uniform noise or normal noise

Hi all,

I'm trying to apply noise on some data I have, the purpose of adding noise is to simiulate the environmental effect on my data measurments of my device that I designed.

should i use uniform noise distribuition or normal noise ditribuition (AWGN)? to apply the effect.

When can I use Uniform white noise and normal white gaussian noise?

thanks

Saleh

[Paul]

Hi Saleh,

This link talks about applications where noise has a uniform distribution. As you noted, you're trying to simulate an effect, so the model of the noise that you choose should be consistent with whatever physical effect you're trying to model.

Answer 1

[John D'Errico]

Not a question at all about MATLAB. But I have a few moments to answer.

When do you add uniform noise versus normal? A simple rule is that noise is almost NEVER uniform. Noise typically results from many small tiny things happening at random. They add up, and according to the law of large numbers, the result is something that looks vaguely normal. So most of the time the noise in your data is Normal (Gaussian).

There are some scenarios where noise would be uniformly distributed. One common one is where your data is rounded. That is, imagine this scenario...

t = 1:100;
ytruth = sin(t);
ydata = round(ytruth,1) % rounding to one digit.

ydata = 1×100

0.8000 0.9000 0.1000 -0.8000 -1.0000 -0.3000 0.7000 1.0000 0.4000 -0.5000 -1.0000 -0.5000 0.4000 1.0000 0.7000 -0.3000 -1.0000 -0.8000 0.1000 0.9000 0.8000 0 -0.8000 -0.9000 -0.1000 0.8000 1.0000 0.3000 -0.7000 -1.0000

So we have a sine wave, but the data is in error. The rounding operation introduces almost pseudo-random uniform noise. (Though it is not random at all.) But this noise will now be approximately uniformly distributed over the interval [-0..05,0.05].

histogram(ytruth-ydata,11,'norm','pdf')

This case is, however, an unusual one. Normally noise is never uniform. Yes, uniform distributions have many uses, but normal in some form is always way more common. One other common case would be a lognormal, but that is just a variation of a normal, in a proportional error context. As far as the case of white noise or not, that just depends upon the situation. Is there some dependency on time that can arise? If so, then the noise will not be white.

[Saleh Komies]

thanks a lot. Well explained.

My idea was to simiuilate different type of noise and see how the effect is going to be. I assumed uniform and non-uniform distribuition. It seems that it depends on the assumption and the system.

[John D'Errico]

Another way of looking at is: Uniform noise has the property that it is strictly bounded between two bounds. And it is equally likely that you will see noise near the bounds as you will find somethign in the center of the range. But true noise in the real world almost never satsifies that kind of behavior. The probabilitly of finding a noise value in the tails gets less and less likely, the farther out you look. That is just what a normal distributiuon looks like.

Of course there are many possible distributions, appropriate for subtly different scenarios. So not all noise is normal, or even close to it. But as I said, it is really quite rare that you would see uniform noise.