Wavelet Toolbox

Meyer Wavelet: meyr

Both and are defined in the frequency domain, starting with an auxiliary function (see [Dau92] pages 117, 119, 137, 152). By typing waveinfo('meyr') at the MATLAB command prompt, you can obtain a survey of the main properties of this wavelet.

Figure 6-16: The Meyer Wavelet

The Meyer wavelet and scaling function are defined in the frequency domain:

• Wavelet function

• and
  
  

• where
  
  

• Scaling function

By changing the auxiliary function, you get a family of different wavelets. For the required properties of the auxiliary function (see References for more information). This wavelet ensures orthogonal analysis.

The function does not have finite support, but decreases to 0 when , faster than any inverse polynomial

• such that

This property holds also for the derivatives

The wavelet is infinitely differentiable.

Note    Although the Meyer wavelet is not compactly supported, there exists a good approximation leading to FIR filters, and then allowing DWT. By typing waveinfo('dmey') at the MATLAB command prompt, you can obtain a survey of the main properties of this pseudo-wavelet.

Biorthogonal Wavelet Pairs: biorNr.Nd

Battle-Lemarie Wavelets

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