% 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;