If you have a Gaussian random function (Brownian motion) in MATLAB or in any other programming language, defined for positive times t, then you have these two properties: the ensemble average is null and the process is delta-correlated in time. A consequence is that the variance grows linearly in time. See the formulas below for a mathematical description. Delta denotes Dirac function.

Hello,

awgn in Matlab help is : Add white Gaussian noise to signal.

Then you can use simply as it :

% define x signal : sinus for exemple.

x=A*sin(-2*pi.*t);

% Noise Level in dB AWGN.

Noise_Level = -10; % dB

x_awgn = awgn(x,Noise_Level,'measured');

plot(t,x_awgn);

% measured : ...(function evaluate) the power of x before adding noise ...

% White : All frequencies are added.

Then you can measure all differences between sinus and AWGN signal.

These differences repeat like a gaussian probability.

For exemple 10.log[awgn/sin] = -10 dB seems to be repeated 33% times around sigma.

Others values (-15, - 20 ...etc.) follow the gaussian probability.

Best regards.

Jean-Paul Cipria