We have become familiar with the digital reduction of music and pictures on CDs and DVDs, but now mathematicians are developing a new way to analyse sounds, images and other forms of information. The new mathematical buzzword is "wavelets". Linked to linear algebra, wavelets provide a very fast and powerful way to zoom in on the fine details in music, art or the minute differences between fingerprints, writes Dick Ahlstrom
An expert in wavelet analysis comes to Dublin next month to deliver the annual Hamilton Lecture on Monday October 16th. Prof Ingrid Daubechies, of the Department of Mathematics at Princeton University in the US will be the guest speaker with a lecture providing a "very simple" explanation of wavelets and a discussion of how they are being used.
"Wavelets are a new approach used in the analysis of sounds and images as well as in many other applications," explains Daubechies, who is professor of applied and computational mathematics at Princeton.
Wavelets can provide "a mathematical analog to a music score", she says. "Just as the score tells a musician which notes to play when, the wavelet analysis of a sound takes things apart into elementary units with a well-defined frequency (which note?) and at a well defined time (when?)."
Wavelets provide the same service for images, first providing the broad picture and then later focusing in on finer aspects. "This is similar to zooming in with a camera," she suggests, providing a service akin to a "mathematical microscope".
Wavelet analysis can be used in many different ways. the US Federal Bureau of Investigation is using a wavelet scheme for the compression of its vast library of fingerprint data, she says. Daubechies will provide other examples of how this versatile mathematical technique can be applied to everyday activities.
Organised by the Royal Irish Academy, The Irish Times and Depfa Bank, the annual Hamilton Lecture takes place each year on October 16th. The lecture focuses on some aspect of mathematical study and celebrates the life and work of Ireland's greatest scientific figure, William Rowan Hamilton (1805-1865). Prof Daubechies's lecture, The Mathematical Microscope: Wavelets and their Applications, takes place on Monday, October 16th, at 7.15pm in the Burke Theatre in Trinity College Dublin's arts block. The event is free and booking is advisable .
For tickets, contact the Academy at www.ria.ie or 01-6764222.