Math 519 - Harmonic Analysis: Introduction to Time-Frequency analysis - Fall 2002
Room: Cupples I, Room 199
Time: TuTh 1:00-2:30
LINKS:
-
Homework Assignments
[.ps],
[.dvi]
TOPICS: Uncertainty Principle.
Short-Time Fourier Transform. Quadratic Time-frequency representations.
Frame theory. Theory of Gabor frames. Theory of Affine frames (Wavelet frames).
Shift-invariant spaces. Pseudodifferential Operators.
TEXTBOOK: Most of the lectures will follow:
K. Groechenig, Foundations of Time-Frequency Analysis, Birkauser.
Other useful reference is H.G. Feichtinger and T, Strohmer Gabor Analysis
and Algorithms . Additional material will be provided in class.
HOMEWORK: Homework problems will be assigned each week and posted
on this page at the link above.
Please, return your solutions to the instructor by the due date by the
end of class.
Please, make special effort to make your proofs rigorous and
easy to follow. Your homework
will be judged for correctness and clarity.
EXAMINATIONS: There will be one MIDTERM EXAM on Tue October 15.
The (take home) FINAL EXAM will be handed in on Tue December 8.
GRADING:
The homework
will count 35% towards the final grade, the midterm exam will
count 30% and the final exam will count 35% towards the final grade.
-
OFFICE HOURS: My office is in Cupples I, room 112 A. Office hours
are Tuesday and Thursday 2:30-3:30 and . If you want to reach me or schedule an
appointment at a different time, please, talk to me at the end of the class
or contact me by e-mail at: dlabate@math.wustl.edu
-
- (Tentative) OUTLINE OF THE COURSE:
- Basic Fourier Analysis (1-2 Weeks)
- Uncertainty Principle (1 Week)
- Short-Time Fourier Transform (2 Weeks)
- Quadratic Time-Frequency Representations (1 Week)
- General Frame Theory (1 Week)
- Theory of Gabor Frames (2-3 Weeks)
- Unified Theory of Reproducing Systems (1 Week)
- Modulation Spaces (1 Week)
- Gabor Analysis of Modulation Spaces (1 Week)
- Pseudodifferential Operators (1 Week)
-
-
LINKS:
-
Top of
this page
-
Last modified August 6, 2002