Statistical Signal Processing in Engineering

4Random Processes and Linear Systems

There are sequences and signals that are random, and these are referred to as random (or stochastic) processes. These random processes can be either discrete‐time or continuous‐time, depending on whether the random function of time is over a discrete set or a continuous one. In order to frame the random processes in the preceding chapters, the discrete‐time random process can be viewed as a sequence of random variables sequentially ordered by the time variable as indexing parameter. This means that the stochastic processes are completely characterized by the Nth oder joint pdf p(x) for the set of rvs obtained by continuous‐time random process x(t) for any choice of the time instant to have . Similarly, for discrete‐time random process x[n] where , one can choose the discrete‐time time sampling to have . The commonality between the continuous/discrete‐time ...