Meyer wavelet
The Meyer wavelet 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 in adaptive filters, fractal random fields, and multi-fault classification.
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:
Valenzuela and de Oliveira give the explicit expressions of Meyer wavelet and scale functions:
and
where
