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Wavelets and multifractal formalism for singular signals: Application to turbulence data
Abstract
The wavelet decomposition is used to generalize the multifractal formalism to singular signals. The singularity spectrum is directly determined from the scaling behavior of partition functions that are defined from the wavelet transform modulus maxima. Illustrations on fractal signals with a recursive structure, e.g., devil's staircases, are shown. Applications to fully developed turbulence data and Brownian signals are reported.
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Cited by
Multifractality in human heartbeat dynamics
Ivanov, P. C., Amaral, L. A. N., Goldberger, A. L., Havlin, S., Rosenblum, M. G., Struzik, Z. R., & Stanley, H. E. (1999) · Nature · doi:10.1038/20924 · Cited by 1,456
Spatiotemporal symmetry and multifractal structure of head movements during dyadic conversation
Ashenfelter, K. T., Boker, S. M., Waddell, J. R., & Vitanov, N. (2009) · Journal of Experimental Psychology: Human Perception and Performance · doi:10.1037/a0015017 · Cited by 101
Metadata
- Authors
- Muzy, J. F., Bacry, E., & Arneodo, A.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 1991-12-16
- Volume
- 67
- Issue
- 25
- Pages
- 3515-3518
- ISSN
- 0031-9007 (ISSN-L)
- OpenAlex
- W1991595392
- Cited by
- 785
- References
- 0
- FWCI
- 36.87
- Type
- journal article
- Language
- en
- Open access
- closed
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- CoChat. (2026). Citation check: Wavelets and multifractal formalism for singular signals: Application to turbulence data. https://app.cochat.ai/papers/10.1103/physrevlett.67.3515
- The paper
- Muzy, J. F., Bacry, E., & Arneodo, A. (1991). Wavelets and multifractal formalism for singular signals: Application to turbulence data. Physical Review Letters. https://doi.org/10.1103/physrevlett.67.3515
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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.
