EE 5531 Exam 2 will be administered
Friday, November 14, 2008,
11:15am - 12:05pm ONLY. (Regular students take the exam
in the regular classroom; Unite students take exam
remotely, but they must take exam during
the designated 50-minute time period and not before or after.)
Here is the relevant information
concerning this exam:
Exam is closed book and closed notes.
A formula sheet will be provided by the instructor.
No personal formula sheets allowed.
No calculators will be allowed.
The coverage of this exam is:
Markov Processes: Transition matrices, stationary dists,
and steady state dists of
discrete-time Markov
chains with finite state space, generating matrices, stationary dists,
and Kolmogorov differential equation for
continuous-time Markov chains with finite state space,
semigroup property (Chapman-Kolmogorov property) for Markov processes.
See Supplement to Chapter 12 and the following from
Chapter 12: Sections 12.1-12.3, Section 12.4 through
Example 12.12 (steady-state behavior for finite state space
only), Section 12.5, Problems 32 and 34 on page 515 (the book's only
coverage of
continuous-time continuous state space Markov processes).
Random Processes Introduction: WSS and SSS processes,
autocorrelation function and power spectral density properties,
autocorrelation function of Markov process,
cross-correlation and cross-power spectral density of joint WSS
processes, filtering WSS processes through LTI systems,
matched filter, Wiener filter scenarios. See Chapter 10,
Sections 10.1-10.2, Section 10.3 except for bottom half of
page 397, Sections 10.4-10.5, Section 10.6 through Example 10.30,
Section 10.7, Section 10.8. Also EE 3025 Notes,
Sections 30.4 through 42.6 (our undergraduate material).
Gaussian and Gaussian WSS Processes: bottom of page 464
through page 465.
ARMA processes with emphasis on MA and AR processes: form
of the power spectral density of ARMA, MA, and AR processes,
autocorrelation function of MA process,
recursion for generating autocorrelation function of AR process,
modeling of MA and AR processes using spectral factorization.
Applications of AR processes to finite-order and infinite
memory predictor design. See Section 15.5 and Homework Sets 7 and 8.
Applications to prediction: Applications of AR processes to
finite-order and infinite
memory predictor design. Predictors for first and second order
Markov processes. See Homeworks 7 and 8.
Poisson process: The shaded in properties on page 444
are the starting point (the undergrad material). Going beyond
that I did three "deeper properties": (1) interarrival
times IID Exponential (Section 32.2 of the EE 3025 Notes);
(2) ``Uniform Distribution Property'' of arrival times (see
Problem 4, Solutions to EE 5531 F2007 Homework 7); and
(3) ``Binomial Distribution Property'' of arrival times
(see Problem 5, Solutions to EE 5531 F2007 Homework 7).
In Section 11.1, read up through Example 11.2.
You might want to go over solutions to Homeworks 5-8.
Also, some Exam 2 review examples have been posted below.
During the exam period, please observe proper etiquette: this
includes starting the exam only when the proctors tell you to start
and turning in your exam precisely when the proctors tell
you that the exam is over.