Syllabus Detail

Department of Mathematics Syllabus

This syllabus is advisory only. For details on a particular instructor's syllabus (including books), consult the instructor's course page. For a list of what courses are being taught each quarter, refer to the Courses page.

MAT 271: Applied and Computational Harmonic Analysis

Approved: 2009-11-01, Naoki Saito and Thomas Strohmer
Winter, alternate years; 4 units; lecture/term paper or discussion
Suggested Textbook: (actual textbook varies by instructor; check your instructor)
No required textbook. Instructor will supply info about some key articles to read during the course. See below for optional reference books.
(MAT 127B or MAT 201C) and (MAT 128B or MAT 167) and (MAT 129 or equivalent), or consent of instructor.
Course Description:
Introduction to mathematical basic building blocks (wavelets, local Fourier basis, and their relatives) useful for diverse fields (signal and image processing, numerical analysis, and statistics). Emphasis on the connection between the continuum and the discrete worlds.
Suggested Schedule:
Lectures Sections Topics/Comments

Fourier series and transforms, the Shannon sampling theorem

Discrete Fourier, cosine, and sine transforms

Karhunen-Loeve transform and principal component analysis

Frame theory

Frames and sparse representations

The uncertainty principle

Windowed (or short-time) Fourier transform

Gabor (Weyl-Heisenberg) systems

Continuous and Discrete wavelet algorithms

Multiresolution analysis and fast wavelet algorithms

Applications to signal/image processing and communication
Additional Notes:
Optional reference books:
  • S. Mallat, A Wavelet Tour of Signal Processing, 3rd Ed., Academic Press, 2009.
  • I. Daubechies, Ten Lectures on Wavelets, SIAM, 1992.
  • S. Jaffard, Y. Meyer, and R. Ryan, Wavelets: Tools for Science and Technology, SIAM, 2001.
  • K. Groechenig, Foundations of Time-Frequency Analysis, Birkhauser, 2001.
  • W. L. Briggs and V. E. Henson, The DFT: An Owner's Manual for the Discrete Fourier Transform, SIAM, 1995.