Subjects for ECE Qualifying Exam in Signals and Systems

 

• Continuous-time and discrete-time signals: unit impulse functions, unit step functions, exponentials, sinusoids
• Solutions of linear constant-coefficient differential and difference equations
• Properties of continuous-time and discrete-time systems : linearity, time-invariance, causality, stability, memory
• Fourier series for continuous-time and discrete-time signals
• Fourier transform for continuous-time and discrete-time signals
• Fourier series and transform properties (e.g., linearity, delay, symmetry)
• Bilateral and unilateral Laplace transforms
• Bilateral and unilateral z-transforms
• Regions of convergence
• Pole-zero diagrams
• Laplace and z transform properties
• Linear time-invariant (LTI) system analysis
• Convolution integral (continuous-time) and sum (discrete-time)
• Impulse response
• Frequency response (including Bode plots)
• Filtering
• Stability and causality of LTI systems
• Relationship of time-domain, frequency-domain, and transform-domain representations of signals and systems
• Nyquist sampling theorem
• Discrete-time processing of continuous-time signals
• Relationship of the Discrete Fourier Transform (DFT) to the Fourier transform for discretetime signals
• DFT properties
• Circular vs. linear convolution

Suggested Reading

1. A.V. Oppenheim and A.S. Willsky with S.H. Nawab, Signals and Systems. Second Edition, Prentice Hall, 1997. Chapters: 1-11.
2. A.V. Oppenheim and R.W. Schafer, with J.R. Buck, Discrete-Time Signal Processing. Second Edition, Prentice-Hall 1999. Chapters: 2 and 3; Sections: 4.0-4.4, 5.0-5.5, 6.0-6.5, 8.0-8.5