The DOI matches its Crossref record; 32 of the 32 references it cites were found in a registry or an index.
Continuous and Discrete Wavelet Transforms
Abstract
This paper is an expository survey of results on integral representations and discrete sum expansions of functions in $L^2 ({\bf R})$ 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 $L^2 ({\bf R})$ 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.
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Cites
A theory for multiresolution signal decomposition: the wavelet representation
Mallat, S. G. (1989) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/34.192463 · Cited by 21,372
Orthonormal bases of compactly supported wavelets
Daubechies, I. (1988) · Communications on Pure and Applied Mathematics · doi:10.1002/cpa.3160410705 · Cited by 8,190
The wavelet transform, time-frequency localization and signal analysis
Daubechies, I. (1990) · IEEE Transactions on Information Theory · doi:10.1109/18.57199 · Cited by 6,483
Decomposition of Hardy Functions into Square Integrable Wavelets of Constant Shape
Grossmann, A., & Morlet, J. (1984) · SIAM Journal on Mathematical Analysis · doi:10.1137/0515056 · Cited by 3,624
A class of nonharmonic Fourier series
Duffin, R. J., & Schaeffer, A. C. (1952) · Transactions of the American Mathematical Society · doi:10.1090/s0002-9947-1952-0047179-6 · Cited by 2,277
An Introduction to Harmonic Analysis.
Weiss, G., & Katznelson, Y. (1970) · The American Mathematical Monthly · doi:10.2307/2316172 · Cited by 1,664
Cycle-octave and related transforms in seismic signal analysis
Goupillaud, P., Grossmann, A., & Morlet, J. (1984) · Geoexploration · doi:10.1016/0016-7142(84)90025-5 · Cited by 1,504
An introduction to non-harmonic Fourier series
Young, R. M. (1980) · Cited by 1,424
An Introduction to Harmonic Analysis
Katznelson, Y. (2004) · Cambridge University Press eBooks · doi:10.1017/cbo9781139165372 · Cited by 1,366
Painless nonorthogonal expansions
Daubechies, I., Grossmann, A., & Meyer, Y. (1986) · Journal of Mathematical Physics · doi:10.1063/1.527388 · Cited by 1,290
Cited by
Some Tools for Functional Data Analysis
Ramsay, J. O., & Dalzell, C. J. (1991) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1991.tb01844.x · Cited by 939
Recent advances in wavelet analyses: Part 1. A review of concepts
Labat, D. (2005) · Journal of Hydrology · doi:10.1016/j.jhydrol.2005.04.003 · Cited by 623
Field computation in natural and artificial intelligence
MacLennan, B. J. (1999) · Information Sciences · doi:10.1016/s0020-0255(99)00053-5 · Cited by 46
Metadata
- Authors
- Heil, C. E., & Walnut, D. F.
- Venue
- SIAM Review
- Published
- 1989-12
- Volume
- 31
- Issue
- 4
- Pages
- 628-666
- ISSN
- 0036-1445 (ISSN-L)
- 1095-7200
- OpenAlex
- W2126777570
- Cited by
- 1,206
- References
- 32
- FWCI
- 32.64
- Type
- journal article
- Language
- en
- Open access
- closed
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
