% claculer TFD de filtre d'ordre 3 

%y(n) = 1/3[u(n + 1) + u(n) + u(n − 1)]
clc;close all;
w = 0 : 0.01 : pi ;
% H_mag=(1+2*cos(w))/3;
% H_magdb=mag2db(H_mag);
figure(1)
subplot( 2 , 1 , 1 )
plot(w/pi, 20*log10(abs(1+2*cos(w))/3));%loglog(w, 20*abs(1+2*cos(w))/3)
ylabel('Magnitude(dB)','FontSize',18);xlabel('$ Normalisation \; \omega \times \pi$','FontSize',12,'interpreter','latex')
subplot( 2 , 1 , 2 )
plot(w/pi, -angle(1+2*cos(w))*180/ pi); %semilogx (w, angle(1+2*cos(w))*180/ pi );
ylabel('Phase','FontSize',18,'interpreter','latex');xlabel('$\omega \times \pi$','FontSize',12,'interpreter','latex')

%% autre methode
figure(2)
b0=1/3;
b1=[1, 1, 1];
a1=[0, 1];
freqz(b0*b1, a1)% la reponse frequentielle discret
G_z=tf(b0*b1, a1,0.01);
%% autre methode
figure(3)
Ts=0.01;
%z = zpk('z',Ts);
z=tf('z',Ts)
H_z=(1/3)*(z+1+z^-1);
num=cell2mat(H_z.num);
den=cell2mat(H_z.den);
freqz(num, den)
% H_z.variable='z^-1'
% zpk(H_z)