I cannot for the life of me figure out why my Matlab code keeps breaking. For some reason when the stopband frequency Ws exceeds 1.2, the code breaks due to the extra pole.
%Using Matlab for lowpass Elliptic filter design
close all; clear all;
Wp=1; %passband frequency
Ws=1.2; %stopband frequency
Rp=1; %maximum attenuation in passband (in dB), alpha_max
Rs=30; %minimum attenuation in stopband (in dB), alpha_min
[n,Wn]=ellipord(Wp,Ws,Rp,Rs,'s') %n is filter order, Wn is cutoff
% frequency, 's' denotes an analog filter
% denormalize to Ws for InvCheby
[b,a]=ellip(n,Rp,Rs,1,'s') %b is coefficients of numerator, a is coefficients of
% denominator where 1st entry is highorder
% coefficient. This is the transfer function of a
% normalized inverse Cheby filter.
% Pass the stopband attenuation Rs for InvCheby
sys=tf(b,a) %calculates the transfer function of the normalized butterworth filter
bode(sys) %plots the bode plot of the transfer function
[z,p,k]=ellip(n,Rp,Rs,Wp,'s') %returns zeros (z) and poles (p) and gain (k) of filter
figure; hold on;
for i=1:n
plot(real(p(i)),imag(p(i)),'x')
plot(real(z(i)),imag(z(i)),'o')
end
%axis([-1 1 -1 1])
%calculate stages from poles
poles=p(1);
zeros=z(1);
for i=3:2:n%n-mod(n,2)
poles=[poles,p(i)];
zeros=[zeros,z(i)];
end
%poles/zeros matching
d11=abs(zeros(1)-poles(1))+abs(zeros(2)-poles(2))
d12=abs(zeros(1)-poles(2))+abs(zeros(2)-poles(1))
% for j=1:n/2
% d(i+j-1)=abs(poles(i)-zeros(i))+abs(imag(poles(i)))
w0=sqrt(real(poles).^2+imag(poles).^2)
Q=-w0./(2*real(poles))
for i=1:(n-mod(n,2))/2
den(i,:)=[1 w0(i)/Q(i) w0(i)^2];
num(i,:)=[1 0 abs(zeros(i))^2];
end
if mod(n,2) %odd order polynomial
den(i+1,:)=[0 1 w0(i+1)];
num(i+1,:)=[0 0 1];
end
%order the stages
[Qs,ind]=sort(Q);
w0s=w0(ind);
nums=num(ind,:);
dens=den(ind,:);
for i=1:(n+mod(n,2))/2
t(i)=tf(nums(i,:),dens(i,:));
end
%K=(dens(1,3)*dens(2,3))/(nums(1,3)*nums(2,3))
K=k
M2=1/K
[m,w]=bode(t(1));
M1=max(m)
k1=K*M2/M1
k2=M1/M2
