ENEE 222: Elements of Discrete Signal Analysis

Course Information

Important ENEE 222 links

• Announcements
• Homework
• Lab
• References
• Slides

Instructor Info

TAs

Office Hours

Course Objectives

• Master basic tools from linear algebra that are particularly useful in modeling real-world signals and systems.
• Learn key concepts in the frequency analysis of signals, in both discrete and continuous time.
• Gain some understanding of what a digital filter is, how it is implemented, and how it can be used in signal processing.
• Become familiar with MATLAB, a powerful computational package, and some of its applications to signal and image processing.

Outline

1. Numbers, Vectors and Signals
   1. Review of complex numbers
   2. Real-valued and complex-valued sinusoids in continuous time
   3. Discrete-time sinusoids
   4. Sampling of sinusoids; aliasing
2. Matrices and Systems
   1. Linear transformations and linear systems
   2. Matrix of a linear transformation; systems view of matrix multiplication
   3. Miscellaneous matrix operations
   4. Nonsingular matrices and their inverse
   5. Solution of simultaneous linear equations via Gaussian elimination
   6. Inner products, distances, projections
   7. Orthogonality and signal approximation
   8. Complex-valued signals and their approximation
3. Signals in the Frequency Domain
   1. Orthogonality of Fourier sinusoidal vectors
   2. The discrete Fourier transform (DFT) and its inverse; significance in the representation and approximation of signal vectors
   3. Basic properties of the DFT
   4. Matrix-based approach to the DFT and its inverse
   5. Signal transformations and the DFT
   6. Combinations and extensions of signals; the duality between convolution and multiplication
   7. Detection of sinusoids using the DFT: theory
   8. Periodic extensions of signal vectors; analogy to continuous-time periodic signals and sums of harmonically related sinusoids
   9. Orthogonality of Fourier sinusoids in continuous time; Fourier series
   10. Fourier series coefficients: properties, analogies to DFT
4. Linear Filters
   1. Examples of finite impulse response (FIR) filters; linearity, time-invariance, frequency selection
   2. Response of FIR filters to sinusoidal, periodic and exponential inputs; frequency response and system function
   3. Classification of frequency selective-filters
   4. Convolution in discrete time; practical implementation of FIR filters
   5. Filters in cascade; convolution as multiplication in the z-domain

Homework

Math is a “Learn it By Doing it” subject. The homework assignments are one of the most important part of the course: you will not be able to succeed in the exams without doing the homeworks. You should be able to complete the assignments without significant assistance from the instructors.

Some homework problems will require the use of MATLAB. Unless otherwise stated, you should submit all MATLAB commands (i.e., code) used, as well as your results.

Typically, homework problems will be assigned every week. It is possible that only some of the problems will be graded, but solutions will always be made available.

All homework assignments are on ELMS, and all completed homework assignments should be turned in at the beginning of class on their due date.

Solution sets will be handed out as soon as reasonably possible after the homework is due. No credit will be given for any homework turned in after the solution set has been made available.

Additionally, some questions on the homework assignments should not be turned in, but their solutions are provided. Despite this, you should take these questions very seriously, in terms of required knowledge for the course and in terms of exam questions.

Late Policy: not turned in at the beginning of class = 10% off, 1 day late = 25% off, 2 days late = 50% off.

Lab

The lab has a dual purpose: (a) providing essential training in MATLAB and (b) illustrating some of the most important applications of the theory taught in class. In each session you will go through a script that includes MATLAB code, which you will run on the lab workstation. Almost every lab will have an assignment due on the following week.

Lab topics are typically not tied to the current lecture topics.

Each MATLAB assignment (including quizzes if given) will be worth a different number of points depending on its difficulty. Attendance at labs is mandatory, and unexcused absences may result in a proportional reduction of the lab grade.

All lab assignments are on ELMS, and all completed lab assignments should be uploaded there on their due date.

Discussion Sections

Discussion sections will be run by a TA, during which selected homework problems, as well as other problems (posted on ELMS), may be discussed. Students are also encouraged to ask clarifying questions concerning the class material.

Quizzes

At lab or at discussion section, students may be asked to take an unannounced written quiz wherein they will be required to solve, without notes, a problem closely related to one already assigned. Several quizzes may be given during the course of the semester.

Exams

• 1^st Exam: Tuesday, March 10
• 2^nd Exam: Tuesday, April 21
• Final Exam: Monday, May 18 10:30am-12:30pm

There will be no make-up exams. See Grading next for missed exam policies.

Grading

Homework, Labs, Quizzes, Particpation, etc.	30%
1st exam	20%
2nd exam	20%
Final exam	30%

In the case of a 1^st or 2^nd exam missed for a legitimate reason, the other exam and the final will be re-weighted, if you give notice to the professor within 24 hours of the missed exam:

1st or 2nd exam:	28% [ = (20%/(20%+30%)) x 70% ]
Final exam:	42% [ = (30%/(20%+30%)) x 70% ]

If you do not request permission for this modified grading within 24 hours of the missed exam, you will receive zero for the missed exam.

MATLAB

MATLAB is required. While you are encouraged to purchase your own copy (the student version is fine), it is not required that you do so. If you do not, however, you will still need to be able to run and print from MATLAB outside of class. There are many computers around campus with MATLAB; the campus OIT web system can tell you which open labs have Matlab.

Academic Honesty

Discussing homework problems, and other ideas, with others is encouraged,

but,

your final write-up must be your own work and cannot include anyone else's work.

The University of Maryland, College Park has a nationally recognized Code of Academic Integrity, administered by the Student Honor Council. This code sets standards for academic integrity at Maryland for all undergraduate and graduate students. As a student you are responsible for upholding these standards for this course. It is very important for you to be aware of the consequences of cheating, fabrication, facilitation, and plagiarism. For more information on the Code of Academic Integrity or the Student Honor Council, please visit http://shc.umd.edu/SHC/.

To be clear and explicit, academic dishonesty includes copying homework answers from any other student's or non-student's work, from any solution sets, from any book, from the web, or any other related source.

Instances of academic dishonesty will be referred to the Office of Judicial Programs.

Learning Assistance Service

If you are experiencing difficulties in keeping up with the academic demands of your courses, you should know about the Learning Assistance Service, 2201 Shoemaker Building, 301-314-7613, or http://www.inform.umd.edu/LASRV/. Their educational counselors can help with time management, reading, math learning skills, note-taking and exam preparation skills. All their services are free to UMD students.

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