How to understand the type of noise
There are several different ways to look at noise:


The probability density function (PDF) of a noise process, $x(t)$ say. It is sometimes written $p_x(x)$.  This tells you how frequently the the variable $x(t)$ takes on specific values.

One way to think of a PDF is as a (normalized) histogram of the possible values that $x(t)$ can take.  The PDF is normalized because $x(t)$ must take on some value between $-\infty$ and $+\infty$, so the integral
$$
\int_{-\infty}^{+\infty} p_x(x) dx = 1.
$$

For example, the figure below shows the PDF (in blue) and the histogram (in black) for a normal (a.k.a. Gaussian) random variable and for a uniform random variable.





Another way to look at noise is whether there is a relationship between the value of $x(t_1)$ and the value $x(t_2)$ (where $t_1 \not= t_2$). If there is no relationship, then the noise is said to be "white".  If there is a relationship, the noise is said to be "colored".

The way this is usually illustrated is using autocorrelation (autocovariance) of the signal.

Below are two plots of the autocorrelation of normally distributed noise.  In the first plot, the noise is white.  In the second plot, there is a high level of correlation between subsequent samples.




scilab CODE BELOE

// 15426

X_gauss = rand(1,1000,'normal');

X_uniform = rand(1,1000,'uniform');


figure(1)
clf
subplot(211)
histplot(100,X_gauss)
vals = [-3:0.1:3];
plot(vals,exp(-vals.^2/2)/sqrt(2*%pi))
subplot(212)
histplot(100,X_uniform)
plot([0 1], [1 1])

figure(2)

X_white = X_gauss;
X_colored = filter(ones(1,50),10,X_white);

figure(2)
clf
subplot(211)
plot(xcorr(X_white))
mtlb_axis([970 1030 -1000 1000])
subplot(212)
plot(xcorr(X_colored))
mtlb_axis([970 1030 -1000 1000])