## EECS 222 - Fundamentals of Signals and Systems

**CATALOG DESCRIPTION: **Comprehensive introduction to analysis of continuous and discrete-time signals and systems. Linear time-invariant systems, convolution; Fourier series representations of periodic signals; Continuous time and discrete time Fourier transforms; Laplace transform; z-transform.

**REQUIRED TEXT: **A. V. Oppenheim and A. S. Willsky (with S. H. Nawab), *Signals and Systems *, Prentice Hall, 2 nd edition, 1997.

**COURSE COORDINATOR: **Aggelos K. Katsaggelos

**COURSE GOALS: **To provide an introduction to sophomores in the field of electrical engineering to the fundamental concepts in the sub-area of signals and systems. This course will be one of five fundamentals courses required of all electrical engineering majors. Another goal is to prepare students to take some more advanced courses in the area of signals and systems, namely in signal and image processing, and networks, communication and control.

**PREREQUISITES: **EECS 202

**PREREQUISITES BY TOPIC: **Basic introduction to electrical engineering concepts **.**

**DETAILED COURSE TOPICS:**

1. Signals and Systems (5 lectures): Continuous-time and discrete-time signals; commonly encountered signals; unit impulse and unit step functions; sampling and aliasing; continuous-time and discrete-time systems; basic properties.

2. Linear Time-Invariant (LTI) Systems (5 lectures): The convolution sum; the convolution integral; properties; difference and differential equations.

3. Fourier Series Representation of Periodic Signals (4 lectures): Continuous and discrete-time periodic signals; properties of continuous and discrete-time Fourier series; Fourier series and LTI

systems.

4. Continuous-Time Fourier Transform (4 lectures): Properties; convolution and multiplication properties.

5. Discrete-Time Fourier Transform (4 lectures): Properties; convolution and multiplication properties.

6. Laplace Transform (3 lectures): Region of convergence; inverse Laplace transform; properties; analysis of LTI systems using the Laplace transform.

7. z-Transform (3 lectures): Region of convergence; inverse z-transform; properties; analysis of LTI systems using the z-transform.

**COMPUTER USAGE: **Programming assignments using MATLAB on PCs to reinforce concepts learned in class.

**HOMEWORK ASSIGNMENTS:**

Homeworks to reinforce the concepts learned in class **.**

**LABORATORY PROJECTS: **None

**GRADES:**

Homeworks – 30%

Exams – 70%

**COURSE OBJECTIVES: **When a student completes this course, s/he should be able to:

• Understand the fundamentals of the systems sub-area within the field of electrical engineering so as to get excited about the area.

• Understand linear time invariant systems.

• Apply the concepts of Fourier series representations to analyze continuous and discrete time periodic signals.

• Understand and apply the continuous time Fourier transform, discrete time Fourier transform, Laplace transform, and z-Transform, to the analysis and description of LTI continuous and discrete-time systems.

• To take advanced courses in the systems area.

**ABET CONTENT CATEGORY: **25% Math and Basic Science, 75% Engineering.