RANDOM SIGNALS

As the main objective of a communication system is to transfer information over a channel.

So all useful messages appear random, i.e., the receiver does not know which of the possible message waveforms will be transmitted.

CONTD..

Also, the noise that accompanies the message signals is due to random electrical signals.

So there is a need to form efficient description of random signals.

RANDOM VARIABLES

A random variable can be thought of as an unknown value that may change every time it is inspected. Thus, a random variable can be thought of as a function, mapping the samples of a random process to the real numbers.

CONTD..

Let a random variable X(A) represents the functional relationship between a random event A and a real number, then we can write a function of random variable as,

F(x)= P(X<x)where P(X<x) is the probability that the taken value is less than real number x.

It is one of the properties of that function that the value of that function remains between 0 and 1.

The random variable may be discrete and continuous as well.

After defining this function we must define probability density function (pdf).

RANDOM PROCESS

A family of signals that correspond to every possible outcome of a certain signal measurement. Each signal in this collection is referred to as a sample function of the process.

As an example of a random process, let us look at the random sinusoid given below.

A random process is usually denoted by X[n] or X(t).

A random process can be viewed as a function of two variables: an event A and time.

NOISE IN COMMUNICATIONSYSTEM The term noise refers to an unwanted

signals that are always present in electrical systems.

Noise arises from a variety of sources, both man made and natural.

Man made noise includes spark-plug ignition and other many sources.

Natural noise includes such elements as the atmosphere, the sun and many others.

Man made noise can be eliminated but natural noise cannot be eliminated.

However, there is one source of natural noise called thermal noise, which cannot be eliminated.

WHITE NOISE The primary characteristics of thermal

noise is that it has an equal power density through out the whole band of frequency.

When the noise power has such a uniform spectral density then it is referred to as white noise.

The term white is used in the same sense as it is with white light, which contains equal amount of all frequencies within the visible band.