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DGaussianWavelet
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DGaussianWavelet

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represents a derivative of Gaussian wavelet of derivative order 2.

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represents a derivative of Gaussian wavelet of derivative order n.

Details

Examples

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Basic Examples  (1)Summary of the most common use cases

Wavelet function:

In[1]:=1
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https://wolfram.com/xid/0do7r05uq7a64o4hi-rgea5u
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0do7r05uq7a64o4hi-7j4bvf
Out[2]=2

Scope  (2)Survey of the scope of standard use cases

DGaussianWavelet is used to perform ContinuousWaveletTransform:

In[1]:=1
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https://wolfram.com/xid/0do7r05uq7a64o4hi-p464vx
In[2]:=2
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https://wolfram.com/xid/0do7r05uq7a64o4hi-50xym5
Out[2]=2

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

In[3]:=3
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https://wolfram.com/xid/0do7r05uq7a64o4hi-yu8t38
Out[3]=3

Use InverseWaveletTransform to reconstruct the signal:

In[4]:=4
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https://wolfram.com/xid/0do7r05uq7a64o4hi-unkpz2
Out[4]=4

Wavelet function as a function of derivative order n:

In[1]:=1
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https://wolfram.com/xid/0do7r05uq7a64o4hi-os7mbq
In[2]:=2
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https://wolfram.com/xid/0do7r05uq7a64o4hi-upws4
Out[2]=2

Properties & Relations  (4)Properties of the function, and connections to other functions

DGaussianWavelet[2] is the same as MexicanHatWavelet:

In[1]:=1
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https://wolfram.com/xid/0do7r05uq7a64o4hi-tcrcaq
Out[1]=1

Wavelet function integrates to zero; :

In[1]:=1
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https://wolfram.com/xid/0do7r05uq7a64o4hi-ic2pkk
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0do7r05uq7a64o4hi-kt1vd3
Out[2]=2

Wavelet function and its Fourier transform:

In[1]:=1
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https://wolfram.com/xid/0do7r05uq7a64o4hi-nrw6n3
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0do7r05uq7a64o4hi-0xiz8m
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0do7r05uq7a64o4hi-kfn202
Out[3]=3
In[4]:=4
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https://wolfram.com/xid/0do7r05uq7a64o4hi-jyhlhp
Out[4]=4

DGaussianWavelet does not have a scaling function:

In[1]:=1
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https://wolfram.com/xid/0do7r05uq7a64o4hi-valwr0
Out[1]=1
Wolfram Research (2010), DGaussianWavelet, Wolfram Language function, https://reference.wolfram.com/language/ref/DGaussianWavelet.html.
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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.

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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.

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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

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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 ]}

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@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 ]}

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@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 ]}