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
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