EECS 551: Mathematical Methods for Signal Processing.

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.

Complete lecture notes

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.