Gaussian noise in a function

How can I insert gaussian noise additive or multiple in a function, where the variance is unknown and the mean is equal to 1.

[John D'Errico]

Looks like you deleted your last question. My comment still applies. What do you mean when you ask to add (or multiply) by noise where you don't know what the parameters of the noise are?

[Katerina]

what I mean is that I made a function in which I want to add gaussian noise.... The exact parameters are not given in my exercise... The only thing that I know is that the noise follows the Gaussian distribution with unknown variance...

Answer 1

[Star Strider]

To create your Gaussian noise, use the randn function.

For an unknown variance, create a variable for it (here ‘varn’). To change the mean, add it. So if your signal is a (Nx1) vector ‘s’, and you want to add Gaussian random noise to it with a mean of 1:

sn = s + sqrt(varn)*randn(N,1)+1;

where ‘sn’ is your signal + noise.

[Katerina]

like this:???

for varn=1:0.01:5
    noise(varn)=sqrt(varn).*randn(1,size(x)); % Create an additive gaussian noisy version of y 
    yna = y + noise(varn);

[Star Strider]

I was thinking of creating your signal with something like this:

varn = 1:0.01:5;                            % Variance
y = 5*sin(4*pi*varn/5);                     % Signal
yn = y + sqrt(varn).*randn(size(varn))+1;   % Signal + Noise

figure(1)
plot(varn, yn)
grid

You will probably need to experiment with it to get the result you want.

I would use the rand (uniform random numbers on the interval (0,1)) to define ‘varn’, but you may have other requirements. In that instance, the code becomes:

k = 1:0.01:5;                               % Time (Index) Vector
y = 5*sin(4*pi*k/5);                        % Signal
varn = rand(size(k));                       % Variance Vector
yn = y + sqrt(varn).*randn(size(k))+1;      % Signal + Noise

figure(1)
plot(k, yn)
grid