%VAs discretas
%Bernouli
% N = 1e6;
% p = 0.5;
% indices0 = find(rand(1,N)<p);
% x = zeros(1,N);
% x(indices0)=1;
% mux = mean(x)
% [rxx,k] = xcorr(x,10,'biased');
% 
% figure(1);
% subplot(211);stem(0:N-1,x);ylim([-0.1 1.1]);grid;
% subplot(212);stem(k,rxx);grid;

% %Random Walk
% N = 100;
% Ui= sign(randn(1,N));
% x = cumsum(Ui);
% [rxx,k] = xcorr(x,10,'unbiased');
% figure(2);
% subplot(211);stem(0:N-1,x);grid;%ylim([-0.1 1.1]);
% subplot(212);stem(k,rxx);

% %WGN
% N = 10000;
% sigmax2 = 2;
% x = sqrt(sigmax2)*randn(1,N);
% [rxx,k] = xcorr(x,10,'unbiased');
% figure(3);
% subplot(211);stem(0:N-1,x);grid;%ylim([-0.1 1.1]);
% subplot(212);stem(k,rxx);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%M?dia M?vel (MA)
N = 10000;
sigmau2 = 1;
u = sqrt(sigmau2)*randn(1,N+1);
x = .5*(u(1:N)+u(2:N+1));
[rxx,k] = xcorr(x,'unbiased',10);
figure(4);
subplot(311);stem(0:N-1,x);grid;%ylim([-0.1 1.1]);
subplot(323);stem(k,rxx);

%Outra forma de gerar
B = [1/2 1/2];
A = 1;
x1 = filter(B,A,u);
[rxx1,k] = xcorr(x1,'unbiased',10);
subplot(324);stem(k,rxx1);

%DEP - Forma 1
omega = linspace(0,pi,1024);
H = 1/2+1/2*exp(-j*omega);
Sxx1 = sigmau2*abs(H).^2;
subplot(325);plot(omega/pi,Sxx1);

%DEP - Forma 2

[H,w] = freqz(B,A,1024);
Sxx2 = sigmau2*abs(H).^2;
subplot(326);plot(w/pi,Sxx2);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Processo Autoregressivo (AR)
N = 1e5;
sigmau2 = 1;
a = 0.9;
u = sqrt(sigmau2)*randn(1,N+1);

B = 1;
A = [1 -a];
x = filter(B,A,u);

%ACS - Sequência de Autocorrelação
[rxx,k] = xcorr(x,'unbiased',50);

% DEP
%DEP - Forma 1
omega = linspace(0,pi,1024);
H = 1./(1-a*exp(-j*omega));
Sxx1 = sigmau2*abs(H).^2;

%DEP - Forma 2
[H,w] = freqz(B,A,1024);
Sxx2 = sigmau2*abs(H).^2;

figure(6);
subplot(311); plot(x);xlim([0 N]);
subplot(312);stem(k,rxx);grid;axis([-50 50 0 6]);
subplot(325);plot(w/pi,Sxx1);
subplot(326);plot(w/pi,Sxx2);


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