MeyerWavelet []
represents the Meyer wavelet of order 3.
MeyerWavelet [n]
represents the Meyer wavelet of order n evaluated on the equally spaced interval {-10,10}.
MeyerWavelet [n,lim]
represents the Meyer wavelet of order n evaluated on the equally spaced interval {-lim,lim}.
MeyerWavelet
MeyerWavelet []
represents the Meyer wavelet of order 3.
MeyerWavelet [n]
represents the Meyer wavelet of order n evaluated on the equally spaced interval {-10,10}.
MeyerWavelet [n,lim]
represents the Meyer wavelet of order n evaluated on the equally spaced interval {-lim,lim}.
Details
- 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 [画像: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 [画像: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.
![画像: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](/index.cgi/contrast/https://reference.wolfram.com/language/ref/Files/MeyerWavelet.en/4.png){kind=link}
![画像: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](/index.cgi/contrast/https://reference.wolfram.com/language/ref/Files/MeyerWavelet.en/6.png){kind=link}
Examples
open all close allBasic Examples (3)
Scaling function:
Wavelet function:
Filter coefficients:
Scope (9)
Basic Uses (4)
Compute primal lowpass filter coefficients:
Primal highpass filter coefficients:
Meyer scaling function of order 3:
Meyer scaling function of order 10:
Meyer wavelet function of order 3:
Meyer wavelet function of order 10:
Wavelet Transforms (4)
Compute a DiscreteWaveletTransform :
View the tree of wavelet coefficients:
Get the dimensions of wavelet coefficients:
Plot the wavelet coefficients:
MeyerWavelet can be used to perform a DiscreteWaveletPacketTransform :
View the tree of wavelet coefficients:
Get the dimensions of wavelet coefficients:
Plot the wavelet coefficients:
MeyerWavelet can be used to perform a StationaryWaveletTransform :
View the tree of wavelet coefficients:
Get the dimensions of wavelet coefficients:
Plot the wavelet coefficients:
MeyerWavelet can be used to perform a StationaryWaveletPacketTransform :
View the tree of wavelet coefficients:
Get the dimensions of wavelet coefficients:
Plot the wavelet coefficients:
Higher Dimensions (1)
Multivariate scaling and wavelet functions are products of univariate ones:
Properties & Relations (10)
Lowpass filter coefficients approximately sum to unity; :
Highpass filter coefficients approximately sum to zero; :
Scaling function integrates to unity; :
Wavelet function integrates to zero; :
satisfies the recursion equation :
Plot the components and the sum of the recursion:
satisfies the recursion equation :
Plot the components and the sum of the recursion:
Frequency response for is given by :
The filter is a lowpass filter:
Frequency response for is given by :
The filter is a highpass filter:
Fourier transform of is given by :
Compare the above result with the exact Fourier transform:
Fourier transform of is given by :
Compare the above result with the exact Fourier transform:
Neat Examples (2)
Plot translates and dilations of scaling function:
Plot translates and dilations of wavelet function:
Tech Notes
Related Guides
History
Text
Wolfram Research (2010), MeyerWavelet, Wolfram Language function, https://reference.wolfram.com/language/ref/MeyerWavelet.html.
CMS
Wolfram Language. 2010. "MeyerWavelet." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/MeyerWavelet.html.
APA
Wolfram Language. (2010). MeyerWavelet. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/MeyerWavelet.html
BibTeX
@misc{reference.wolfram_2025_meyerwavelet, author="Wolfram Research", title="{MeyerWavelet}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/MeyerWavelet.html}", note=[Accessed: 10-January-2026]}
BibLaTeX
@online{reference.wolfram_2025_meyerwavelet, organization={Wolfram Research}, title={MeyerWavelet}, year={2010}, url={https://reference.wolfram.com/language/ref/MeyerWavelet.html}, note=[Accessed: 10-January-2026]}