ECE1635 Signals and Systems

For Fall 2009. 

This is a graduate course on signals and systems, the pre-requisite being an undergraduate course on that subject. 

The course has four goals: 

1. To do a unified treatment of Fourier analysis in Hilbert space and show the sampling theorem in this context. Fourier analysis of a signal means its expansion with respect to an orthonormal basis, usually sinusoids. The construction formula of a signal from its sample values is such an expansion. Reference: "Fourier Series and Integrals," H. Dym and H. P. McKean. Reference for Hilbert space: "Introduction to Hilbert Space," S. K. Berberian.

2. To introduce the theory of distributions so that you can make sense of, for example, the Fourier transform of a step function. References: "Distribution Theory and Transform Analysis," A. H. Zemanian; B. Osgood's EE261 Stanford course on "Fourier Transform and Applications," Lectures 13 and 14, online. The theory of distributions is due to the French mathematician Laurent Schwartz. Here's his brief biography.

3. To present a theory for optimal system design and apply it to some multirate DSP problems, such as subband coding and the playback of audio signals. References: journal papers, e.g., S. Mirabbasi, B. A. Francis, and T. Chen, "Controlling distortions in maximally decimated filter banks," IEEE Trans. Circuits and Systems, Part II, July 1997, pp. 597-600.

4. Along the way, we'll spend time on the art of mathematical writing.

Instructor

Professor Bruce Francis

Course Notes

See Downloads at the bottom of this page.

Grade components

midterm test 25%, project 25%, exam 50%

Classes

Wednesday, 9 am - 12 noon, BA4164, starting Sept 16; lecture is 9-11, tutorial is 11-12.

Tutorial problems

The format of the tutorials is that students will volunteer to present solutions to the suggested problems below. I do not post solutions.

For Sept 16	Problems 6 and 9
For Sept 23	Problems 3,5,7,8
For Sept 30	these,  solution of problem 10
For Oct 7	these
For Oct 14	Problems 16,17,18,19
For Oct 21	these
For Nov 4	The problems will be announced at the tutorial itself.
For Nov 11	Problems 25,26,28,30
For Nov 18	these
For Nov 25	Problems 41,42,43,45
For Dec 2	Problems 46,47,48,52

Lecture timetable

Sept 14	Introduction.
Sept 16	Problems 6,9. Section 1.1.
Sept 23	Part of Section 1.2.
Sept 30	Finish 1.2 and do Section 1.3; start Section 1.4.
Oct 7	Sections 1.4, 1.5, and some of 1.6.
Oct 14	Sections 1.7 and 1.10.
Oct 21	Review for test. Start Chapter 2.
Oct 28	Midterm test.
Nov 4	Finish Chapter 2.
Nov 11	Chapter 5.
Nov 18	Finish Chapter 5. Start multirate DSP; fundamentals.
Nov 25	Finish fundamentals; subband coding.
Dec 2	Last lecture; course wrap-up.
Dec 9	Projects: 9 am - noon
Dec 11	Projects: noon - 2 pm
Dec 17	Exam. 9:30 am - noon. Usual room.

Midterm test and exam

Open book: You may use the course notes, your notes from the lectures, and homework solutions you've gathered. No books. No calculator. The test is two hours long and the exam two and one-half hours. They take place in the usual lecture room.

Project

Select a recent research paper or topic that interests you and that relates to this course in some way. Check with me that the paper/topic is ok.

Read the paper or papers and prepare a 20-minute presentation, either blackboard or computer slides. Give the presentation, followed by 10 minutes of discussion. 

Prepare a write-up of 5 - 10 pages in Latex. It must be your own writing. Hand it in and email to me the source paper(s).

Grading scheme:

Presentation: 15 marks

You will try to be interesting, clear, correct, and adhere to the rules for a good presentation (see "On giving a talk").

Write-up: 10 marks

The mark will be based mostly on quality of the technical writing; that includes grammar, equation layout, etc. As a model, use the course notes.

Chosen topics 

Dec 9, 9 am - noon

Zhou	MRI
Behnad	wavelets and application to image proocessing
Wang	cooperative MIMO systems
Sacher	KKR relations
Hong	wavelets
Badr	a history of generalized functions

Dec 11, noon - 2 pm

Zhang	string stability in adaptive cruise control
Mahanta	beamforming algorithms for ultrasound imaging
Fotuohi	H-infinity control
Alamdar-Yazdi	compressed sensing

Prerequisites

An undergrad signals and systems course.

Downloads

Course notes
Errata
Test solution
Chap 5
Exam solution