Try this:
% Make sample data.
x = linspace(0, 3*pi, 640);
period = 2*pi;
y = cos(2 * pi * x / period); % Noise-free signal.
% Noise is 5% of the signal value at each location,
% which means sigma is not a constant at each location.
amplitudes = y * 0.05;
noise = amplitudes .* randn(1, length(y));
% Add the noise to the noise-free signal.
yNoisy = y + noise;
% Plot everything.
plot(x, yNoisy, 'r.', 'MarkerSize', 8);
hold on;
plot(x, y, 'b-', 'LineWidth', 2);
grid on;
