Characterization of scaling sets of multiresolution analysis

Keywords

Wavelets (Mathematics), Multiresolution analysis (MRA), Scaling sets of indicator functions, Characterization of measurable sets E, Fourier-transform support of scaling functions, Haar-type and Shannon-type wavelet constructions

Abstract

The purpose of this thesis is to study a special class of MRA wavelet with special scaling functions. The first known wavelet is the Haar wavelet. The scaling function associated with the Haar wavelet is the characteristic function cp(x) == X[o,l) · We will characterize all the scaling function associated with Haar-type wavelets. More explicitly, we will characterize all the set E such that XE is a scaling function for some MRA. Another well known wavelet is the Shannon wavelet. In this case, the Fourier­ Transform of the associated scaling function cp is also a characteristic func­tion. We characterize all the set E such that XE(��) is the Fourier-transform of the scaling function cp. In this case, associated with Shannon-type wavelets.

Notes

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Graduation Date

2003

Advisor

Han, Deguang

Degree

Master of Arts (M.A.)

College

College of Arts and Sciences

Department

Mathematics

Format

PDF

Pages

29 pages

Language

English

Length of Campus-only Access

None

Access Status

Masters Thesis (Open Access)

Identifier

DP0029097

Subjects

Arts and Sciences -- Dissertations; Academic; Dissertations; Academic -- Arts and Sciences; Wavelets (Mathematics); Haar system (Mathematics); Harmonic analysis; Characteristic functions; Dissertations, Academic--Mathematics

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