Random Processes - Random Signals and Processes Primer with MATLAB - page 441

6.10 Questions

Q.6.1. Can a random process have only one realization?
Q.6.2. Is there a difference between a stochastic process and a random process?
Q.6.3. Is there a difference between a random process and a random signal?
Q.6.4. An autocorrelation function for a WS stationary process has the property
( 6.45 ):
The maximum value of the autocorrelation function is at t ¼ 0

j R XX ðtÞ j R XX ð 0 Þ: (6.260)

Why is this condition not written as:

j R XX ðtÞ j<R XX ð 0 Þ: (6.261)

Q.6.5. Can two WS stationary processes have equal PDFs and different autocor-
relation functions?
Q.6.6. A second-order stationary process is also a WS stationary. Is the opposite
true (i.e., is a WS stationary process also stationary to order 2)?
Q.6.7. Is it possible to obtain the mean value of a WS stationary process from its
autocorrelation function?
Q.6.8. Can an autocorrelation function be a delta function?
Q.6.9. What is the average normalized power in a random process?
Q.6.10. Does an average normalized power depend on type of signals, that is,
whether signal is a voltage or current?
Q.6.11. Can processes with different realizations have the same autocorrelation
function?
Q.6.12. Is it possible for an autocorrelation function to have negative values?
Q.6.13. Can two WS stationary processes not be jointly WS processes?
Q.6.14. A random process has a mean value which is a function of time t . Why is it
that this process cannot be a mean ergodic?
Q.6.15. The autocorrelation function of a process is a function of both a time t and a
time difference t . Why is this process cannot be autocorrelation ergodic?
Q.6.16. If we know a joint PDF we can find the autocorrelation function. Can we
find a joint PDF if we know the autocorrelation function?

6.11 Answers

A.6.1. A random process cannot be only one realization, just as a random variable
cannot be only one number. Remember that a random process is an
abstraction based on the mapping of a sample space to a collection of