How we can generate generate a noise signal from gauss distribution ??

I want to generate a noise signal from gauss distribution ,whose mean is 'x' and variance is 'y'

Which formula and command should i use?

Answer 1

[Thiago Henrique Gomes Lobato]

the randn function in matlab is a gaussian distribution with variance 1. So you can generate a gaussian with mean x and variance y as:

Samples = 10;
Noise   = x+randn(Samples,1)*y;

[ABTJ]

If we plot this Noise, will it have a bell shape??

[Thiago Henrique Gomes Lobato]

If you generate enough samples, yes

Samples = 10000;
x       = 5;
y       = 2;
Noise   = x+randn(Samples,1)*y;
figure,histogram(Noise)

[ABTJ]

Can we use plot command instead of histogram?

[Thiago Henrique Gomes Lobato]

Sure, but what you actually want to see? Distribution shapes cannot be seen if you just plot the data, you need to plot the probability of the data, which is roughly the histogram counts times a constant. If you want that your noise data have a bell shape than you actually don't want a gaussian noise, but rather a signal that looks like a gaussian.

[Sean Corby]

Why does MATLAB show random values that appear to go beyond the variance?

Answer 2

[Chuguang Pan]

This is a example for generating a bivariate normal distribusion which is a duplicate of MATLAB Documentation. Maybe it can help you.

Generate values from a bivariate normal distribution with specified mean vector and covariance matrix.

 mu = [1 2]; %mean vector
sigma = [1 0.5; 0.5 2]; %covariance matrix
R = chol(sigma);
z = repmat(mu,10,1) + randn(10,2)*R

Here is the result. Maybe you will get a different result because of random.

z =

    1.3271    3.3688
    2.0826    3.3279
    2.0061    2.9663
    0.3491    3.3285
    1.2571    3.3585
    0.0556    1.8450
   -0.3218    0.4258
    1.9248    1.6005
    1.0000    3.5770
    0.9451   -0.1597

[ABTJ]

If we plot this Noise, will it have a bell shape??