Notes

%% FILTR BESSELA
%% Dane
n=2;
m=8;

%% Obliczenia
%% Krok 1
% s=tf('s');
% t2=1/s+1/(3/s)
% t3=1/s+1/((3/s)+1/(5/s))
% t4=1/s+1/((3/s)+1/((5/s)+1/(7/s)))
% t5=1/s+1/((3/s)+1/((5/s)+1/((7/s)+1/(9/s))))
% t6=1/s+1/((3/s)+1/((5/s)+1/((7/s)+1/((9/s)+1/(11/s)))))
% t7=1/s+1/((3/s)+1/((5/s)+1/((7/s)+1/((9/s)+1/((11/s)+1/(13/s))))))
% t8=1/s+1/((3/s)+1/((5/s)+1/((7/s)+1/((9/s)+1/((11/s)+1/((13/s)+1/(15/s)))))))

%% Krok 2
t2=3/(s*s+3*s+3);
t3=15/(15+15*s+6*s*s+s^3);
t4=105/(s^4+10*s^3+45*s*s+105*s+105)
t5=945/(945+s^5+15*s^4+105*s^3+420*s*s+945*s)
t6=10395/(10395*s+10395+4725*s*s+1260*s^3+210*s^4+21*s^5+s^6)
t7=135135/(s^7+s^6*28+378*s^5+3150*s^4+17325*s^3+62370*s*s+135135*s+135135)
t8=2027000/(s^8+36*s^7+630*s^6+6930*s^5+51975*s^4+270270*s^3+945945*s^2+2027000*s+2027000)

%% Wykresy
figure(1)
bode(t2)
hold on
bode(t3)
hold on
bode(t4)
hold on
bode(t5)
hold on
bode(t6)
hold on
bode(t7)
hold on
bode(t8)
hold on

figure(2)
step(t2)
hold on
step(t3)
hold on
step(t4)
hold on
step(t5)
hold on
step(t6)
hold on
step(t7)
hold on
step(t8)
hold on

figure(3)
impulse(t2)
hold on
impulse(t3)
hold on
impulse(t4)
hold on
impulse(t5)
hold on
impulse(t6)
hold on
impulse(t7)
hold on
impulse(t8)
hold on

%% FILTR BUTTERWORTHA
for n = 2 : 1 : 7
%% Dla rzędów nieparzystych
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

%% Dla rzędów nieparzystych
if(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

for i = 2 : 1 : 7
figure(1);
bode(H(i));
hold on
end
legend('Rząd 2', 'Rząd 3', 'Rząd 4', 'Rząd 5', 'Rząd 6', 'Rząd 7');

for i = 2 : 1 : 7
figure(2)
pzplot(H);
hold on
end
legend('Rząd 2', 'Rząd 3', 'Rząd 4', 'Rząd 5', 'Rząd 6', 'Rząd 7');

%% FILTR CZYBYSZEWA
%%Rp=0.5
rzad=1;
Rp1=0.5;
for n=2:8

[b,a]=cheby1(n,Rp1,rzad,'s');
H=tf(b,a)

figure(1)
bode(H)
legend('n=2','n=3','n=4','n=5','n=6','n=7','n=8')
hold on
figure(2)
step(H)
legend('n=2','n=3','n=4','n=5','n=6','n=7','n=8')
hold on
figure(3)
pzmap(H)
legend('n=2','n=3','n=4','n=5','n=6','n=7','n=8')
hold on
end
%% Rp= 1
rzad=1;
Rp2=1;
for n=2:8

[b,a]=cheby1(n,Rp2,rzad,'s');
H=tf(b,a)

figure(4)
bode(H)
legend('n=2','n=3','n=4','n=5','n=6','n=7','n=8')
hold on
figure(5)
step(H)
legend('n=2','n=3','n=4','n=5','n=6','n=7','n=8')
hold on
figure(6)
pzmap(H)
legend('n=2','n=3','n=4','n=5','n=6','n=7','n=8')
hold on
end

%% Rp=3
rzad=1;
Rp3=3;
for n=2:8

[b,a]=cheby1(n,Rp3,rzad,'s');
H=tf(b,a)

figure(7)
bode(H)
legend('n=2','n=3','n=4','n=5','n=6','n=7','n=8')
hold on
figure(8)
step(H)
legend('n=2','n=3','n=4','n=5','n=6','n=7','n=8')
hold on
figure(9)
pzmap(H)
legend('n=2','n=3','n=4','n=5','n=6','n=7','n=8')
hold on
end

%%LP2LP
syms s
s=tf('s');
w2=2
filtr = 1/(s^3 + 2* s^2 + 2*s + 1);
figure(1)
hold on
bode(filtr)
s = s/w2;
filtr = 1/(s^3 + 2* s^2 + 2*s + 1);
bode(filtr);

%%LP2HP
syms s
s=tf('s');
w2=2
filtr = 1/(s^3 + 2* s^2 + 2*s + 1);
figure(1)
hold on
bode(filtr)

s = 1/s;
filtr = 1/(s^3 + 2* s^2 + 2*s + 1);
bode(filtr);

%%LP2BP
syms s
s=tf('s');
w2=2
filtr = 1/(s^3 + 2* s^2 + 2*s + 1);
figure(1)
hold on
bode(filtr)

s = 1/s + s/1;
filtr = 1/(s^3 + 2* s^2 + 2*s + 1);
figure(2)
bode(filtr);

%%LP2BS
syms s
s=tf('s');
w1=1
w2=2
w0=sqrt(w2*w1);
beta=w0/(w2-w1);

filtr = 1/(s^3 + 2* s^2 + 2*s + 1);
s = 1/(beta*w0/s+s/w0);
filtr = 1/(s^3 + 2* s^2 + 2*s + 1);
figure(1)
bode(filtr);