% 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;