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Some results on biorthogonal wavelet matrices and their applications黃永樑, Wong, Wing-leung. January 2000 (has links)
published_or_final_version / Mathematics / Master / Master of Philosophy
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On framelets and their applications: a discrete approachSze, Chuen-kan., 施泉根. January 2004 (has links)
published_or_final_version / abstract / toc / Mathematics / Doctoral / Doctor of Philosophy
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Some results in wavelet theory and their applications張英傑, Cheung, Ying-kit, Alan. January 1997 (has links)
published_or_final_version / Mathematics / Master / Master of Philosophy
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Some results on biorthogonal wavelet matrices and their applications /Wong, Wing-leung. January 2000 (has links)
Thesis (M. Phil.)--University of Hong Kong, 2000. / Includes bibliographical references (leaves xiii-xix).
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Some results in wavelet theory and their applications /Cheung, Ying-kit, Alan. January 1997 (has links)
Thesis (M. Phil.)--University of Hong Kong, 1998. / Includes bibliographical references (leaf 53).
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Some results on biorthogonal wavelet matrices and their applicationsWong, Wing-leung. January 2000 (has links)
Thesis (M.Phil.)--University of Hong Kong, 2000. / Includes bibliographical references (leaves xiii-xix) Also available in print.
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Theory and application of frequency selective wavelets /Tomas, Brian. January 1992 (has links)
Thesis (Ph. D.)--University of Washington, 1992. / Vita. Includes bibliographical references (leaves [75]-76).
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Aproximações multiresolução e bases ortonormais wavelet de L2 (R)Aseka, Ivanilda Basso January 1995 (has links)
Dissertação (mestrado) - Universidade Federal de Santa Catarina, Centro de Ciencias Fisicas e Matematica / Made available in DSpace on 2012-10-16T08:47:38Z (GMT). No. of bitstreams: 0Bitstream added on 2016-01-08T19:25:51Z : No. of bitstreams: 1
99946.pdf: 1632897 bytes, checksum: 0e51a6b533c328f8cb3c4ae44abd3845 (MD5) / Estudo da caracterização e propriedades de uma aproximação multiresolução. É mostrada a existência de uma função em L² (R) tal que suas translações e dilatações formam uma base ortonormal da aproximação multiresolução. A caracterização da aproximação multiresolução se dá através de uma função 2p - periódica e, reciprocamente, sob certas condições, podemos, a partir de uma função 2p - periódica, obter uma aproximação multiresolução. É mostrado, também, que, a partir de uma aproximação multiresolução, podemos construir uma função, tal que suas translações e dilatações geram uma base ortonormal de L² (R). Essa função é chamada de Wavelet, e a base gerada de base gerada Wavelet.
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Frames de waveletsRachelli, Janice January 1995 (has links)
Dissertação (mestrado) - Universidade Federal de Santa Catarina, Centro de Ciencias Fisicas e Matematicas / Made available in DSpace on 2012-10-16T08:49:47Z (GMT). No. of bitstreams: 0Bitstream added on 2016-01-08T19:34:13Z : No. of bitstreams: 1
99949.pdf: 1839807 bytes, checksum: 6c279f29fc4c75b84f85a4b5ddc3df75 (MD5) / Expansões não necessariamente ortogonais de funções no espaço de Hilbert das funções reais quadrado integráveis, através de uma família de funções gerada a partir de uma única função Wavelet. Se a família gera um frame, então para qualquer função f no espaço de Hilbert citado, existe uma expansão semelhante à expansão ortogonal.
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A multiresolutional approach to the construction of spline waveletsRohwer, Birgit 04 1900 (has links)
Thesis (MSc) -- University of Stellenbosch, 2000. / ENGLISH ABSTRACT: In this thesis we study a wavelet construction procedure based on a multiresolutional
method, before specializing to the case of spline wavelets.
First, we introduce and analyze the concepts of scaling functions and their
duals, after which we analyze the multiresolutional analysis (MM) which they
generate. The advantages of orthonormality in scaling functions are pointed out
and discussed. Following the methods which were introduced in two standard
texts of Chui, we next show how a minimally supported wavelet and its dual
can be explicitly constructed from a given MM, thereby yielding an orthogonal
decomposition of the space of square-(Lebesgue)integrable functions on the real
line. We show that our method applied to orthonormal scaling functions also
yields orthonormal wavelets, including as a special case the Daubechies wavelet.
General decomposition and reconstruction algorithms are explicitly formulated,
and the importance of the vanishing moments of a wavelet in practical applications
is shown.
We next introduce and analyze cardinal B-splines, in particular showing that
these functions are refinable, and that they satisfy the criteria of Riesz stability.
Thus the cardinal B-spline is an admissible choice for a scaling function, so that the
previously developed wavelet construction procedure based on a MM yields an
explicit formula for the minimally supported B-spline wavelet. The corresponding
vanishing moment order is calculated, and the resulting ability of the B-spline
wavelet to detect singularities in a given function is demonstrated by means of a
numerical example. Finally, we develop an explicit procedure for the construction
of minimally supported B-spline wavelets on a bounded interval. This method,
as developed in work by de Villiers and Chui, is then compared with a previous
boundary wavelet construction method introduced in work by Chui and Quak. / AFRIKAANSE OPSOMMING: In hierdie tesis bestudeer ons 'n golfie konstruksieprosedure wat gebaseer is op 'n
multiresolusiemetode, voordat ons spesialiseer na die geval van latfunksie-golfies.
Eerstens word die konsepte van skaalfunksies en hulle duale bekendgestel en geanaliseer,
waarna ons die multiresolusie analise (MM) wat sodoende gegenereer
word, analiseer. Die voordeel van ortonormaliteit by skaalfunksies word uitgewys
en bespreek. Deur die metodes te volg wat bekendgestel is in twee standaardtekste
van Chui, wys ons vervolgens hoe 'n minimaal-gesteunde golfie en die duaal
daarvan eksplisiet gekonstrueer kan word vanuit 'n gegewe MM, en daarmee 'n
ortogonale dekomposisie van die ruimte van kwadraties-(Lebesgue)integreerbare
funksies op die reële lyn lewer. Ons wys dat ons metode toegepas op ortonormale
skaalfunksies ook ortonormale golfies oplewer, insluitende as 'n spesiale geval die
Daubechies golfie. Algemene dekomposisie en rekonstruksie algoritmes word eksplisiet
geformuleer, en die belangrikheid in praktiese toepassings van 'n golfie met
die nulmomenteienskap word aangetoon.
Vervolgens word kardinale B-Iatfunksies bekendgestel, en word daar in die
besonder aangetoon dat hierdie funksies verfynbaar is, en dat hulle aan die Rieszstabiliteit
vereiste voldoen. Dus is die kardinale B-Iatfunksie 'n toelaatbare keuse
vir 'n skaalfunksie, sodat die golfie konstruksieprosedure gebaseer op 'n MM,
soos vantevore ontwikkel, 'n eksplisiete formule vir die minimaal-gesteunde Blatfunksiegolfie
oplewer. Die ooreenkomstige nulmomentorde word bereken, en die
gevolglike vermoë van 'n B-Iatfunksiegolfie om singulariteite in 'n gegewe funksie
raak te sien en uit te wys word gedemonstreer deur middel van 'n numeriese voorbeeld.
Laastens ontwikkelons 'n eksplis.iete prosedure vir die konstruksie van
minimaal-gesteunde B-Iatfunksiegolfies op 'n begrensde interval. Hierdie metode,
soos ontwikkel in werk deur de Villiers en Chui, word dan vergelyk met 'n vorige
randgolfie konstruksie wat bekendgestel is in werk deur Chui en Quak.
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