The DOI matches its Crossref record; 2 of the 2 references it cites were found in a registry or an index.
Generalized Morse wavelets
Abstract
This paper examines the class of generalized Morse wavelets, which are eigenfunction wavelets suitable for use in time-varying spectrum estimation via averaging of time-scale eigenscalograms. Generalized Morse wavelets of order k (the corresponding eigenvalue order) depend on a doublet of parameters (/spl beta/, /spl gamma/); we extend results derived for the special case /spl beta/ = /spl gamma/ = 1 and include a proof of "the resolution of identity." The wavelets are easy to compute using the discrete Fourier transform (DFT) and, for (/spl beta/, /spl gamma/) = (2m, 2), can be computed exactly. A correction of a previously published eigenvalue formula is given. This shows that for /spl gamma/ > 1, generalized Morse wavelets can outperform the Hermites in energy concentration, contrary to a conclusion based on the /spl gamma/ = 1 case. For complex signals, scalogram analyses must be carried out using both the analytic and anti-analytic complex wavelets or odd and even real wavelets, whereas for real signals, the analytic complex wavelet is sufficient.
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Citations
Cites
Handbook of Mathematical Functions
McQuarrie, D. A. (1966) · American Journal of Physics · doi:10.1119/1.1972842 · Cited by 40,433
Daubechies, I. (1992) · doi:10.1137/1.9781611970104 · Cited by 15,979
Cited by
Generalized Morse Wavelets as a Superfamily of Analytic Wavelets
Lilly, J. M., & Olhede, S. C. (2012) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2012.2210890 · Cited by 508
Self-citationHigher-Order Properties of Analytic Wavelets
Lilly, J. M., & Olhede, S. C. (2009) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2008.2007607 · Cited by 346
Self-citationThe developmental basis of fingerprint pattern formation and variation
Glover, J. D., Sudderick, Z. R., Shih, B. B.-J., Batho-Samblas, C., Charlton, L., Krause, A. L., Anderson, C., Riddell, J., Balic, A., Li, J., et al. (2023) · Cell · doi:10.1016/j.cell.2023.01.015 · Cited by 136
Huggins, C. J., Escudero, J., Parra, M. A., Scally, B., Anghinah, R., Vitória Lacerda De Araújo, A., Basile, L. F., & Abasolo, D. (2021) · Journal of Neural Engineering · doi:10.1088/1741-2552/ac05d8 · Cited by 105
Metadata
- Authors
- Olhede, S. C., & Walden, A. T.
- Venue
- IEEE Transactions on Signal Processing
- Published
- 2002-11
- Volume
- 50
- Issue
- 11
- Pages
- 2661-2670
- ISSN
- 1053-587X (ISSN-L)
- OpenAlex
- W2080271204
- Cited by
- 358
- References
- 2
- FWCI
- 4.20
- Type
- journal article
- Language
- en
- Open access
- closed
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- Olhede, S. C., & Walden, A. T. (2002). Generalized Morse wavelets. IEEE Transactions on Signal Processing. https://doi.org/10.1109/tsp.2002.804066
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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