MeyerWavelet

MeyerWavelet[]
represents the Meyer wavelet of order 3.

MeyerWavelet[n]
represents the Meyer wavelet of order n evaluated on the equally spaced interval .

MeyerWavelet[n,lim]
represents the Meyer wavelet of order n evaluated on the equally spaced interval .

DetailsDetails

  • MeyerWavelet defines a family of orthonormal wavelets.
  • MeyerWavelet[n] is equivalent to MeyerWavelet[n,8].
  • MeyerWavelet[n,lim] is defined for any positive integer n and real limit lim.
  • The scaling function () and wavelet function () have infinite support. The functions are symmetric.
  • The scaling function () is given by its Fourier transform as 1 TemplateBox[{omega}, Abs]<=(2 pi)/3; cos(1/2 pi nu((3 TemplateBox[{omega}, Abs])/(2 pi)-1)) (2 pi)/3<=TemplateBox[{omega}, Abs]<=(4 pi)/3.  »
  • The wavelet function () is given by its Fourier transform as exp((ⅈ omega)/2) sin(pi/2 nu((3 TemplateBox[{omega}, Abs])/(2 pi)-1)) (2 pi)/3<=TemplateBox[{omega}, Abs]<=(4 pi)/3; exp((ⅈ omega)/2) cos(pi/2 nu((3 TemplateBox[{omega}, Abs])/(4 pi)-1)) (4 pi)/3<=TemplateBox[{omega}, Abs]<=(8 pi)/3.
  • The polynomial is a polynomial of the form , where is the order of the Meyer wavelet.
  • MeyerWavelet can be used with such functions as DiscreteWaveletTransform and WaveletPhi, etc.
Introduced in 2010
(8.0)