## ECEN 3300 - Linear Systems

Catalog Data ECEN 3300 (3). Linear Systems. Characterization of linear and time-invariant systems in time and frequency domains. Continuous time systems are analyzed using differential equations and Laplace and Fourier transforms. Discrete time systems, which can be implemented using a modern digital signal processing framework, use difference equations, z-transforms and discrete time Fourier transforms for their analysis and design. Applications of linear systems include communications, signal processing, and control systems.
Credits and Design 3 credit hours. Required core course for EE program, selected elective course for ECE program.
Prerequisite(s) ECEN 2260, Circuits as Systems
Corequisite(s) None.
Instructor(s) John Hauser, Peter Mathys, David Meyer, Francois Meyer.
Textbook Alan V. Oppenheim, Alan S. Willsky, with S. Hamid Nawab, Signals & Systems, Second Edition, Prentice Hall, 1997, ISBN 0-13-814757-4.

Course Objectives For students to:
1. Understand and use the benefits of analyzing and designing systems at a higher level that is independent of a particular hardware implementation.
2. Understand how mathematical transformations can yield insight and simplify the design and analysis of linear systems.
3. Understand the differences, similarities, limitations, and benefits of continuous and discrete time systems.
Learning Outcomes After taking this course students will be able to recognize and use the following concepts, ideas, and/or tools:
1. Linearity and time-invariance, including impulse response, step response, and convolution.
2. Continuous-time (CT) versus discrete-time (DT), including CT and DT signals and systems, differential and difference equations, and sampling and interpolation.
3. Time domain versus transformed domain, including Laplace and z-transforms, system functions, Fourier transforms, frequency response, and filter analysis/design.
Student Outcomes
 3a 3b 3c 3d 3e 3f 3g1 3g2 3h 3i 3j 3k Math/Sci Exper-iments Design Teams EngrProblems Respon-sibility Oral Written Engr SolnsImpact LLLearning Contem-porary Tools H M M M
Topics Covered
1. Continuous time (CT) and discrete time (DT) signals
2. CT and DT linear and time-invariant (LTI) systems
3. Time domain analysis of CT LTI systems
• Differential equations
• Unit impulse/step response
• Convolution
4. Transformed domain analysis of CT LTI systems
• Laplace transform, pole/zero plots
• Fourier transform, Fourier series
• System function and frequency response
5. Time domain analysis of DT LTI systems
• Difference equations
• Unit impulse/step response
• Convolution
6. Transformed domain analysis of DT LTI systems
• z-transform, pole/zero plots
• DT Fourier transform, discrete Fourier series
• System function and frequency response
7. Relationship between CT and DT signals, sampling theorem
8. Relationship between CT and DT systems, step invariance, bilinear transformation

Last revised: 05-11-11, PM, ARP.