RANDOM PROCESSES
INTRODUCTION :
We studied in detail about probability theory. In those chapters, we were
concerned with outcomes of random experiments and the random variable
used to represent them. We know that a random variable is a mapping of an
event sS where S is the sample space to some real number X(s).
The random variable approach is applied to random problems that are
not functions of time. However, in certain random experiments, the outcome
may be a function of time. Especially in engineering, many random problems
are time dependent.
, For example, speech signal which is a variation in voltage due to speech
utterance is a function of time. Similarly, in a communication system, a set of
messages that are to be transmitted over a channel is also a function of time.
Such time functions are called random processes.
In communication systems, a desired deterministic signal is often
accompanied by undesired random waveform known as noise which limits the
performance of the system. Since the noise is a function of time and cannot be
represented by a mathematical equation, it can be treated as a random process.
, In this chapter, we will study such random processes which may
be viewed as a collection of random variables with t as a parameter.
That is, instead of a single number X(s), we deal with X(s, t) where
t T and T is called the parameter set of the process. For a random
process X(s, t), the sample space is a collection of time function.
Figure.1 shows a few members of collection. A realization of X(s, t) is a
time function, also called a sample function and member function.
INTRODUCTION :
We studied in detail about probability theory. In those chapters, we were
concerned with outcomes of random experiments and the random variable
used to represent them. We know that a random variable is a mapping of an
event sS where S is the sample space to some real number X(s).
The random variable approach is applied to random problems that are
not functions of time. However, in certain random experiments, the outcome
may be a function of time. Especially in engineering, many random problems
are time dependent.
, For example, speech signal which is a variation in voltage due to speech
utterance is a function of time. Similarly, in a communication system, a set of
messages that are to be transmitted over a channel is also a function of time.
Such time functions are called random processes.
In communication systems, a desired deterministic signal is often
accompanied by undesired random waveform known as noise which limits the
performance of the system. Since the noise is a function of time and cannot be
represented by a mathematical equation, it can be treated as a random process.
, In this chapter, we will study such random processes which may
be viewed as a collection of random variables with t as a parameter.
That is, instead of a single number X(s), we deal with X(s, t) where
t T and T is called the parameter set of the process. For a random
process X(s, t), the sample space is a collection of time function.
Figure.1 shows a few members of collection. A realization of X(s, t) is a
time function, also called a sample function and member function.
