Open Access Senior Thesis
Bachelor of Science
Jon T. Jacobsen
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.
Gussin, Sara, "Wavelets and Wavelet Sets" (2008). HMC Senior Theses. 206.