Quantization of a signal

clc
clear all

% Data
start = 0;
finish = 4*pi;
x = linspace(start, finish, 100);
y = sin(x);
MIN = min(y);
MAX = max(y);
% Levels
R = 4;
num_levels = 2 ^ R;
differ = (MAX - MIN) / num_levels;
levels = zeros(1, num_levels);
for i = 1 : num_levels
    levels(i) = MIN + (2*i - 1) * differ / 2;
end

% Searching 'y' to snap the values
multiplier = 3;                     % Must be an integer!
LEN = round(multiplier * length(y));
q = zeros(1, LEN);
t = zeros(1, LEN);

for i = 1 : LEN
    pos = round(i / multiplier);
    if pos == 0
        value = y(1);
        t(i) = x(1);
    else
        value = y(pos);
        t(i) = x(pos);
    end
    index = -1;
    d = MAX - MIN;
    for j = 1 : length(levels)
        level = levels(j);
        if abs(level-value) <= d
            d = abs(level-value);
            index = j;
        end
    end
    q(i) = levels(index);
end


% PLOTS
levels
plot(x, y);
hold on
plot(t, q);