Overview

This course deals with signals, systems, and transforms, from their theoretical mathematical foundations to practical implementation in circuits and computer algorithms. Fundamentally important, ELEC 301 acts as a bridge between the introductory ELEC 241/2 and more advanced courses such as ELEC 302, 430, 431, 437, 439, ...

Goals

At the conclusion of ELEC 301, you should have a solid understanding of the mathematics of

• signals in continuous and discrete time
• linear time invariant systems and convolution
• Fourier transforms

and how these tools are used in real applications.

---

Prerequisites

ELEC 241 Fundamentals of Electrical Engineering I (home page, Connexions course)

ELEC 242 Fundamentals of Electrical Engineering II (home page)

CAAM 335 Matrix Analysis (home page, Connexions course)

MATH 211 Ordinary Differential Equations and Linear Algebra (optional) (home page)

Textbook

Elec 301 textbook on Connexions

Recommended Further Reading (these and more books on two-hour reserve in the library)

G. Strang, Introduction to Linear Algebra, Wellesley-Cambridge Press

Z. Karu, Signals and Systems Made Ridiculously Simple, ZiZi Press, zizipress.com

M. J. Roberts, Signals and Systems, McGraw-Hill, 2004

A. Oppenheim and A. Willsky, Signals and Systems, Prentice-Hall, 2000

S. Haykin and B. Van Veen, Signals and Systems, Wiley, 1999

B. P. Lathi, Signal Processing and Linear Systems, Berkeley Cambridge Press, ISBN 0-941413-35-7, 1998.
(He has several very similar books with similar titles; they are all good.)

Who Is Fourier? A Mathematical Adventure, Transnational College of LEX, ISBN 0964350408.

And for the ambitious and mathematically inclined, the first five chapters of:
N. Young, An Introduction to Hilbert Space, Cambridge Mathematical Textbooks, 1988

Grading

30% - Test 1

30% - Test 2 ("Final")

17% - Homework

17% - Group Project

6% - Notebook and classroom participation

ALL assignments must be completed, or you will receive an incomplete.

Study Groups

To encourage group learning, students are expected to form study groups of 3-4 members. Homework (but not the Individual Projects) may be completed in groups. On a weekly basis, each group will turn in (with homework solutions) a report on their activities and a summary of the material covered in the previous week of class. Of course, group work should not substitute for study on your own; at test time, only a pencil will accompany you.

Homework Policy

Homework will be posted on the class web page each week, and is due at 5pm on the due date (typically Friday afternoon). Please slip your homework under the door at DH2121. After the due date, but before solutions are handed out, homework can be turned in for 50% credit. After solutions are handed out, 0% credit will be issued. However, all assignments must be turned in, or an incomplete grade will be assigned. You are encouraged to work in groups on homework problems, as long as you ultimately formulate your own solution, but homework will be graded on an individual basis, that is, each student turns in their own set of solutions. You are expected to understand any solution you turn in.

Homework, tests, and solutions from previous offerings of this course are off limits, under the honor code.

Individual Projects

At various times though the semester, we will accelerate our progress by an in-depth project on a specific topic. These projects must be completed individually and not in a group.

Group Project

Towards the end of the semester, students will form groups of 3-4 members and complete a project applying the concepts they have learned in the class. Groups will write a project report in Connexions and present their projects in a poster session (think "science fair") open to the public. More info on the project.

Suggestions

Remember the big picture.

Read the Connexions notes and explore the connections.

Learn linear algebra.

Prepare your own summaries from texts and notes.

Work in groups for homework and studying, and explain the main concepts to each other.

Know and cater to your learning style.

This course is not about solving specific problems but about developing a problem solving process that you can apply to general problems.

Students with disabilities

Any student with a documented disability needing academic adjustments or accommodations is requested to speak with me during the first two weeks of class. All discussions will remain confidential. Students with disabilities should also contact Disabled Student Services in the Ley Student Center.

Introduction

Motivation: Why signal processing is important

Mathematical preliminaries

A. Signal Basics

Types of signals (continuous-time, discrete-time, analog, digital, ...)

Elementary signals

B. Time-Domain Analysis of Continous-Time Systems

Types of systems

Linear time invariant (LTI) systems

Convolution

C. Time-Domain Analysis of Discrete-Time Systems

Linear time invariant (LTI) systems

Convolution

D. Continuous-Time Fourier Series (CTFS)

CTFS derivation

CTFS properties

Convergence

E. Discrete Fourier Transform (DFT)

CTFS derivation

CTFS properties

Fast Fourier Transform (FFT)

F. Mathematical Foundation for CTFS and DFT

Linear vector spaces and linear algebra

Eigenanalysis

Hilbert spaces

G. Discrete-Time Fourier Transform (DTFT)

CTFT derivation

CTFT properties

CTFT, convolution, and LTI systems

Convergence

H. Continuous-Time Fourier Transform (CTFT)

DTFT derivation

DTFT properties

DTFT, convolution, and LTI systems

Convergence

I. Sampling and Reconstruction

Sampling and the Nyquist theorem

Sinc interpolation

Practical reconstruction

J. Laplace Transform (time permitting)

Region of convergence

Implementing continuous-time systems

K. z Transform (time permitting)

Region of convergence

Implementing discrete-time systems

L. Discrete-Time Filter Design (time permitting)

Filter design problem

Remez exchange algortithm

Back to Elec 301 homepage