%% Parte 1
    clear;clc;

    N = 512;
    % criar variavel y
    load trab03.mat;

    figure(1);
    imagesc(reshape(y,N,N));
    colormap(gray);
    colorbar;

% (1)
    simbolos = length( unique(y) )

% (1).a
    % faz o array de [0:255] <=> 8bits
    gama = unique(y);
    % conta o nº de simbolos para um array;
    % p.ex [ 22 13 ... ] conta desde os 0s ate aos 255s
    size_bar = histc( y(:),gama );

    figure(2);
    bar(gama,size_bar)

% (1).b = 8bits. 2^8 = 256;

% (2).a
    dc_y = mean(y)
    ytx = y - dc_y;
    dc_ytx = mean(ytx)

    %EXEMPLO: gerar sinal Wn com potencia de 5W e media nula:
        % desvio padrao
        sigma = 5;
        % media
        m = 0;
        %ruido
        wn = sigma * randn(size(y))+m;

        powerwn_exp = mean(wn.^2)
        powerwn_teo = sigma.^2

        powerytx = mean(ytx.^2);

        SNR = powerytx./powerwn_exp

        figure(3);
        imagesc( reshape(ytx,N,N) )
        colormap(gray);

% (2).b
    % 0db = 1 of SNR
    % 5db = 3.2 of SNR
    % 10db = 10 of SNR
    % 15db = 32 of SNR

    SNR = [1 3.2 10 32];

    % Wn = sigma * randn( size(y) ) + m;
    % sigma = sqrt(mean(ytx.^2)./SNR)
    wn = sqrt(powerytx./SNR).*randn( size(ytx) );
    %valor medio ja é 0 <=> DC eliminada

    img1 = y + wn(:,1);
    img2 = y + wn(:,2);
    img3 = y + wn(:,3);
    img4 = y + wn(:,4);

    figure(4)
    colormap(gray);
    subplot(2,2,1),imagesc( reshape(img1,N,N) ),title('0dB')
    subplot(2,2,2),imagesc( reshape(img2,N,N) ),title('5dB')
    subplot(2,2,3),imagesc( reshape(img3,N,N) ),title('10dB')
    subplot(2,2,4),imagesc( reshape(img4,N,N) ),title('15dB')

% (3)
    clear;clc;close all;
    load trab03.mat;
    N=512;

    % conversao para binario [0 1]
    yb = rem( double(dec2bin(y,8)),2 );
    % conversao para binario polarizado [ -1 1]
    ybp = 2*yb-1;

    % potencia sinal binario polarizado == 1W
    power_y = mean(ybp(:).^2)

    for dB=0:5:20
        SNR = 10.^(dB./10);
        sigma = sqrt(power_y./SNR);
        % criar ruido
        wn = sigma * randn( size(ybp) );

        y_withnoise = ybp + wn;

        % conversao de [-1 1] para [0 1]
        ybp_decision = y_withnoise > 0;

        % conversao de digital para analogico
        y_withnoise_analogic = ybp_decision * [128 64 32 16 8 4 2 1]';

        figure((dB./5)+1);
        subplot(2,3,dB/5+1)
        imagesc( reshape(y_withnoise_analogic,N,N) )
        colormap(gray)
    end

% (5)
    clear;clc;close all;
    load 'trab03.mat';

    % conversao para binario [0 1]
    yb = rem( double(dec2bin(y,8)),2 );
    % 7LSB e DAC
    yq = yb(:,2:8)*[64 32 16 8 4 2 1]';