University of Michigan, Fall 2008

Instructor: Clayton Scott

Classroom: 1690 CSE

Time: TTh 9:00--10:30

Office: 4433 EECS

Office hours: Tuesday 2-4.

__Topics__

Hilbert spaces, L^p function spaces, Fourier
transforms, sampling theory, Fourier series, sampling rate conversion,
projections, the orthogonality principle, least squares problems,
eigenvalue decompositions, singular value decompositions. Applications
possibly including linear prediction, the Karhunen-Loeve transform,
principle component analysis, multidimensional scaling, procrustes
rotations, landmark-based image registration, wavelets and multiresolution
analysis, and other topics as time allows.

__Textbook__: *Mathematical Methods and Algorithms for
Signal Processing*, by Todd K. Moon, and Wynn C. Stirling. The book has
been placed on reserve at the AAE library. Please note that the book has
several typos. The authors maintain a list of corrections.
I advise you to go through your copy and make the corrections for relevant
chapters at the beginning of the course.

__Additional references__:

- Mallat,
*A Wavelet Tour of Signal Processing*: Good introductory chapters on Fourier transforms and sampling. - Frank Jones,
*Lebesgue Integration on Euclidean Space*: Advanced and rigorous treatment of integration, L^p spaces, Fourier tranforms, and Fourier series - Oppenhiem and Schafer,
*Discrete-Time Signal Processing*: Fourier transforms, sampling, and sampling rate conversion from at an engineering level - Proakis and Manolakis,
*Digital Signal Processing*: Fourier transforms, sampling, and sampling rate conversion from at an engineering level - Steven Roman,
*Advanced Linear Algebra*: Linear algebra at an advanced and rigorous level. - N. Young,
*An Introduction to Hilbert Space*: Accessible but rigorous treatment of the basics of normed, inner product, and Hilbert spaces.

- Homework: 50%
- Participation and attendance: 5%
- Midterm: 15% (Thursday, Oct. 9, 5 pm)
- Final exam: 30% (Friday, Dec. 12, 1:30-3:30 pm)

__Computer programming__

Some assignments may involve programming exercises in MATLAB.

__Collaboration__

All homework assignments are to be
completed on your own. You may consult with other students
in the current class regarding the conceptualization of the problem
and possible methods of solution, but you may not share details,
whether in the form of scrap work, final writeups, or computer code.
All written and programming work is to be generated by you working
alone. You are not allowed to discuss the problem set with students who
have taken the class previously, nor anyone else who has significant
knowledge of the problem set. You are also not allowed to possess, look
at, use, or in anyway derive advantage from existing solutions that
you may come across. Collaboration of any kind is not allowed on exams.

__Honor Code__

All undergraduate and graduate students are expected to abide by the
College of Engineering Honor Code as stated in the Student Handbook and
the Honor Code Pamphlet. This applies to all aspects of the course. If the
grader or I detect a violation of the Honor Code, we will
bring the matter before the Honor Council.

__Students with Disabilities__

Any student with a documented disability needing academic adjustments or
accommodations is requested to speak with me during the first two weeks of
class. All discussions will remain confidential.