Ex 1
clear variables;

Fp = [4000 6000]; %banda de trecere
Fs = [3000 8000]; %banda de oprire
Rp = 1;
Rs = 40;
Fes = 20*10^3;

Wp = 2*pi*Fp;
Ws = 2*pi*Fs;
%domeniul analogic
[n, Wn] = buttord(Wp,Ws,Rp,Rs,'s');
[b, a] = butter(n,Wn,'s');
%rasp la frecventa
[Ha, wa] = freqs(b,a,2^10);
figure,
subplot(2,1,1); plot(wa/pi, abs(Ha));
subplot(2,1,2); plot(wa/pi, angle(Ha));
figure, impulse(b,a); %raps la impuls
figure, pzmap(b,a); %diagrma poli zerouri
if roots(a) <0 %stabilitate
    disp('FTB analogic stabil');
else
    disp('FTB analogic instabil');
end
%domeniul digital
[num, den] = impinvar(b,a,Fes); %rasp la impuls
[Hz, wz] = freqz(num, den, 2^10);
figure,
subplot(2,1,1); plot(wa/pi, abs(Hz));
subplot(2,1,2); plot(wa/pi, angle(Hz));

figure, impz(num, den);
figure, zplane(num, den);

if abs(roots(den)) <1 %stabilitate
    disp('FTB digital stabil');
else
    disp('digital instabil');
end


Ex 2
clear variables;

Fp = [4000 6000]; %banda de trecere
Fs = [3000 8000]; %banda de oprire
Rp = 1;
Rs = 40;
Fes = 20*10^3;

Wp = 2*pi*Fp;
Ws = 2*pi*Fs;
%domeniul analogic
[n, Wn] = cheb1ord(Wp,Ws,Rp,Rs,'s');
[b, a] = cheby1(n,Rp,Wn,'s');
%rasp la frecventa
[Ha, wa] = freqs(b,a,2^10);
figure,
subplot(2,1,1); plot(wa/pi, abs(Ha));
subplot(2,1,2); plot(wa/pi, angle(Ha));
figure, impulse(b,a); %raps la impuls
figure, pzmap(b,a); %diagrma poli zerouri
if roots(a) <0 %stabilitate
    disp('FTB analogic stabil');
else
    disp('FTB analogic instabil');
end
%domeniul digital
[num, den] = impinvar(b,a,Fes); %rasp la impuls
[Hz, wz] = freqz(num, den, 2^10);
figure,
subplot(2,1,1); plot(wa/pi, abs(Hz));
subplot(2,1,2); plot(wa/pi, angle(Hz));

figure, impz(num, den);
figure, zplane(num, den);

if abs(roots(den)) <1 %stabilitate
    disp('FTB digital stabil');
else
    disp('digital instabil');
end

Ex3
clear variables;

Fp = [4000 6000];
Fs = [3000 8000];
Rp = 1;
Rs = 40;
Fes = 20*10^3;
Wp = 2*pi*Rp;
Ws = 2*pi*Rs;

%domeniul analogic
[n, Wn] = buttord(Wp,Ws,Rp,Rs,'s');
[b, a] = butter(n, Wn, 's');
[Ha, wa] = freqs(b,a,2^10);
figure,
subplot(2,1,1); plot(wa/pi, abs(Ha));
subplot(2,1,2); plot(wa/pi, angle(Ha));
figure, impulse(b,a);
figure, pzmap(b,a);
if roots(a) < 0
    disp('Stabil');
else
    displ('Instabil');
end

%domeniul digital
[num, den] = impinvar(b,a,Fes);
[Hz, wz] = freqz(num, den, 2^10);
figure,
subplot(2,1,1); plot(wa/pi, abs(Ha));
subplot(2,1,2); plot(wa/pi, angle(Ha));
figure, impz(num, den);
figure, zplane(num, den);

if abs(roots(den)) < 1
    disp('Stabil');
else
    displ('Instabil');
end


Ex4
clear variables;

Fp = [4000 6000];
Fs = [3000 8000];
Rp = 1;
Rs = 40;
Fes = 20*10^3;
Wp = 2*pi*Rp;
Ws = 2*pi*Rs;

%domeniul analogic
[n, Wn] = ellipord(Wp,Ws,Rp,Rs,'s');
[b, a] = ellip(n,Rp,Rs, Wp, 's');
[Ha, wa] = freqs(b,a,2^10);
figure,
subplot(2,1,1); plot(wa/pi, abs(Ha));
subplot(2,1,2); plot(wa/pi, angle(Ha));
figure, impulse(b,a);
figure, pzmap(b,a);
if roots(a) < 0
    disp('Stabil');
else
    displ('Instabil');
end

%domeniul digital
[num, den] = impinvar(b,a,Fes);
[Hz, wz] = freqz(num, den, 2^10);
figure,
subplot(2,1,1); plot(wa/pi, abs(Ha));
subplot(2,1,2); plot(wa/pi, angle(Ha));
figure, impz(num, den);
figure, zplane(num, den);

if abs(roots(den)) < 1
    disp('Stabil');
else
    disp('Instabil');
end


Ex5
clear variables;

b = 2*[1 0 2];
a = conv([1 2],[2 3 2]);

figure, freqs(b,a,2^10);

if roots(a) < 0
    disp('FTJ analogic stabil');
else
    disp('FTJ analogic instabil');
end

Fes = 1/0.8;
[bz, az] = bilinear(b, a, Fes);
figure, freqz(bz,az)
%FTj
figure, zplane(bz, az);
%FTJ digital stabil


Ex6
clear variables;
N=5; fc=0.2;
[b,a]=butter(N,2*pi*fc/pi);
figure, freqz(b,a)


Ex7
dp = 0.1;
ds = 0.01;
fp = 0.22;
fs = 0.25;
Rp = 20*log10((1+dp)/(1-dp));
Rs = -20*log10(ds);
Wp = 2*pi*Rp;
Ws = 2*pi*Rs;

[N,w]=buttord(Wp,Ws,Rp,Rs,'s');

[b,a]=butter(N,w,'s');
figure, freqz(b,a);

figure, grpdelay(b,a)
%%filtru digital filt, filtru analogic tf
H=filt(b,a);

%stabilitate
if isstable(b,a)==1
    disp('Filtru digital este stabil')
else
    disp('Filtru digital este instabil')
end

Ex8
dp = 0.1;
ds = 0.01;
fp = 0.22;
fs = 0.25;
Rp = 20*log10((1+dp)/(1-dp));
Rs = -20*log10(ds);
Wp = 2*pi*Rp;
Ws = 2*pi*Rs;

[n,w]=cheb1ord(Wp,Ws,Rp,Rs,'s');

[b,a]=cheby1(n,Rp,Wp,'s');
figure, freqz(b,a);

figure, grpdelay(b,a)
%%filtru digital filt, filtru analogic tf
H=filt(b,a)

%stabilitate
if isstable(b,a)==1
    disp('Filtru digital este stabil')
else
    disp('Filtru digital este instabil')
end

Ex9
clear variables;
n=0:199;
fr=0.22;
N=10;
SBw=0.1; TBw=0.02;
fs=[fr-SBw/2 fr+SBw/2];
fp=[fs(1)-TBw fs(2)+TBw];
Rs=40; Rp=3;
x1=cos(2*pi*0.05*n); x2=cos(2*pi*0.22*n);

%Chebyshev I
[b1,a1]=cheby1(N/2,Rp,2*fp,'stop');
figure, freqz(b1,a1)

y11=filter(b1,a1,x1);
y12=filter(b1,a1,x2);

figure,
subplot, stem(n(100:160), x1(100:160)), hold all
stem(n(100:160), y11(100:160),'--'),hold off; grid, xlim([99 159])
subplot, stem(n(100:160), x2(100:160)), hold all
stem(n(100:160), y12(100:160),'--'),hold off; grid, xlim([99 159])
legend('input,output'), legend boxoff



%Chebyshev II
[b2,a2]=cheby2(N/2,Rs,2*fp,'stop');
figure, freqz(b2,a2)

y11=filter(b2,a2,x1);
y12=filter(b2,a2,x2);

figure,
subplot, stem(n(100:160), x1(100:160)), hold all
stem(n(100:160), y11(100:160),'--'),hold off; grid, xlim([99 159])
subplot, stem(n(100:160), x2(100:160)), hold all
stem(n(100:160), y12(100:160),'--'),hold off; grid, xlim([99 159])
legend('input,output'), legend boxoff