The BRADLEY DEPARTMENT of ELECTRICAL and COMPUTER ENGINEERING

# ECE 3704 Continuous and Discrete System Theory | ECE | Virginia Tech

### Course Information

#### Description

Continuous- and discrete-time system theory. Block diagrams, feedback, and stability theory. System analysis with Bode diagrams. Discrete-time stability, difference equations, Z-transforms, transfer functions, Fourier transforms, and frequency response. Sampling of continuous systems and an introduction to digital filtering, Hands-on projects to illustrate and integrate the various continuous- and discrete-time concepts and tools.

#### Why take this course?

This course introduces the practical applications of signal and systems analysis in continuous and discrete time. Whereas 2704 introduces the fundamental mathematical tools necessary for the study of individual circuits and signals, this course broadens the applications to interconnected networks of filters, plants, and signal sources. Concepts such as stability and stabilization via feedback are important for design work in controllers, communications systems, and power systems. The study of signals and systems in discrete-time prepares the students for modern computer implementations, digital filtering, and numerical methods. The various concepts are illustrated and integrated by means of a couple of hands-on projects (one in the continuous-time domain, another in the discrete-time domain).

Required for all EE majors; Technical elective for CPE majors

#### Prerequisites

C- or better in 2704

This course requires the students to know the transform methods necessary for block-diagram level systems analysis. Many of the methods require knowledge of calculus and complex analysis normally taught during the course of the sophomore year. Some applications require an understanding of random variables. Because students do not normally have all these tools prior to the junior year, this course is designated as junior level.

### Major Measurable Learning Objectives

• Describe general systems with the use of block diagrams and signal flow graphs
• Analyze the performance and stability of interconnected linear systems, including feedback systems
• Construct Bode plots for systems and interpret these plots to predict system responses.
• Solve difference equations by using Z-transforms
• Analyze discrete-time systems with Z-transforms and transfer functions.
• Sample continuous-time systems to create a discrete-time system model
• Compute discrete-time Fourier transforms and use fast Fourier transforms
• Make experimental measurements on a continuous-time physical system and compare the results to time and frequency-domain analytical results
• Make experimental measurements on a discrete-time physical system and compare the results to time and frequency-domain analytical results.

### Course Topics

#### Percentage of Course

1. Review of stability 5%
2. Block diagrams and signal flow graphs 10%
3. Introduction to state equations 5%
4. Bode plots 5%
5. Application of continuous-time concepts in a hands-on assignment 5%
6. Difference equations and Z-transforms 15%
7. Sampling of continuous-time systems 10%
8. Z-domain analysis, transfer functions, stability, and frequency response 15%
9. Discrete Fourier transforms and FFTs 10%
10. Introduction to digital filtering 10%
11. Application of discrete-time concepts in a hands-on assignment 10%