### Table of Contents

# Syllabus - ECE 671

## Introduction

The objective of this course is to help you develop the mathematical skills needed to pursue research in the general area of signals and systems. Research topics in this area include (1) signal and image processing (2) communication systems (3) control systems. While there is a lot of hype about the half life of knowledge in electrical engineering being about 2-3 years, the material introduced in the course is timeless, in the sense that the course covers general principles that will never go out of date. The material covered in this course is to signals and systems, what Maxwell's equations are to electro-magnetics and what Newton's laws are to dynamics. During the 60's, 70's and 80's, signal processing and control solutions were usually implemented in analog circuitry. With the advent of powerful computing technology, signal processing solutions are now almost always implemented on a digital computer. The flexibility that comes from programming digital hardware makes it possible to implement algorithms that were impossible to implement in analog circuitry. As this trend continues, efficient algorithm design will become one of the most critical design steps in engineering systems. While the ability to write computer code is important, it does not enable an engineer to design good algorithms. Writing code is similar to the ability to use a word processor. Being able to use a word processor does not guarantee that the writer will produce good prose. Good prose comes from learning the principles of good writing (which have nothing to do with typing). Similarly, if you want to design good algorithms, the kind that make products successful, and that guarantee the engineer a good stable salary, you need to understand the principles of good algorithm design. Many of these principles are mathematical in nature. The objective of this course is teach the mathematical techniques that will allow you to design state-of-the-art signal processing algorithms over the lifetime of your career (a very ambitious objective).

Many of you will find this course mathematically challenging. There is a great deal of systems engineering that cannot be mastered without some mathematical sophistication. Mathematical maturity can be obtained by anyone willing to work at it. This course offers you an opportunity to refine your mathematical and analytical skills and if you work hard at the material you will be rewarded by increased engineering insight and skill.

## Learning Outcomes

The objective of the course is to help you develop the following technical skills.

- Develop a foundation of basic linear algebra concepts useful in modern signal processing, including vector spaces, norms and inner products, orthogonality, linear operators, matrix inverses, approximations in vector spaces, eigenvalues, and eigenvectors;
- Understand advanced topics in linear algebra and some of their applications to real-world engineering problems, including important matrix factorization techniques, singular value decomposition, and special matrices and their applications;
- Develop a basic familiarity with the theory of constrained optimization.

## Text

Moon & Stirling, *Mathematical Methods and Algorithms,* Prentice Hall, 2000.

## Prerequisites

Graduate level status. We assume undergraduate courses in linear algebra, differential equations, and calculus. An introductory signal processing course like ECE 380 will be helpful.

## Grading

Final grades in the course will be based on the following distribution:

Homework | 20% |

Midterm 1 | 20% |

Midterm 2 | 20% |

Project | 20% |

Final | 20% |

### Homework

Homework will be assigned weekly and is due in class on the day indicated on the schedule. Late homework will not be accepted. The homework will not be graded: full credit will be given if the problem has been attempted. The solutions to the homework will be placed on the web after it is due. You are strongly encouraged to look at the homework solution to make sure that you understand the material.

### Midterm Exam

There will be two take-home midterm exams. The first midterm will be handed out October 3 and will be due at the beginning of class on October 7. The second midterm will be handed out on November 7 and will be due at the beginning of class on November 11.

### Project

A student project will be due on the last day of class. Each student is responsible for defining their own project. The project should show an interesting application of the ideas discussed in the class.

The grade for the project consists of two parts:

- A one page project proposal is due to the instructor on November 7.
- A written project description due on December 8, the last day of class. The project description should not be longer than 10 double space pages, including figures.

### Final Exam

The final exam will be an in class, three hour, open book, open note, comprehensive exam. The scheduled date is Monday, December 12, 11:00 a.m. to 2:00 p.m

### Teacher Evaluations

At the end of the semester I will send out information about on-line teacher evaluations. Teacher evaluations are an important part of faculty evaluation and development. The success of the program depends upon student participation. To encourage participation, I will give 5 extra credit points on the final exam to those who fill out the form. To let me know that you have filled out the form, either (1) check the box that allows your name to be released on the evaluation form (note that names will not be correlated with evaluations), or (2) send me an email indicating that you have filled out the on-line form.

## Miscellaneous

### Office Hours

Please respect my office hours. If they are not accommodating, make an appointment with me via email.

### Honor Code Standards

In keeping with the principles of the BYU Honor Code, students are expected to be honest in all of their academic work. Academic honesty means, most fundamentally, that any work you present as your own must in fact be your own work and not that of another. Violations of this principle may result in a failing grade in the course and additional disciplinary action by the university.

Students are also expected to adhere to the Dress and Grooming Standards. Adherence demonstrates respect for yourself and others and supports an effective learning and working environment. It is the university’s expectation, and my own expectation in class, that each student will abide by all Honor Code standards. Please contact the Honor Code Office (4440 WSC, 422-2847, hco@byu.edu) if you have questions about those standards.

### Preventing Sexual Discrimination or Harassment

Sexual discrimination or harassment (including student-to-student harassment) is prohibited both by the law and by Brigham Young University policy. If you feel you are being subjected to sexual discrimination or harassment, please bring your concerns to the professor. Alternatively, you may lodge a complaint with the Equal Employment Office (D-240C ASB, 422-5895, eeo@byu.edu) or with the Honor Code Office (4440 WSC, 422-2847, hco@byu.edu)

### Students with Disabilities

If you have a disability that may affect your performance in this course, you should get in touch with the office of University Accessibility Center (1520 WSC, 422-2767, uac@byu.edu). This office can evaluate your disability and assist the professor in arranging for reasonable accommodations.