CDFWavelet
✖
CDFWavelet
Details

- CDFWavelet defines a set of biorthogonal wavelets.
- The following "type" forms can be used:
-
"5/3" used in lossless JPEG2000 compression "9/7" used in lossy JPEG2000 compression - The scaling function (
) and wavelet function (
) have compact support. The functions are symmetric.
- CDFWavelet can be used with such functions as DiscreteWaveletTransform, WaveletPhi, etc.
Examples
open allclose allBasic Examples (3)Summary of the most common use cases

https://wolfram.com/xid/0fq4yj0wmxo02-gpi6tg


https://wolfram.com/xid/0fq4yj0wmxo02-gb8f9b


https://wolfram.com/xid/0fq4yj0wmxo02-vc7o0g


https://wolfram.com/xid/0fq4yj0wmxo02-xdbxfp


https://wolfram.com/xid/0fq4yj0wmxo02-kjry2h

Scope (16)Survey of the scope of standard use cases
Basic Uses (10)
Compute primal lowpass filter coefficients:

https://wolfram.com/xid/0fq4yj0wmxo02-5q3vbl

Dual lowpass filter coefficients:

https://wolfram.com/xid/0fq4yj0wmxo02-8wgk6z

Primal highpass filter coefficients:

https://wolfram.com/xid/0fq4yj0wmxo02-ghmu0m

Dual highpass filter coefficients:

https://wolfram.com/xid/0fq4yj0wmxo02-5utoqa


https://wolfram.com/xid/0fq4yj0wmxo02-u5x0a9


https://wolfram.com/xid/0fq4yj0wmxo02-1x7frz

Generate function to compute lifting wavelet transform:

https://wolfram.com/xid/0fq4yj0wmxo02-nfjqzn


https://wolfram.com/xid/0fq4yj0wmxo02-ol7ejo


https://wolfram.com/xid/0fq4yj0wmxo02-7bq5gu


https://wolfram.com/xid/0fq4yj0wmxo02-1hi2ld


https://wolfram.com/xid/0fq4yj0wmxo02-cpb7tk

Plot scaling function using different levels of recursion:

https://wolfram.com/xid/0fq4yj0wmxo02-jvaues


https://wolfram.com/xid/0fq4yj0wmxo02-4fzw6t


https://wolfram.com/xid/0fq4yj0wmxo02-pq6kvv

Plot scaling function using different levels of recursion:

https://wolfram.com/xid/0fq4yj0wmxo02-b0lb5q

Wavelet Transforms (5)
Compute a DiscreteWaveletTransform:

https://wolfram.com/xid/0fq4yj0wmxo02-xhbmxi

View the tree of wavelet coefficients:

https://wolfram.com/xid/0fq4yj0wmxo02-gtqy6c

Get the dimensions of wavelet coefficients:

https://wolfram.com/xid/0fq4yj0wmxo02-mrjnjd

Plot the wavelet coefficients:

https://wolfram.com/xid/0fq4yj0wmxo02-qx915m

Compute a DiscreteWaveletPacketTransform:

https://wolfram.com/xid/0fq4yj0wmxo02-vtrxi2

View the tree of wavelet coefficients:

https://wolfram.com/xid/0fq4yj0wmxo02-j3n0f1

Get the dimensions of wavelet coefficients:

https://wolfram.com/xid/0fq4yj0wmxo02-wuwmcl

Plot the wavelet coefficients:

https://wolfram.com/xid/0fq4yj0wmxo02-x0l386

Compute a StationaryWaveletTransform:

https://wolfram.com/xid/0fq4yj0wmxo02-lgbd1m
View the tree of wavelet coefficients:

https://wolfram.com/xid/0fq4yj0wmxo02-jbb9sz

Get the dimensions of wavelet coefficients:

https://wolfram.com/xid/0fq4yj0wmxo02-msff83

Plot the wavelet coefficients:

https://wolfram.com/xid/0fq4yj0wmxo02-kn3y3t

Compute a StationaryWaveletPacketTransform:

https://wolfram.com/xid/0fq4yj0wmxo02-4fxpz9
View the tree of wavelet coefficients:

https://wolfram.com/xid/0fq4yj0wmxo02-9rgpx

Get the dimensions of wavelet coefficients:

https://wolfram.com/xid/0fq4yj0wmxo02-ngfrzh

Plot the wavelet coefficients:

https://wolfram.com/xid/0fq4yj0wmxo02-b9yp0h

Compute a LiftingWaveletTransform:

https://wolfram.com/xid/0fq4yj0wmxo02-6vbut6
View the tree of wavelet coefficients:

https://wolfram.com/xid/0fq4yj0wmxo02-xwj8z0

Get the dimensions of wavelet coefficients:

https://wolfram.com/xid/0fq4yj0wmxo02-56ffkm

Plot the wavelet coefficients:

https://wolfram.com/xid/0fq4yj0wmxo02-zrhgbc

Higher Dimensions (1)
Multivariate scaling and wavelet functions are products of univariate ones:

https://wolfram.com/xid/0fq4yj0wmxo02-rk8e1w

https://wolfram.com/xid/0fq4yj0wmxo02-tvf11


https://wolfram.com/xid/0fq4yj0wmxo02-yf2o9


https://wolfram.com/xid/0fq4yj0wmxo02-s16yjj


https://wolfram.com/xid/0fq4yj0wmxo02-gmiius

Properties & Relations (16)Properties of the function, and connections to other functions
Lowpass filter coefficients sum to unity; :

https://wolfram.com/xid/0fq4yj0wmxo02-v1t5fi

Highpass filter coefficients sum to zero; :

https://wolfram.com/xid/0fq4yj0wmxo02-jrlqqz

Dual lowpass filter coefficients sum to unity; :

https://wolfram.com/xid/0fq4yj0wmxo02-80xeur

Dual highpass filter coefficients sum to zero; :

https://wolfram.com/xid/0fq4yj0wmxo02-vggc8o

Scaling function integrates to unity; :

https://wolfram.com/xid/0fq4yj0wmxo02-3k44bm

Dual scaling function integrates to unity; :

https://wolfram.com/xid/0fq4yj0wmxo02-50secc

Wavelet function integrates to zero; :

https://wolfram.com/xid/0fq4yj0wmxo02-7te20t

Dual wavelet function integrates to zero; :

https://wolfram.com/xid/0fq4yj0wmxo02-cqbh6v

satisfies the recursion equation
:

https://wolfram.com/xid/0fq4yj0wmxo02-yjbxzh

https://wolfram.com/xid/0fq4yj0wmxo02-i0fiys
Plot the components and the sum of the recursion:

https://wolfram.com/xid/0fq4yj0wmxo02-tb4pjl

https://wolfram.com/xid/0fq4yj0wmxo02-wvsqxu

satisfies the recursion equation
:

https://wolfram.com/xid/0fq4yj0wmxo02-32ph7g

https://wolfram.com/xid/0fq4yj0wmxo02-lfizfd
Plot the components and the sum of the recursion:

https://wolfram.com/xid/0fq4yj0wmxo02-pv65od

https://wolfram.com/xid/0fq4yj0wmxo02-siy44p

satisfies the recursion equation
:

https://wolfram.com/xid/0fq4yj0wmxo02-sr719e

https://wolfram.com/xid/0fq4yj0wmxo02-761w33
Plot the components and the sum of the recursion:

https://wolfram.com/xid/0fq4yj0wmxo02-bdrs22

https://wolfram.com/xid/0fq4yj0wmxo02-ckzrbh

satisfies the recursion equation
:

https://wolfram.com/xid/0fq4yj0wmxo02-4xlw98

https://wolfram.com/xid/0fq4yj0wmxo02-seqsk7
Plot the components and the sum of the recursion:

https://wolfram.com/xid/0fq4yj0wmxo02-or3keu

https://wolfram.com/xid/0fq4yj0wmxo02-n5sx2h

Frequency response for is given by
:

https://wolfram.com/xid/0fq4yj0wmxo02-y5x0mm
The filter is a lowpass filter:

https://wolfram.com/xid/0fq4yj0wmxo02-za6vn3

Fourier transform of is given by
:

https://wolfram.com/xid/0fq4yj0wmxo02-idptzz

https://wolfram.com/xid/0fq4yj0wmxo02-4mxsvj

https://wolfram.com/xid/0fq4yj0wmxo02-i4smhk

Frequency response for is given by
:

https://wolfram.com/xid/0fq4yj0wmxo02-n4u9y2
The filter is a dual lowpass filter:

https://wolfram.com/xid/0fq4yj0wmxo02-jod7ab

Fourier transform of is given by
:

https://wolfram.com/xid/0fq4yj0wmxo02-le5e5v

https://wolfram.com/xid/0fq4yj0wmxo02-qp24bt

https://wolfram.com/xid/0fq4yj0wmxo02-ofeok2

Frequency response for is given by
:

https://wolfram.com/xid/0fq4yj0wmxo02-6u603k
The filter is a lowpass filter:

https://wolfram.com/xid/0fq4yj0wmxo02-3n6ywg

Fourier transform of is given by
:

https://wolfram.com/xid/0fq4yj0wmxo02-b8inb0

https://wolfram.com/xid/0fq4yj0wmxo02-vsncry

https://wolfram.com/xid/0fq4yj0wmxo02-h8wifj

https://wolfram.com/xid/0fq4yj0wmxo02-rzs5ol

Frequency response for is given by
:

https://wolfram.com/xid/0fq4yj0wmxo02-sjcfi0
The filter is a lowpass filter:

https://wolfram.com/xid/0fq4yj0wmxo02-my0oxb

Fourier transform of is given by
:

https://wolfram.com/xid/0fq4yj0wmxo02-69ezed

https://wolfram.com/xid/0fq4yj0wmxo02-go2zbw

https://wolfram.com/xid/0fq4yj0wmxo02-53vj8h

https://wolfram.com/xid/0fq4yj0wmxo02-eytnvi

Neat Examples (2)Surprising or curious use cases
Plot translates and dilations of scaling function:

https://wolfram.com/xid/0fq4yj0wmxo02-yz9dxl

https://wolfram.com/xid/0fq4yj0wmxo02-evsjio


https://wolfram.com/xid/0fq4yj0wmxo02-p5xgws

Plot translates and dilations of wavelet function:

https://wolfram.com/xid/0fq4yj0wmxo02-iu0uje

https://wolfram.com/xid/0fq4yj0wmxo02-b9ooxs


https://wolfram.com/xid/0fq4yj0wmxo02-hts69i

Wolfram Research (2010), CDFWavelet, Wolfram Language function, https://reference.wolfram.com/language/ref/CDFWavelet.html.
Text
Wolfram Research (2010), CDFWavelet, Wolfram Language function, https://reference.wolfram.com/language/ref/CDFWavelet.html.
Wolfram Research (2010), CDFWavelet, Wolfram Language function, https://reference.wolfram.com/language/ref/CDFWavelet.html.
CMS
Wolfram Language. 2010. "CDFWavelet." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/CDFWavelet.html.
Wolfram Language. 2010. "CDFWavelet." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/CDFWavelet.html.
APA
Wolfram Language. (2010). CDFWavelet. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/CDFWavelet.html
Wolfram Language. (2010). CDFWavelet. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/CDFWavelet.html
BibTeX
@misc{reference.wolfram_2025_cdfwavelet, author="Wolfram Research", title="{CDFWavelet}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/CDFWavelet.html}", note=[Accessed: 05-June-2025
]}
BibLaTeX
@online{reference.wolfram_2025_cdfwavelet, organization={Wolfram Research}, title={CDFWavelet}, year={2010}, url={https://reference.wolfram.com/language/ref/CDFWavelet.html}, note=[Accessed: 05-June-2025
]}