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