Notes

CZYBYSZEW!!!
eps = [0.5,1,3];
for i = 1:1:3
eps(i) = sqrt((10^(eps(i)/10))-1);
end

for j = 1:1:3

for n = 2:1:8
if(mod(n,2) == 0) % uwzglednienie rzedow przarzystych
H=tf(1,1);
for k = 1:1:n/2
alfak = ((2*k - 1) * pi)/(2*n): % wspolczynnik pomocniczy
u = (1/n).* asinh(1/eps(j));
Bk = 1/(cosh(u)^2 - cos(alfak)^2);
Ak = 2 * Bk * sinh(u) * cos(alfak);
% wyznaczamy pulsacje omega c
omega_c = 1/(cosh((1/n) * acosh(sqrt((2 * eps(j)^2 + 1)/eps(j)^2))));
ak = Ak/omega_c;
bk = Bk/(omega_c^2);
H = H * tf(1,[bk ak 1])
end
end

if(mod(n,2) == 1) % uwzglednienie rzedow nieparzystych
u = asinh(1/eps(j))/n;
B1 = 0;
Al = 1/sinh(u);
omega_c=1/(cosh((1/n)*acosh(sqrt((2*(eps(j)^2)+1)/eps(j)^2))));
a1 = A1/omega_c;
b1 = B1/(omega_c.^2);
H = tf(1,[b1 a1 1])
for k = 2:1:((n+1)/2)

betak = ((k-1) * pi)/n; % - wspolczynnik pomocniczy
Bk = 1/((cosh(u)^2) - (cos(betak)^2));
Ak = 2 * Bk * sinh(u) * cos(betak);
ak = Ak/omega_c;
bk = Bk/(omega_c^2);
H = H * tf(1,[bk ak 1])
end
end
figure(j);
hold on
bode(H);
hold off

figure(j+3);
hold on
step(H);
hold off

figure(j+6):
hold on
pzmap(H);
hold off'
end
end

BUTTERWORTH!!!

for n = 2 : 1 : 8
% Rzad parzysty
if(mod(n, 2) == 0)
for k = 1 : 1 : n / 2
a(k) = 2 * cos((2 * k - 1) / (2 * n) * pi);
b(k) = 1;
R(k) = tf(1, [b(k), a(k), 1]) ;
if (k == 1)
H(n) = R(k);
else
H(n) = H(n) * R(k);
end
end
% Brad nieparzysty
elseif(mod(n, 2) == 1)
for k = 2 : 1 : (n + 1) / 2
a(1) = 1;
b(1) = 0;
a(k) = 2 * cos(((k - 1) / n) * pi);
b(k) = 1;
PP = tf(1, [b(1), a(1), 1]);
R(k) = tf(1, [b(k), a(k), 1]);
if (k == 2)
H(n) = R(k) * PP;
else
H(n) = H(n) * R(k);
end
end
end
end

BESSEL!!!

for n = 2 : 1 : 8

for i= n : -1: 1
if i==n
B(i)=tf(2*i-1,[1,0]);
else
B(i)=tf(2*i-1,[1,0])+(1/B(i+1));
end
end
num=B.num{1};
den=B.den{1};
Q=tf(num,1)+tf(den,1);
k=Q.num{1}(size*(Q.num{1},2));

Bessel(n)=k/Q;
end

for n = 2 : 1 : 8
figure(1)
grid on
hold on
bode(Bessel(n))
end
legend('n=2','n=3','n=4','n=5','n=6','n=7','n=8')
for n = 2 : 1 : 8
figure(2)
grid on
hold on
step(Bessel(n))
end
legend('n=2','n=3','n=4','n=5','n=6','n=7','n=8')