The Meyer wavelet is an orthogonal wavelet proposed by Yves Meyer.[1] As a type of a continuous wavelet, it has been applied in a number of cases, such as in adaptive filters,[2] fractal random fields,[3] and multi-fault classification.[4]
The Meyer wavelet is infinitely differentiable with infinite support and defined in frequency domain in terms of function as
where
There are many different ways for defining this auxiliary function, which yields variants of the Meyer wavelet.
For instance, another standard implementation adopts
The Meyer scale function is given by
In the time domain, the waveform of the Meyer mother-wavelet has the shape as shown in the following figure:
^Meyer, Yves (1990). Ondelettes et opérateurs: Ondelettes. Hermann. ISBN 9782705661250.
^Xu, L.; Zhang, D.; Wang, K. (2005). "Wavelet-based cascaded adaptive filter for removing baseline drift in pulse waveforms". IEEE Transactions on Biomedical Engineering. 52 (11): 1973–1975. doi:10.1109/tbme.2005.856296. hdl:10397/193. PMID 16285403. S2CID 6897442.
^Elliott, Jr., F. W.; Horntrop, D. J.; Majda, A. J. (1997). "A Fourier-Wavelet Monte Carlo method for fractal random fields". Journal of Computational Physics. 132 (2): 384–408. Bibcode:1997JCoPh.132..384E. doi:10.1006/jcph.1996.5647.
^Abbasion, S.; et al. (2007). "Rolling element bearings multi-fault classification based on the wavelet denoising and support vector machine". Mechanical Systems and Signal Processing. 21 (7): 2933–2945. Bibcode:2007MSSP...21.2933A. doi:10.1016/j.ymssp.2007.02.003.
The Meyerwavelet is an orthogonal wavelet proposed by Yves Meyer. As a type of a continuous wavelet, it has been applied in a number of cases, such as...
F. Meyer (French: [mɛjɛʁ]; born 19 July 1939) is a French mathematician. He is among the progenitors of wavelet theory, having proposed the Meyer wavelet...
wavelet series is a representation of a square-integrable (real- or complex-valued) function by a certain orthonormal series generated by a wavelet....
the practically relevant discrete wavelet transforms (DWT) and the justification for the algorithm of the fast wavelet transform (FWT). It was introduced...
associated with the orthogonal Daubechies wavelet and the biorthogonal CDF wavelet. A wavelet from this family of wavelets is now used in the JPEG 2000 standard...
wavelets, to accommodate the fact that multivariate functions are typically governed by anisotropic features such as edges in images, since wavelets,...
popularizer, textbook author, and book publisher, known for her books on wavelet transforms and multivariable calculus. Burke Hubbard is the daughter of...
and wavelets are distributed by the wave provider of the originating user to the providers of all other participants in a particular wave or wavelet so...
Yves Meyer "For fundamental contributions to number theory, operator theory and harmonic analysis, and his pivotal role in the development of wavelets and...
case behavior for the Haar wavelet packet analysis. In other words, noiselets are totally incompressible by the Haar wavelet packet analysis. Like the...
trigonometric polynomials using Fourier series. Another possibility is to use wavelets. The Whittaker–Shannon interpolation formula can be used if the number...
are essentially the same as the three purposes indicated by Friendly & Meyer: prediction, estimation, description. The three purposes correspond with...
populations were 100 to 4000 times higher than at their lowest levels. A wavelet decomposition showed a clear, relatively stationary annual cycle in the...
PMID 25883885. Meyer, Yves; Roques, Sylvie (1993). Progress in wavelet analysis and applications: proceedings of the International Conference "Wavelets and Applications"...
It is rare for large SMDs to be obtained. Robert E. McGrath; Gregory J. Meyer (2006). "When Effect Sizes Disagree: The Case of r and d" (PDF). Psychological...
Norwegian Academy of Science and Letters. Retrieved 21 July 2022. "2017: Yves Meyer". The Norwegian Academy of Science and Letters. Retrieved 21 July 2022....