Mt department Nazirova E. Sh

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

Figure 1.8 Spectrum of the Meyer wavelet (numerically computed).

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

Figure 1.9 Meyer scale function (numerically computed)

In the time domain, the waveform of the Meyer mother-wavelet has the shape as shown in the following figure:

Figure 1.10 waveform of the Meyer wavelet (numerically computed)