UMBC CSEE Department

EE Reading List - Comprehensive (Qualifying) Exam

Revised: May 2003

ENEE 601 Signal and Linear Systems Theory

Contemporary Linear Systems using MATLAB, by R. D. Strum & D. E. Kirk, ISBN 0-534-37172-8, Brooks/Cole, 2000.

Linear System Theory and Design, 3rd Ed, by C.-T. Chen, ISBN 0-19-511777-9, Oxford Univ. Press, 1999.

Topics:

Representations and domains of CT/DT signals

CT/DT transforms and regions of convergence

Causal and anti-causal systems

Conversion between CT and DT signals, and sampling theorem

Basic linear space concepts: vectors, matrices, quadratic forms,

matrix calculus, eigenvalues & eigenfunctions

Correlation and convolution

Differential & difference equations

State-variable equations

Input-output representations: impulse response, transition matrix,

transfer function

Time-invariant vs. time-variant systems

Linear feedback

Signal flow graph concepts and direct form structures

Stability, controllability, observability

ENEE 620 Probability and Random Processes

Processes: A Mathematical Approach for Engineers, by R.M. Gray and L.D. Davission, Random Prentice-Hall, 1986. [Also available on Internet.]

Probability and Random Processes with applications to signal Processing, by H. Stark and J.W. Woods, 3rd ed., Prentice-Hall, 2002.

Topics:

Random Variables and Vectors

Functions of Random Variables

Conditional Probabilities

Conditional Expectation

Random Sequences

Convergence modes (Random Processes)

Second-order random processes

Stationary processes

Wide-sense stationary processes

Independent increments processes (Wiener processes, Gaussian-Markov processes)

ENEE 621 Detection and Estimation Theory

Fundamentals of Statistical Signal Processing, by Steven M. Kay, Volume 1: Estimation Theory (1993) & Volume 2: Detection Theory (1998), Prentice Hall.

Additional Reference:

An Introduction to signal Detection and Estimation, Springer-Verlag, by H.V. Poor, 2nd ed., 1994.

Topics:

Parametric Estimation Theory

o Minimum Variance Unbiased Estimation

o Cramer-Rao Lower Bound

o Linear Models

o General Minimum Variance Unbiased Estimation (Sufficient statistics, Neyman-Fisher, Rao-Blackwell-Lehman-Scheffe theorems)

o Maximum Likelihood Estimation

o Least Squares Estimation

o Best Linear Unbiased Estimators

o Bayesian Estimators

o General Bayesian Estimators (MMSE and MAP estimators)

o Linear Bayesian Estimators (Linear MMSE estimation, Wiener filtering)

o Kalman Filters

Statistical Decision Theory

o Neyman-Pearson Theorem

o Operating Characteristics

o Bayes risk

o Minimax approach

o Matched Filters

o Estimator-correlators

o Binary and M-ary detection

o Composite Hypothesis Testing (Bayesian approach, Generalized likelihood ratio tests)

o Performance evaluation

ENEE 622 Information Theory

Elements of Information Theory, by T. M. Cover and J A Thomas, Wiley, 1991. [Most of the material included in the topic section below is discussed in Chapters 2, 3, 4, 5, 8, 9, 10, and 13 of this book].

Additional References:

Information Theory and Reliable Communication, by R. G. Gallager, Wiley, 1968.

A First Course in Information Theory, by R. W. Yeung, Kluwer, 2002.

Topics:

Shannon's information measures: entropy, differential entropy, entropy rate, information divergence, mutual information, and their basic properties.

Stationary sources, Markov sources, Discrete-alphabet memoryless (i.i.d.) sources.

Asymptotic equipartition property. Weak and strong typicality. Joint typicality.

Shannon’s source coding theorem and its converse.

Uniquely decodable and prefix-free source codes. Huffman and Shannon codes.

Source-coding with a fidelity criterion: the rate-distortion function and its achievability.

Discrete-alphabet memoryless channels. Channel capacity.

Shannon’s channel coding theorem and its weak converse.

Feedback capacity.

Joint source-channel coding.

Discrete- and continuous-time additive Gaussian channels. Parallel additive Gaussian channels: waterfilling.

Topics not to be examined:

ü Numerical techniques for the computation of channel capacity and the rate-distortion function.

ü Rate-distortion function for continuous-alphabet sources