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Zbl 0683.42031
Heil, Christopher E.; Walnut, David F.
Continuous and discrete wavelet transforms. (English)
[J] SIAM Rev. 31, No.4, 628-666 (1989). ISSN 0036-1445; ISSN 1095-7200/e

Summary: This paper is an expository survey of results on integral representations and discrete sum expansions of functions in $L\sp 2({\bbfR})$ in terms of coherent states. Two types of coherent states are considered: Weyl- Heisenberg coherent states, which arise from translations and modulations of a single function, and affine coherent states, called ``wavelets'', which arise as translations and dilations of a single function. In each case it is shown how to represent any function in $L\sp 2({\bbfR})$ as a sum or integral of these states. Most of the paper is a survey of literature, most notably the work of I. Daubechies, A. Grossmann, and J. Morlet. A few results of the authors are included.

MSC 2000:: *42C40 Wavelets
42A38 Fourier type transforms, one variable

Keywords: Gabor transform; Weyl-Heisenberg group; integral representations; discrete sum expansions; wavelets

Cited in: Zbl 0971.42023 Zbl 0916.22005 Zbl 0790.42019

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