Reading List for the Comprehensive/Qualifying Examination- Problem 1

1

Fourier analysis of continuous-time signals: Fourier series and Fourier transform representations of continuous time signals, properties

(Amengonu)

Sample Problem

2

The z-transform – region of convergence, properties, frequency response, poles and zeros.

(Deeba)

Sample Problem

Discrete Time Signal Processing, by Oppenheim, Schafer, and Buck, 2^nd edition, chapter 3, and section 5.3.

3

Probability theory and random variables: concepts of probability and random variables, functions of one and two random variables, joint statistics.

(Arafa)

Sample Problem

4

Laplace transforms: pole-zero plots, properties, transfer function, steady state response characteristics due to standard inputs like step, ramp, exponential, sinusoidal, and their composite inputs. Bode plots.

(Cox)

Sample Problem

Signals and Systems, by Oppenheim, Willsky, and Nawab, 2^nd edition, sections 9.1 – 9.7

5

Counting techniques, Recurrence Relations, Graphs. Boolean Algebra. Order analysis (Big-Oh notation).

(Sass)

Sample Problem

Discrete Mathematics and Its Applications, 7th Ed. by Kenneth H. Rosen. Chapters 3, 5, 8, 9, 10.

6

Linear algebra: Matrix inversion, solutions to fully determined systems of linear equations, method of elimination, determinants and Cramer’s rule.

(Manjrekar)

Sample Problem

7

Differential equations: Solutions to first and second order linear ODEs with constant coefficients, solutions to linear systems of differential equations

(Zhang)

Sample Problem