DGaussianWavelet
✖
DGaussianWavelet
Details

- DGaussianWavelet defines a family of non-orthogonal wavelets.
- The wavelet function (
) is given by
.
- DGaussianWavelet can be used with such functions as ContinuousWaveletTransform, WaveletPsi, etc.
Examples
open allclose allBasic Examples (1)Summary of the most common use cases
Scope (2)Survey of the scope of standard use cases
DGaussianWavelet is used to perform ContinuousWaveletTransform:

https://wolfram.com/xid/0do7r05uq7a64o4hi-p464vx

https://wolfram.com/xid/0do7r05uq7a64o4hi-50xym5

Use WaveletScalogram to get a time scale representation of wavelet coefficients:

https://wolfram.com/xid/0do7r05uq7a64o4hi-yu8t38

Use InverseWaveletTransform to reconstruct the signal:

https://wolfram.com/xid/0do7r05uq7a64o4hi-unkpz2

Wavelet function as a function of derivative order n:

https://wolfram.com/xid/0do7r05uq7a64o4hi-os7mbq

https://wolfram.com/xid/0do7r05uq7a64o4hi-upws4

Properties & Relations (4)Properties of the function, and connections to other functions
DGaussianWavelet[2] is the same as MexicanHatWavelet:

https://wolfram.com/xid/0do7r05uq7a64o4hi-tcrcaq

Wavelet function integrates to zero; :

https://wolfram.com/xid/0do7r05uq7a64o4hi-ic2pkk


https://wolfram.com/xid/0do7r05uq7a64o4hi-kt1vd3

Wavelet function and its Fourier transform:

https://wolfram.com/xid/0do7r05uq7a64o4hi-nrw6n3


https://wolfram.com/xid/0do7r05uq7a64o4hi-0xiz8m


https://wolfram.com/xid/0do7r05uq7a64o4hi-kfn202


https://wolfram.com/xid/0do7r05uq7a64o4hi-jyhlhp

DGaussianWavelet does not have a scaling function:

https://wolfram.com/xid/0do7r05uq7a64o4hi-valwr0

Wolfram Research (2010), DGaussianWavelet, Wolfram Language function, https://reference.wolfram.com/language/ref/DGaussianWavelet.html.
Text
Wolfram Research (2010), DGaussianWavelet, Wolfram Language function, https://reference.wolfram.com/language/ref/DGaussianWavelet.html.
Wolfram Research (2010), DGaussianWavelet, Wolfram Language function, https://reference.wolfram.com/language/ref/DGaussianWavelet.html.
CMS
Wolfram Language. 2010. "DGaussianWavelet." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/DGaussianWavelet.html.
Wolfram Language. 2010. "DGaussianWavelet." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/DGaussianWavelet.html.
APA
Wolfram Language. (2010). DGaussianWavelet. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/DGaussianWavelet.html
Wolfram Language. (2010). DGaussianWavelet. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/DGaussianWavelet.html
BibTeX
@misc{reference.wolfram_2025_dgaussianwavelet, author="Wolfram Research", title="{DGaussianWavelet}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/DGaussianWavelet.html}", note=[Accessed: 21-June-2025
]}
BibLaTeX
@online{reference.wolfram_2025_dgaussianwavelet, organization={Wolfram Research}, title={DGaussianWavelet}, year={2010}, url={https://reference.wolfram.com/language/ref/DGaussianWavelet.html}, note=[Accessed: 21-June-2025
]}