Meyer wavelet
The Meyer wavelet is an orthogonal wavelet proposed by Yves Meyer. It 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
![](../I/m/Spectrum_Meyer_wavelet.png)
Spectrum of the Meyer wavelet.
The Meyer scale function is given by:
![](../I/m/Spectrum_Meyer_scalefunction.png)
Meyer scale function.
In the time-domain, the waveform of the Meyer mother-wavelet has the shape as shown in the following figure:
![](../I/m/Meyer_wavelet.png)
Meyer wavelet.
In 2015, Victor Vermehren Valenzuela and H. M. de Oliveira gave the explicitly expressions of Meyer wavelet and scale functions:
and
where
and
References
- Meyer (Y.), Ondelettes et Opérateurs, Hermann, 1990.
- Daubechies, (I.), Ten lectures on wavelets, CBMS-NSF conference series in applied mathematics, SIAM Ed., pp. 117–119, 137, 152, 1992.
- Victor Vermehren Valenzuela and H. M. de Oliveira, Close expressions for Meyer Wavelet and Scale Function, 2015, p.4.
External links
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