Math 118 - Fourier Analysis, Wavelets and Signal Processing - Spring 2010

Lecture: Tuesday and Thursday 12:30-2:00, 75 Evans

Course Home Page: http://math.berkeley.edu/~strain/118.S10/index.html

Professor: J Strain, strain@math.berkeley.edu

Office Hours week of May 2-7: Tuesday 1:00-2:00 pm and Wednesday 10:00-11:00 am, 1099 Evans.

Office Hours week of May 9-14: Tuesday 1:00-2:00 pm, Wednesday 11:00-12:00 am, and Thursday 1:00-2:00 pm, 1099 Evans.

Description: Introduction to signal processing including Fourier analysis and wavelets. Theory, algorithms, and applications to one-dimensional signals and multidimensional images.

Prerequisites: Math 53 and 54 or equivalent knowledge of calculus and linear algebra.

Required Text: Albert Boggess and Francis J. Narcowich, A First Course in Wavelets with Fourier Analysis, second edition (Wiley, 2009).

Other Recommended Reading:

  • G. Kaiser, A Friendly Guide to Wavelets
  • E. Hernandez and G. Weiss, A First Course on Wavelets
  • S. Mallat, A Wavelet Tour of Signal Processing, Third Edition
  • Syllabus: This course will cover the basic mathematical theory and practical applications of Fourier analysis and wavelets, including one-dimensional signal processing and multi-dimensional image processing:

  • Fourier series, orthogonal systems, sampling and aliasing, FFT
  • Fourier integrals and transforms, linear filters, sampling theorem, uncertainty principle, two-dimensional Fourier analysis
  • Haar wavelets, Daubechies wavelets, scaling functions, multiresolution analysis, filter banks
  • approximation with wavelets, linear and nonlinear techniques, image approximation and adaptive basis selection, edge detection
  • transform coding, signal compression, quantization, high bit-rate compression, image and video compression
  • Grading: 50% for 10 best of 12 weekly problem sets, 20% midterm, 30% final

    Exams:

  • Midterm: Tuesday, March 9 in class.
  • Final Exam: Thursday, May 13, 3-6 pm, 9 Evans.
  • Special accomodations: Students requiring special accomodations for exams should contact the instructor well in advance of the first exam so that suitable arrangements can be made.

    Announcements and Handouts

  • Sample final exam problems are available here
  • Solutions to Problem Set #10 are available here
  • Solutions to Problem Set #9 are available here
  • Solutions to Problem Set #8 are available here
  • Solutions to Problem Set #7 are available here
  • Handout #4 (A survey paper by Slepian on band and time limited functions) here
  • Solutions to Problem Set #6 are available here
  • Solutions to the midterm are available here
  • Lectures will move to 122 Barrows for two weeks, beginning Tuesday 16 March.
  • Solutions to Problem Set #5 are available here
  • Handout #3 (including problems 1-2 for Problem Set 7) is available here
  • Extra office hours Friday 5 March, 2-4 pm in 35 Evans. The midterm (Tuesday 9 March, in class) will be open book and open notes.
  • Handout #2 (including problems 1-4 for Problem Set 7) is available here
  • Solutions to Problem Set #4 are available here
  • Reading assignments and problem sets for the next few weeks are updated here
  • Solutions to Problem Set #3 are available here
  • The classic proof for pointwise convergence of Fourier series is here A similar but much more abstract proof for the Fourier transform is here
  • Solutions to Problem Set #2 are available here
  • Solutions to Problem Set #1 are available here
  • Handout #1 (including problems 1-5 for Problem Set 3) is available here
  • Reading assignments and problem sets for the first few weeks are available here