RANDOM NOISE IN MATLAB

Anyone may help me to explain the difference between Uniform distribution (rand) and Normal distribution (randn).

I understand that

• rand: generate the noise from 0 to 1.
• randn: generate the noise from negative to positive infinity.

Why the NORMAL DISTRIBUTION is more common used and popular in Signal Processing?

Answer 1

[Star Strider]

The rand function (uniform distribution) creates random numbers between 0 and 1.

The randn function creates normally-distributed random numbers that can theoretically go from -Inf to +Inf. They are defined as having a mean of 0 and a standard deviation of 1.

EDIT —

The normal distribution is more common and is used in signal processing because most noise in nature is normally-distributed, so randn models it more closely. Even if the individual components of a noise signal are not normally-distributed, the sum of them will tend to a normal distribution according to the Central Limit Theorem.

Answer 2

[KSSV]

You can check this on your self....there is difference in the distribution of rand and randn.

% rand has uniform distribution 
x1 = rand(10000,1)  ;
figure(1)
hist(x1)
title("Uniform distribution") ;

% randn has normal distribution 
x2 = randn(100000,1) ;
figure(2)
hist(x2)
title("Normal distribution") ;

Answer 3

[Ameer Hamza]

Because normally distributed noise is the most common type of noise occurring in the natural process: https://en.wikipedia.org/wiki/White_noise. Besides, a theorem proves that if you sum a large number of independent random variables, their combined distribution will tend to be normally distributed: https://en.wikipedia.org/wiki/Central_limit_theorem. Therefore, the normal distribution is a good approximation if only naturally occurring noises are being added to a signal. However, if there is an external agency contributing to the noise, then the distribution can change.

Answer 4

[Walter Roberson]

Noise is associated with uncontrolled energy sources, or with input sources not being exactly controlled.

There is energy associated with noise. That energy is seldom equally probable. It turns out that many many cases, the energy is most probable near zeros and less and less probable as the magnitude of the energy increases.

Some of the noise sources are quantum. Quantum processes are probabilistic and not usually uniform random.

Remember too that noise sources can be the result of multiple particles acting on a target. It might even be the case that each particle contributes a uniform random energy, but the total result is the sum of those uniform random events, and the Central Limit Theorem says that the sum of uniform random events tends to normal distribution. The sum of two 6 sided dies is not equally probable from 2 to 12: 7 is the most probable, 6 times more likely than 2, and that only took two dies (two particles) to experience.