How to understand the type of noise

Suppose that I am receiving RF signals contaminated with noise through antenna. This signal is digitally sampled. How can I understand the type of noise(Gaussian,Uniform etc). Any algorithm is there to test the type of noise.

• Did you try generating a histogram of the noise? – John Apr 4 '14 at 9:17

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])


The way I'm familiar with is:

1- Send the RF Image multiple times. Say 100 times. 2- Compare by "subtraction" in case of an Image for example .. between the received image/ and transmitted one. 3- The subtraction will give you the noisy image. 4- Plot a histogram statistics for the noisy image, for every received image. You'll then be able to roughly model the noise based on the experimental results.

The most familiar ones are, Guassian, or even Uniform.

if it's not of these familiar ones. Run a regression code to represent this model as an equation. By that means you can take the inverse of it to compensate for the noise.

• Butterworth noise? Do you have a reference for what that is? – Jason R Apr 4 '14 at 13:32
• I haven't passed across a similar thing. But you can call a noise butter-worth if it had a similar histogram distribution as how a butter-worth filter would be. The model is experimental, so you can simply get a similar histogram as the response of a butter-worth filter. I will edit that part to avoid any future confusion. – Adel Bibi Apr 4 '14 at 13:38
• remember that (assuming "noise" is a random process) there is a difference in concept between the PDF of a random process (gaussian vs. uniform) and the power spectrum of the random process (white vs. something else). the PDF and the power spectrum are different spaces of properties. they are not about the same thing. – robert bristow-johnson Apr 4 '14 at 16:34
• @robertbristow-johnson I've considered them to be equivelent for a long time. I had a hard time to grasp the actualy difference between them. Could you link me to a source or something please? – Adel Bibi Apr 4 '14 at 17:45
• As robert bristow-johnson has pointed out, what this will give is the pdf of the process (assumed to be stationary etc), not the power spectrum. So, Gaussian and uniform are reasonable descriptions of the end result of what Adel Bibi is telling the OP to do; white is not. In fact, depending on the details of the implementation, a Rayleigh pdf is a distinctly possible result instead of Gaussian. – Dilip Sarwate Apr 4 '14 at 19:49