**Instructor:** Jon Wilkening

**Lectures:** TTh 2-3:30, Room 2 Evans

**Course Control Number:** 54290

**Office:** 1091 Evans

**Office Hours:** Monday 10:30-11:55 AM, Tues 3:45-5:00 PM

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

**Required Text:** A First Course in Wavelets with Fourier Analysis, 2nd Edition,
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, image compression, JPEG, JPEG-2000
- (if time permits) introduction to compressive sensing, L1 minimization techniques

**Course Webpage:** I will post handouts and assignments on
B-Space.
Please e-mail me if you do not have access to the B-Space page.

**Grading:**

homework: | 50% | (2 lowest scores dropped) |

Midterm: | 20% | Tues, March 8, in class |

Final exam: | 30% | Mon, May 9, 11:30-2:30 |

**Homework:** 12 assignments, some involving programming in Matlab