Smoothing a noisy signal

I want to smooth my noisy data using the moving average. I also want to vary the rolling window and check how different rolling windows smooth my noisy data. I have written the code for a dummy sinusoidal signal. The only problem is that my data after each rolling window gets overwritten. I understand why it is but don't know how to fix it. May I request you to please suggest how to fix it?

%% how to create a noisy data
x = 0:0.1:20; %creating a dummy data
y = sin(x); %finding a sine of the variable x
n = randn(1, length(x)); % generating a random (Gaussian) noise of size 1x length(x) 
y_noisy = y+n; % creating the sine function noisy by adding the Gaussian noise

%% how to smooth the noisy data wout using any filter but using moving average

for rollingwindow = [2,20] % specify the rolling averaging window
    N = length(y_noisy);
    m = N - rollingwindow + 1;
    newy_noisy =zeros(m,1); % initializing the matrix
    for i = 1:m
        newy_noisy(i) = mean(y_noisy(i:i+(rollingwindow-1)));
    end
 %% here newy_noisy has to be defined in such a way it is not overwritten. But how?
    figure();
    plot(y, 'b');
    hold on
    plot(y_noisy, 'r')
    hold on
    plot(newy_noisy, 'k', 'linewidth', 1)
    legend('theoretical','noisy','smooth')
    title('noisy vs smooth', sprintf('rollwindow = %d', rollingwindow));
    outputFileName = sprintf('rollwin%d', rollingwindow); 
    outputFullFileName = fullfile('C:\Users\anusu\Desktop',outputFileName);
    saveas(gcf, outputFullFileName, 'png');
    hold off
end

Answer 1

[KALYAN ACHARJYA]

%% how to create a noisy data
x = 0:0.1:20; %creating a dummy data
y = sin(x); %finding a sine of the variable x
n = randn(1, length(x)); % generating a random (Gaussian) noise of size 1x length(x) 
y_noisy = y+n; % creating the sine function noisy by adding the Gaussian noise
%% how to smooth the noisy data wout using any filter but using moving average
for rollingwindow=2:20 % specify the rolling averaging window
    N = length(y_noisy);
    m = N - rollingwindow + 1;
    newy_noisy =zeros(m,1); % initializing the matrix
    for i = 1:m
        newy_noisy(i) = mean(y_noisy(i:i+(rollingwindow-1)));
    end
    %% here newy_noisy has to be defined in such a way it is not overwritten. But how?
    figure();
    plot(y, 'b');
    hold on
    plot(y_noisy, 'r')
    hold on
    plot(newy_noisy, 'k', 'linewidth', 1)
    legend('theoretical','noisy','smooth')
    title(['noisy vs smooth', sprintf('rollwindow = %d', rollingwindow)]);
    outputFileName = sprintf('rollwin%d', rollingwindow); 
    outputFullFileName = fullfile('C:\Users\anusu\Desktop',outputFileName);
    %saveas(gcf, outputFullFileName, 'png');
    hold off
end

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