**Research Experience for Undergraduates (REU) Seminar
**

Speaker: Eva Curry , Graduate Student, Mathematics Department, Rutgers University.

Title:

Date: Wednesday, July 3, 2002.

Time and location: 12:30 pm - 2 pm, DIMACS Center, Room 431,
Rutgers University

Lunch will be served.

**Abstract**

If we take a wavelet *j*(*x*),
its translations by integers *j*(*x-k*) and the dyadic dilations *j*(
2^{j} *x-k*) of all these functions, then we get a collection of
functions which acts more or less like a basis for other functions. Writing a functions, such as sound or other
signal or a line of pixels in an image, in terms of this “basis” is the first
step in a lot of useful data analysis.
For example, to filter noise in a signal you can remove terms
corresponding to the noise in a wavelet expansion of the signal. Smoothing a blocky image can also be
accomplished by changing only certain terms in the corresponding wavelet
expansion. Both cases are examples of
applying a filter to data.

In this talk I will introduce multiresolution analysis wavelets (the standard, nice sort of wavelets) and what a filter is in this mathematical context. I will then describe my thesis project, which involves the classification of low-pass filters.