If the index set is a countable set, is called a discrete-time process. Such a random process can be represented as and called a random sequence. Sometimes the notation is used to describe a random sequence indexed by the set of positive integers.

            We can define a discrete-time random process on discrete points of time. Particularly, we can get a discrete-time random process by sampling a continuous-time process \ at a uniform interval such that  

            The discrete-time random process is more important in practical implementations. Advanced statistical signal processing techniques have been developed to process this type of signals.

Example 3 Suppose where is a constant and is a random variable uniformly distributed between and .

            is an example of a discrete-time process illustrated in Figure 2.