clear;

F0 = 6000;
F1 = 2000;
Fe = 48000;
Te = 1/Fe;
Ts = 1/300;
Ns = floor(Ts/Te);

% Question 3.1.1.1
%bits = randi([0, 1], 1, 300);
load('DonneesBinome1.mat');
NRZ = repelem(bits, Ns);
T = 0:Te:Ns*84000/Fe-Te;

% Question 3.1.1.2
%plot(T, NRZ);
%xlabel("temps (s)");
%ylabel("NRZ(t)");

% Question 3.1.1.3
%N_fft = 48000;
%F = 0:1/N_fft:Fe;
%perio = abs(fft(NRZ, N_fft)).^2/N_fft;
%semilogy(perio);
%periodogram(NRZ);

% Question 3.1.2.1
phi = 2*pi*rand(2, 1);
X = (1-NRZ).*cos(2*pi*F0*T + phi(1)) + NRZ.*cos(2*pi*F1*T + phi(2));
%plot(T, X);
%xlabel("temps (s)");
%ylabel("X(t)");

% Question 3.1.2.4
%periodogram(X);

% Question 3.2
N = Ns*84000;
Px = mean(abs(X).^2);
Pb = Px / 10^(10/10);
sigma = sqrt(Pb);
bruit = sigma*randn(1, N);
Xb = X + bruit;
%periodogram(Xb);
%plot(Xb);
%semilogy([0:N-1]/N*Fe, abs(fft(Xb, N)));
%hold;


% Question 3.3.1 : Passe-bas
fc_tild = 4000/Fe;
A = 1;
ordre = 100;
B = 2*fc_tild*sinc(2*fc_tild*[-ordre/2:1:ordre/2]);
Xf = filter(B, A, Xb);
%plot(Xf);
%plot(abs(fft(B, N)));
%plot([-ordre/2:1:ordre/2], B);
%semilogy([0:N-1]/N*Fe, abs(fft(Xf, N)));
%periodogram(Xf);
%hold;

% Question 3.3.2 : Passe-haut
fc_tild = 4000/Fe;
ordre = 100;
B = -2*fc_tild*sinc(2*fc_tild*[-ordre/2:1:ordre/2]);
A = 1;
B(ordre/2+1) = 1 - 2*fc_tild;
Xf = filter(B, A, [Xb zeros(1, ordre/2)]);
Xf = Xf(ordre/2:length(Xf));
% Le filtre est une version tronquée de la réponse idéale
%plot(abs(fft(B, N)));
%plot(Xf);
%semilogy([0:N-1]/N*Fe, abs(fft(Xf, N)));
%periodogram(Xf);
%plot(B);

% Question 3.3.5
K = 70;
recup = [];
bits_recup = [];
for i = 0:N/Ns-1
    somme = sum( Xf( i*Ns+1 : (i+1)*Ns ).^2 );
    recup = [recup, somme];
    if somme >= K
        bits_recup = [bits_recup, 0];
    else
        bits_recup = [bits_recup, 1];
    end
end

bits - bits_recup;
erreur = sum((bits - bits_recup).^2)/N*Ns

%image 
pcode reconstitution_image;
reconstitution_image(bits_recup);
which reconstitution_image;

%legend("Xb", "Xf");