Course Description

Goals

A student who completes this course should gain three key abilities:

• Calculate the qualitative shape of a Fourier Transforms as a quick mental step in reasoning about a signal processing problem.
  
  
• Critique applications of Fourier Transforms and related mathematical tools to signal processing problems, particularly recognizing common conceptual errors.
  
  
• Use the extensive literature on transforms effectively in future work.

Summary of Content

We study the use of mathematical transforms to reveal the frequency or scale structure of signals, such as vibrations and visual scenes. We cover the continuous and discrete Fourier, wavelet, Laplace, and Z transforms, and others if time permits. We do not prove the relevant mathematical theorems: we state them and use them to calculate and reason rigorously about interesting properties of signals, and about transformations of signals by filters.

The text provides most of the basic information. We go well beyond the text in exploring the pitfalls of naive applications of transforms. A student who completes the course successfully can apply mathematical transforms entirely correctly, paying attention to phase as well as magnitude, and recognizing the confusion introduced by framing and discretization. Finally, we study recent research articles on frameless time-frequency analysis.

Prerequisites

Students entering the course must have a basic familiarity with the differential and integral calculus, sine and cosine functions, addition, subtraction, multiplication, division and exponentiation of complex numbers. Deep mathematical knowledge or virtuosic ability is not required. We will review the mathematical prerequisites very briefly to fill in gaps.

Students are not required to program in a general-purpose programming language. They are required to perform computational exercises using an interactive numerical system such as Octave (Matlab) or Scilab.

Electronic Communications

We use three forms of electronic communication in CMSC 34910: shared files, the World Wide Web (WWW), and electronic mail. Use of these forms of communication is required.

• You must provide a publicly readable directory named CMSC34910 in your home directory on the CS computer file system. I will collect links to these in my own public class directory: /stage/archive/<year>/<quarter>/34910-1/Roster. Store all online materials that you develop for this class in your public directory, so that we can share work. I also encourage you to develop your own WWWeb materials.
  
  
• I will also provide course materials in a form accessible through WWW, at the URL http://www.classes.cs.uchicago.edu/classes/<year>/<quarter>/34910-1/. You may view this material with any standards-compliant Web browser from graphics terminals and Lynx from character terminals.
  
  
• There is a public class discussion, consisting of comments attached by students and the instructor to various online course materials. All questions and comments that are not personal or confidential should be added to this discussion, so that everyone can benefit from them.
  
  
• Personal discussions, particularly about grading, and requests for appointments, may be addressed to me by electronic mail at odonnell@cs. These will normally be the only types of correspondence that should be made by electronic mail.

You must check for new information in the WWW materials at least three times a week: on Wednesday, Friday, and the weekend. I recommend that you check it daily, particularly the class discussion.

Outline of Topics

Coming soon.

Grading Scheme

Coming soon.

Student evaluations from previous years

None, because this is the first year of the course.

Copyright Michael J. O'Donnell <michael_odonnell@acm.org>. Licensed for free use.
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