% 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;