Math 152: Fourier and Wavelet Series, Winter 2018

TuTh 9:30-10:50am, Center 109

General Description

This course covers useful bases for representing signals and functions, with an emphasis on both theory and computation. The goal of the course is to introduce the student to some basic concepts of Fourier analysis and wavelet theory, as well as to some of their applications in engineering (specifically to signal processing). Topics include: Fourier series, Discrete Fourier analysis, the Haar system, Multiresolution Analysis and wavelets bases, and frames, with some discussion of the Fourier transform and Shannon sampling theorem. A non-complete list of applications of these techniques are audio and image analysis, multiresolution analysis, filters, and wavelet-based image compression like JPEG2000.

Textbook

A. Boggess & F. J. Narcowich, A First Course in Wavelets with Fourier Analysis, Prentice Hall, (2001).

Additional textbook: David F. Walnut, An Introduction to Wavelet Analysis, Birkhauser Boston (2002).

Tentative Course Outline and Homework

Course Calendar

Final is scheduled for Tuesday 3-20 from 8-11am

Syllabus

A full syllabuls for the course can be found here

Announcements

  • Homework 7 is posted here. The due date is Thursday 3-15 at noon.

  • Midterm 2 will be 3-6 in class. A study guide can be found here.

  • Homework 6 is posted here. The due date is Thursday 3-1 at noon.

  • Homework 5 is posted here. The due date is Thursday 2-22 at noon.

  • Midterm 1 will be 2-8 in class. A study guide can be found here.

  • Homework 4 is posted here. The due date is Thursday 2-8 at noon.

  • Homework 3 is posted here. The due date is Thursday 2-1 at noon.

  • Homework 2 is posted here. The due date is Thursday 1-25 at noon.

  • Homework 1 is posted here. The due date is Thursday 1-18 at noon.

Class Notes

  • The folder of all class notes can be found here.

Instructor: Alex Cloninger

  • Email: acloninger (at) ucsd (dot) edu

  • Phone: 534-4889

  • Office: AP&M 5747 (5th floor annex)

  • Office hours: Wednesday 9am-12pm, in AP&M 5747

TAs: Jingwen Liang

  • Email: jil343 (at) ucsd (dot) edu

  • Office: AP&M 6442

  • Office hours: Tuesday 1-3pm, in AP&M 6442

TAs: Eric Evert

  • Email: eevert (at) ucsd (dot) edu

  • Office: SDSC E293

  • Office hours: Wednesday 3-5pm, in SDSC E293