Computational Fourier Transforms course webpage
Policy on grading and syllabus for SM472
Spriing 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:
-
Each student produces a written report resulting from several iterations
of review and editing.
-
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
(here 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. Attendence and presentation
at the SASMC conference may replace the class presentation, if the student
wishes.
Possible topics:
-
DCT and DST
-
Applications of FTs to DEs
-
Convolution and applications
-
Shannon's sampling theorem
-
Parseval's identity and Poisson's summation formula
-
Filters and FTs
-
FFTs
-
DWTs and wavelets.
-
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),
class notes (html)
Additional resource:
Articles on Fourier series.
(If this is dead, here is the local version, posted here by permission:
Articles on Fourier series.)
SAGE examples
Created 1-2-2007.
Last modified 5-2-2007 by
wdj