Telecommunication System

clc
clear all

% Define the function
t0 = 0;
tf = 8*pi;
N = 1000;
% 1. Sampled signal of info, named "m(t)"
t = linspace(t0, tf, N);
m = cos(t) + 0.5*t;
figure(1);
subplot(2,2,1);
plot(t, m);
title("1. Sampled signal m(t)");
% 2. Quantization
M = 5;
numOfLevels = 2^M;
quantizedAndLevels = quantization(m, numOfLevels);
LEN_ALL = length(quantizedAndLevels);
LEN1 = LEN_ALL - numOfLevels;
quantized = quantizedAndLevels([1:LEN1]);
levels = quantizedAndLevels([LEN1+1 : LEN_ALL]);
subplot(2, 2, 2);
plot(t, quantized);
title(strcat("2. Quantized signal with ", num2str(numOfLevels), " levels"));
% 3. Digitization - Info bitstream
LEN = length(quantized);
bitstream = zeros(1, M*LEN);
for i = 1:LEN
    % For every qValue, I will add M digits 0,1 in bitsream list
    qValue = quantized(i);
    for j = 1:length(levels)
        level = levels(j);
        if qValue == level
                decimal = j-1;
                binary = decimalToBinary(decimal);
                binaryPad = pad(binary, M);
                % Binary variable is the M-digit word I will add in
                % my bitsream list
                for offset = 1:M
                    bitstream(M *(i-1) + offset) = binaryPad(offset);
                end
            break
        end
    end
end
bitstream

% ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
% ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
% ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
% ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

% Function 1 - Quantization
function quantizedAndLevels = quantization(m, numOfLevels)
    MAX = max(m);
    MIN = min(m);
    LEVELS = linspace(MIN, MAX, numOfLevels+2);
    levels = zeros(1, numOfLevels);
    for i = 2:length(LEVELS)-1
        levels(i-1) = LEVELS(i);
    end
    % levels is done, now I have to quantize the values
    quantized = zeros(1, length(m));
    for i = 1:length(m)
        value = m(i);
        difference = 10^8;
        optimumLevel = -1;
        for j = 1:length(levels)
            level = levels(j);
            if abs(value - level) < difference
                difference = abs(value - level);
                optimumLevel = level;
            end
        end
        quantized(i) = optimumLevel;
    end
    quantizedAndLevels = [quantized levels];
end


% Function 2 - Decimal to binary
function binary = decimalToBinary(decimal)
    sum = decimal;
    if decimal == 0
        binary = 0;
    else
        N = floor(log2(decimal) + 1);
        binary = zeros(1, N);
        for i = N-1: -1: 0
            if sum >= 2^i
                sum = sum - 2^i;
                binary(N - i) = 1;
            else
                binary(N - i) = 0;
            end
        end
    end
end


% Function 3 - Pad with zeros
function binaryPad = pad(binary, M)
    binaryPad = zeros(1:M);
    if length(binary) < M
        difference = M - length(binary);
        PAD = 1:difference;
        for i = 1:difference
            PAD(i) = 0;
        end
        binaryPad = [PAD binary];
    elseif length(binary) == M
            binaryPad = binary;
    else
        display('Cannot do that');
    end
end

% Function 3 - Digitization
function digitized = digitization(N)
    decimalList = 1:N;
    for i = 1:length(decimalList)
        decimal = decimalList(i);
        binary = decimalToBinary(decimal);
    end
end