The Discovering Wavelets Web Site
maintained by Edward Aboufadel and Steven Schlicker

Our goal for this site is to make it a center of activity for incorporating wavelets into the undergraduate curriculum. We believe that wavelets can be accessible to people other than research mathematicians -- that anyone with a background in basic linear algebra (for example, graduate and undergraduate students, and nonspecialists) can learn about and work with wavelets. Undergraduates at GVSU, many who are prospective mathematics teachers, have completed projects based on wavelets, along with undergraduate research projects. The challenge to mathematics professors is to present wavelets in way that is accessible without being trivial.

New and Noteworthy

November 2008: All files should be available again on this site. We plan to do some updating by checking for broken links and adding new content. Updates will be done by the end of 2008.

Each summer at Grand valley State University, two students work on a project related to wavelets. Learn about projects from 2000-2006 on the student projects web page.

Oxford University Press has published Advanced Engineering Mathematics (3rd edition), by M. Potter, J. Goldberg, and E. Aboufadel. This textbook has the typical topics for engineering mathematics (e.g. differential equations, linear algebra, numerical methods), but it also includes a new chapter on wavelets, aimed at undergraduate engineering majors, and enhanced with Maple and Excel.

Read an article from January 2005 that raises questions about digitized fingerprint images. Note that IAFIS uses wavelets, but wavelets don't appear to be the problem here.

Included in the Apple Macintosh operating system is Pixlet, a wavelet-based codec with some connections to Pixar corporation. According to Apple, "Pixlet is the first studio-grade codec for filmmakers. Pixlet provides 20-25:1 compression, allowing a 75MB/sec series of frames to be delivered in a 3MB/sec movie, similar to DV data rates. Or a series of frames that are over 6GB in size can be contained within a 250MB movie. Pixlet lets high-end digital film frames play in real time with any Panther Mac, without investing in costly, proprietary playback hardware."

An article from Science magazine, late 2001, concerning NSF funding of mathematics research, begins, "Wavelets used to be merely curios of the mathematical realm, visually boring wiggles .... But their ability to represent shapes and patterns compactly -- from storing fingerprint data on suspected terrorists to preparing targets for a missile strike against enemy forces -- has suddenly made them very popular in some pretty important places."

Another article in Science magazine (not available here, see Jan 18, 2002 issue) discusses a recent successful court challenge to using fingerprints. Here is an interesting image from that article that isn't in the PDF file. In a follow-up article (Mar 22, 2002), the judge in the court case reconsidered his decision.

Site Map

Tutorials on Wavelets Sites accessible to undergraduates and non-specialists.
Discovering Wavelets, the book Includes errata and comments
Wavelets for Undergraduates A discussion of wavelets in undergraduate linear algebra.
Student Projects and Undergraduate Research Includes descriptions of "Creating Bivariate Wavelets", "Wavelet-Based Cryptography", "Breaking CAPTCHAs", and "Finding Airplanes in Aerial Photographs".
Maple Files, Software Includes Maple, Java, and Windows software.
Wavelet Links Applications of wavelets, and more!
Ed Aboufadel's Home Page
Steve Schlicker's Home Page
Fingerprints at the FBI

A fingerprint examiner, above, pulls up a fingerprint from the FBI's database of 32 million criminals at the FBI's Criminal Justice Information Services Division in Clarksburg, W. Va. Below, a fingerprint chart and powders used in the collection of fingerprints are displayed at the Bureau of Criminal Identification and Investigation building in London, Ohio. (From an article by Malcolm Ritter of the Associated Press. Photos are also AP.)