**Contact Info**

Department of Applied Mathematics

University of Waterloo

Waterloo, Ontario

Canada N2L 3G1

Phone: 519-888-4567, ext. 32700

Fax: 519-746-4319

PDF files require Adobe Acrobat Reader

Offered in the fall term in odd-numbered years.

Wavelets are setting the new standards for digitization, for example MPEG-4 for high-definition TV and JPEG-2000 for digital still images. This course covers the mathematical development from Fourier analysis to wavelets, with special emphasis on the conversion of a signal from the analog (continuous) to the digital (discrete) domain and its subsequent reconstruction. The material with linear algebra, is interspersed with concrete examples and numerical applications such as experimentation with audio signals.

Inner product spaces, least squares approximations; Fourier series (FS), Fourier transform (FT); classical sampling theorem; decay and smoothness under FS and FT, uncertainty principle; denoising, oversampling, aliasing; Haar wavelet, multiresolution analysis; data compression by thresholding; singularity detection; spline wavelets, outlook on multidimensional digitization and image processing.

(AMATH 231 or SYDE 252 or ECE 342) and (MATH 136/146/115 or SYDE 114).

The level of presentation of the material will make the course suitable for undergraduates in Applied Mathematics, Computational Mathematics, Pure Mathematics, Computer Science, Physics and Engineering.

A. Boggess and F. J. Narcowich, "A First Course in Wavelets with Fourier Analysis", Prentice Hall, Upper Saddle River, 2001.

**Contact Info**

Department of Applied Mathematics

University of Waterloo

Waterloo, Ontario

Canada N2L 3G1

Phone: 519-888-4567, ext. 32700

Fax: 519-746-4319

PDF files require Adobe Acrobat Reader

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1

The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is centralized within our Office of Indigenous Relations.