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First lecture is on Wednesday,
January 5.
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Description: The aim of this
two-term course is to cover the interactions existing
between applied mathematics, namely applied and
computational harmonic analysis, approximation theory,
etc. and statistics and signal processing. Matlab will
be the scientific programming language for this
course. Assignments would typically involve a fair
amount of scientific programming in matlab together with
more classical exercises
Prerequisite: - ACM 104
(Linear algebra), ACM 105 (Real analysis) or
undergraduate equivalent or consent of instructor. Some
programming experience or some willingless to learn.
Prior knowledge of matlab not
required.
Syllabus:
- The Fourier transform; the continuous Fourier
transform, the discrete Fourier transform, FFT
- Time-frequency analysis, short-time Fourier
transform, Wigner Ville distribution
- The wavelet transform; the continuous wavelet
transform discrete wavelet transforms and orthogonal
bases of wavelets
- Wavelets and algorithms; fast wavelet
transforms, wavelet packets, cosine packets.
These transforms have natural applications in the
information sciences . The course will develop topics
in:
- Statistical estimation and applications to
signal/image denoising
- Inverse problems and applications to
signal/image reconstruction
- Linear and nonlinear approximation and
applications to data compression
Textbooks:
- Stephane
Mallat"A Wavelet Tour of Signal Processing" Second edition, Academic
Press (required)
-
Stephane Jaffard, Yves Meyer and Robert Ryan"Wavelets: Tools for
Science and Technology" SIAM, Philadelphia (optional)
- Yves
Meyer"Wavelets and Operators"Cambridge University Press (optional)
- Ingrid
Daubechies" Ten Lectures on Wavelets"SIAM, Philadelphia (optional)
Handouts: I will do my best to
post online all the handouts given in class. By the way,
Sheila Shull (217 Firestone) is a person you can contact
at any time (between 9:30am and 5pm) if you need
administrative information. Her phone number is
626-395-4560.
Teaching
Assistant and Office Hours:
Laurent Demanet, T 4-6, 210 Firestone
demanet@acm.caltech.edu
Grading:
Homework assignments: 60%
Homework will generally be distributed on Wednesdays and
due in class the following Wednesday.
There will be about 5 assignments, and your
lowest score will be dropped in the final grade.
Late homeworks will NOT be accepted for grading
(medical emergencies excepted with proof).
Final exam: 40%. There will be a
take-home final exam.
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