Research Experience for Undergraduates (REU) Seminar
Speaker: Eva Curry , Graduate Student, Mathematics Department, Rutgers University.
Title: Wavelets, Multiresolution Analyses, Filters, and My Summer Research Project.
Date: Wednesday, July 3, 2002.
Time and location: 12:30 pm - 2 pm, DIMACS Center, Room 431,
Lunch will be served.
If we take a wavelet j(x), its translations by integers j(x-k) and the dyadic dilations j( 2j 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.