Proposed Syllabus For Preliminary Examination In Communications

Revised January 1999

The examination will cover the following subjects:

1. Fourier Transform in discrete and continuous time, (unilateral) Laplace and Z-transforms

2. Modulation: AM (DSB and SSB) and FM, without noise calculations

3. Nyquist's sampling theorem

4. Definition and basic properties of probability and random variables

5. Commonly encountered probability distributions

6. Convergence (a.s., in probability, in distribution, in Lp)

7. Expectation, conditional expectation, linear least squares estimation

8. Random processes and wide sense stationary properties

9. Brownian motion, Poisson process, Markov chains (DT and CT)

10. Transformation of deterministic and second order random processes by LTI system, incontinuous time, discrete time, and mixed

11. Wiener Filtering (at level of Gray and Davisson)

STUDENTS WILL BE EXPECTED TO APPLY THIS MATERIAL TO SIMPLE APPLICATIONS.

Primary References:

• Grimmett and Stirzaker, Probability and Random Processes, 2nd ed., Oxford Science Publishers, 1992.
• Oppenheim and Willsky: Signals and Systems, Prentice-Hall 1983. [Chapters 1-5, 7-8]

Courses:

• EECS 226A
• EECS 120

Supplementary References:

• Gray and Davisson: Random Processes, Prentice-Hall, 1986.
• Wong: Introduction to Random Processes, Springer-Verlag, 1983.
• Bremaud: An Introduction to Probabilistic Modeling, Springer-Verlag, 1988.

NOTE: The following courses may not be used to fulfill the prelim breadth requirement if you take the communications prelim: EE 120, 121, 123, 126, 224, 225ABD, 226AB, 228AB, 229, 290Q, 290S, and 290T.