David Joyner, Math Department

# Computational Fourier Transforms course

## Computational Fourier Transforms course webpage

Policy on grading and syllabus for capstone course SM472
Spring 2006-2007

Text: James Walker, Fast Fourier Transforms, 2nd edition, CRC Press, 1996. This course is designed to cap, complete and finish the major. Specific requirements for the course are:
1. Each student produces a written report resulting from several iterations of review and editing.
2. Each student gives several oral presentations.
This course will require a 15 page (typed) paper, completed homework assignments, and several presentations. The paper must be clearly and carefully written, containing precise definitions, theorems and rigorous proofs.
• 6 week grade: This will be based on
• homework done,
• a 5 page outline of your paper (some examples: Culver, Hess, Nelan and Tyler are good ones to try to base yours on), and
• one 10-15 minute presentation (seen in the Fourier Transforms and Convolutions document is an example - a PowerPoint presentation converted to pdf).
• 12 week grade: This will be based on homework done, a 10 page outline of your paper (some examples: Culver, Eubanks, Nelan, Tyler), and one 20-30 minute presentation.
• 16 week grade: This will be based on homework done, the 15 page final version of your paper, and the final presentation. Attendance and presentation at the SASMC conference may replace the class presentation, if the student wishes.
Possible topics:
1. DCT and DST
2. Applications of FTs to DEs
3. Convolution and applications
4. Shannon's sampling theorem
5. Parseval's identity and Poisson's summation formula
6. Filters and FTs
7. FFTs
8. DWTs and wavelets.
9. Statistics (based on the extra credit exercises from ch 5).
Syllabus and hmwk:
• chapter 1: exercises: 1-4, 6-7, 9-12, 14-15, 21, 23-27
• chapter 2: exercises 1-3, 6, 8-9
• chapter 3: extra credit exercises: 1-3
• chapter 5: exercises: 1, 7, 16, 23, 49-50
extra credit: 39-48, 62-63
class notes (pdf)