Advanced Signals and Systems

EEG 501 provides a rigorous graduate-level examination of advanced signals and systems theory, building upon undergraduate foundations. Students will explore complex continuous-time and discrete-time signal representations, including Fourier series, Fourier transforms, Laplace transforms, and Z-transforms, analyzing their properties and applications in depth. The course emphasizes understanding system behavior through impulse responses, convolution, and transfer functions, alongside advanced techniques for stability analysis in both time and frequency domains. Practical applications in filtering, modulation, and communication systems are integrated throughout to bridge theoretical concepts with real-world engineering challenges. The curriculum is designed to equip students with the analytical tools necessary for designing and evaluating sophisticated signal processing systems. Topics include state-space representations, sampling theory, multirate signal processing fundamentals, and an introduction to adaptive filtering concepts. Through problem-solving, simulations, and design exercises, students will develop a comprehensive understanding of how to characterize, analyze, and manipulate signals and systems to meet complex performance specifications in various electronics engineering technology fields. This course is essential for those pursuing advanced work in communications, control systems, digital signal processing, and related areas.

Course outline

Lectures, virtual labs, and graded assignments — completed in your browser.

01Review of foundational continuous and discrete-time signals and systemslecture

02Fourier series and continuous-time Fourier transform propertieslecture

03Continuous-time Fourier transform applications and spectral analysislecture

04Laplace transform for continuous-time system analysislecture

05Inverse Laplace transform and system transfer functionslecture

06Z-transform for discrete-time system analysislecture

07Inverse Z-transform and discrete-time system functionslecture

08Sampling theory and reconstruction of signalslecture

09Discrete Fourier transform and fast Fourier transformlecture

10System stability analysis in time and frequency domainslecture

11State-space representation of continuous and discrete systemslecture

12Frequency response and filter design techniqueslecture

13Introduction to multirate signal processing and adaptive filterslecture

14Advanced topics and course project presentationslecture

Syllabus

Week 1: Review of foundational continuous and discrete-time signals and systems
Week 2: Fourier series and continuous-time Fourier transform properties
Week 3: Continuous-time Fourier transform applications and spectral analysis
Week 4: Laplace transform for continuous-time system analysis
Week 5: Inverse Laplace transform and system transfer functions
Week 6: Z-transform for discrete-time system analysis
Week 7: Inverse Z-transform and discrete-time system functions
Week 8: Sampling theory and reconstruction of signals
Week 9: Discrete Fourier transform and fast Fourier transform
Week 10: System stability analysis in time and frequency domains
Week 11: State-space representation of continuous and discrete systems
Week 12: Frequency response and filter design techniques
Week 13: Introduction to multirate signal processing and adaptive filters
Week 14: Advanced topics and course project presentations