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Wavelets

Petr Holman, Karel Najzar (1999)

Pokroky matematiky, fyziky a astronomie

Wavelets generated by the Rudin-Shapiro polynomials

Abdolaziz Abdollahi, Jahangir Cheshmavar, Mohsen Taghavi (2011)

Open Mathematics

In this paper, we consider the well-known Rudin-Shapiro polynomials as a class of constant multiples of low-pass filters to construct a sequence of compactly supported wavelets.

Wavelets obtained by continuous deformations of the Haar wavelet.

Aline Bonami, Sylvain Durand, Guido Weiss (1996)

Revista Matemática Iberoamericana

One might obtain the impression, from the wavelet literature, that the class of orthogonal wavelets is divided into subclasses, like compactly supported ones on one side, band-limited ones on the other side. The main purpose of this work is to show that, in fact, the class of low-pass filters associated with reasonable (in the localization sense, not necessarily in the smooth sense) wavelets can be considered to be an infinite dimensional manifold that is arcwise connected. In particular, we show...

Wavelets on fractals.

Dorin E. Dutkay, Palle E.T. Jorgensen (2006)

Revista Matemática Iberoamericana

We show that there are Hilbert spaces constructed from the Hausdorff measures Hs on the real line R with 0 < s < 1 which admit multiresolution wavelets. For the case of the middle-third Cantor set C ⊂ [0,1], the Hilbert space is a separable subspace of L2(R, (dx)s) where s = log3(2). While we develop the general theory of multiresolutions in fractal Hilbert spaces, the emphasis is on the case of scale 3 which covers the traditional Cantor set C.

Wavelets on the integers.

Philip Gressman (2001)

Collectanea Mathematica

In this paper the theory of wavelets on the integers is developed. For this, one needs to first find analogs of translations and dyadic dilations which appear in the classical theory. Translations in l2(Z) are defined in the obvious way, taking advantage of the additive group structure of the integers. Dyadic dilations, on the other hand, pose a greater problem. In the classical theory of wavelets on the real line, translation T and dyadic dilation T obey the commutativity relation DT^2 = TD. We...

Wavelets with composite dilations.

Guo, Kanghui, Labate, Demetrio, Lim, Wang-Q, Weiss, Guido, Wilson, Edward (2004)

Electronic Research Announcements of the American Mathematical Society [electronic only]

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