Try this:
% Make noise-free signal.
period = 40;
amplitude = 5;
x = linspace(0, 40, 500);
y = amplitude * sin(2 * pi * x / period);
plot(x, y, 'b-', 'LineWidth', 2);
grid on;
fontSize = 20;
xlabel('x', 'FontSize', fontSize);
ylabel('y', 'FontSize', fontSize);
% Make a noisy signal
noiseAmplitude = 60;
noise = noiseAmplitude * rand(size(y)) - noiseAmplitude/2;
% Blur the noise to make it smoother.
noise = movmean(noise, 80);
noisyy = y + noise;
hold on;
plot(x, noisyy, 'r-', 'LineWidth', 2);
% Compute the sum
ySum = y + noisyy;
darkGreen = [0, 0.5, 0];
plot(x, ySum, '-', 'Color', darkGreen, 'LineWidth', 2);
legend('y1', 'y2', 'y1+y2');
