**Instructor:** Jon Wilkening

**Lectures:** TTh 11-12:30, Room 71 Evans

**Course Control Number:** 54491

**Office:** 1091 Evans

**Office Hours:** Tues 9:45-10:45, Tues 3-4

**Prerequisites:** Math 53 and 54 or equivalent

**Required Text:** A First Course in Wavelets with Fourier Analysis, by Boggess and Narcowich

**Recommended Reading:**

Wavelets Made Easy, by Yves Nievergelt

A Wavelet Tour of Signal Processing, by Stephane Mallat

**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

**Course Webpage:** http://math.berkeley.edu/~wilken/118.S09

**Grading:**

homework: | 50% | |

Midterm: | 20% | Tues, March 10, in class |

Final exam: | 30% | Tues, May 19, 8-11 AM, 4 Evans. (2 pages of notes allowed.) |

**Homework:** 8-10 assignments, some involving programming in Matlab