Graduation Year
2008
Document Type
Open Access Senior Thesis
Degree Name
Bachelor of Science
Department
Mathematics
Reader 1
Jon T. Jacobsen
Reader 2
Darryl Yong
Abstract
Wavelets are functions that are useful for representing signals and approximating other functions. Wavelets sets are defined in terms of Fourier transforms of certain wavelet functions. In this paper, we provide an introduction to wavelets and wavelets sets, examine the preexisting literature on the subject, and investigate an algorithm for creating wavelet sets. This algorithm creates single wavelets, which can be used to create bases for L2(Rn) through dilation and translation. We investigate the convergence properties of the algorithm, and implement the algorithm in Matlab.
Recommended Citation
Gussin, Sara, "Wavelets and Wavelet Sets" (2008). HMC Senior Theses. 206.
https://scholarship.claremont.edu/hmc_theses/206
