0)/(1+omega0);
end
w=(0+eps):pi/300:pi;
Hw2=1./(1+((c-cos(w))./(omega0*sin(w))).^(2*N));
plot(w/pi,Hw2);
grid;
（8）IIR帶阻濾波（Butterworth）
% IIR Bandstop Use Butterworth
% copyright by Etual
clear;
fs=20;fpa=1.5;fpb=4.5;fsa=2;fsb=4;
Ap=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(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);
end
G=zeros(1,K);a1=zeros(1,K);a2=zeros(1,K);
for i=1:K
??? G(i)=omega0^2/(1-2*omega0*cos(theta(i))+omega0^2);
end
for i=1:K
??? a1(i)=2*(omega0^2-1)/(1-2*omega0*cos(theta(i))+omega0^2);
end
for i=1:K
??? a2(i)=(1+2*omega0*cos(theta(i))+omega0^2)/(1-2*omega0*cos(theta(i))+omega0^2);
end
if K<(N/2)
??? G0=omega0/(omega0+1);a0=(omega0-1)/(omega0+1);
end
w=(0+eps):pi/300:pi;
Hw2=1./(1+(sin(w)./(omega0*(c-cos(w)))).^(2*N));
plot(w/pi,Hw2);
grid;
（9）IIR低通濾波（chebyshev 1）
% IIR Lowpass Use Chebyshev Type 1
% copyright by Etual
clear;
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(e^2-1))/log(w+sqrt(w^2-1)));
a=log(1/ep+sqrt(1/ep^2+1))/N;
omega0=omegap*sinh(a);
K=floor(N/2);
theta=zeros(1,K);omega=zeros(1,K);
for i=1:K
??? theta(i)=pi*(N-1+2*i)/(2*N);
end
for i=1:K
??? omega(i)=omegap*sin(theta(i));
end
G=zeros(1,K);a1=zeros(1,K);a2=zeros(1,K);
for i=1:K
??? G(i)=(omega0^2+omega(i)^2)/(1-2*omega0*cos(theta(i))+omega0^2+omega(i)^2);
end
for i=1:K
??? a1(i)=2*(omega0^2+omega(i)^2-1)/(1-2*omega0*cos(theta(i))+omega0^2+omega(i)^2);
end
for i=1:K
??? a2(i)=(1+2*omega0*cos(theta(i))+omega0^2+omega(i)^2)/(1-2*omega0*cos(theta(i))+omega0^2+omega(i)^2);
end
if K<(N/2)
??? G0=omega0/(omega0+1);a0=(omega0-1)/(omega0+1);??
else
??? H0=sqrt(1/(1+ep^2));
end
f=0:1/300:10;
Hf2=1./(1+ep^2*(cheby(N,tan(pi*f/fs)/omegap)).^2);
plot(f,abs(Hf2));
grid;
?（9）IIR低通濾波（chebyshev 1）
% IIR Lowpass Use Chebyshev Type 2
% copyright by Etual
clear;
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(e^2-1))/log(w+sqrt(w^2-1)));
a=log(es+sqrt(es^2+1))/N;
omega0=omegas/sinh(a);
K=floor(N/2);
for i=1:K
??? theta(i)=pi*(N-1+2*i)/(2*N);
end
for i=1:K
??? omega(i)=omegas/sin(theta(i));
end
for i=1:K
??? G(i)=(1+omega(i)^-2)/(1-2*omega0^-1*cos(theta(i))+omega0^-2+omega(i)^-2);
end
for i=1:K
??? a1(i)=2*(1-omega0^-2+omega(i)^-2)/(1-2*omega0^-1*cos(theta(i))+omega0^-2+omega(i)^-2);
end
for i=1:K
??? a2(i)=(1+2*omega0^-1*cos(theta(i))+omega0^-2+omega(i)^-2)/(1-2*omega0^-1*cos(theta(i))+omega0^-2+omega(i)^-2);
end
for i=1:K
??? b1(i)=2*(1-omega(i))/(1+omega(i));
end
if K<(N/2)
??? G0=omega0/(omega0+1);a0=(omega0-1)/(omega0+1);??
else
??? H0=sqrt(1/(1+ep^2));
end
f=(0+eps):1/100:10;
Hf2=(cheby(N,omegas./tan(pi*f/fs))).^2./((cheby(N,omegas./tan(pi*f/fs))).^2+es^2);
plot(f,abs(Hf2));
grid;
（10）chebyshev 中用到的函數 cheby.m
function CN=cheby(N,x)
if x<=1
??? CN=cos(N*acos(x));
else
??? CN=cosh(N*log(x+sqrt(x.^2-1)));
end
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