represents a Paul wavelet of order 4.
PaulWavelet[n]
represents a Paul wavelet of order n.


PaulWavelet
represents a Paul wavelet of order 4.
PaulWavelet[n]
represents a Paul wavelet of order n.
Details

- PaulWavelet defines a family of complex non-orthogonal wavelets.
- The wavelet function (
) is given by
.
- PaulWavelet can be used with such functions as ContinuousWaveletTransform and WaveletPsi, etc.
Examples
open all close allScope (3)
Wavelet function as a function of order n:
PaulWavelet is used to perform ContinuousWaveletTransform:
Use WaveletScalogram to get a time scale representation of wavelet coefficients:
Use InverseWaveletTransform to reconstruct the signal:
Properties & Relations (3)
Wavelet function integrates to zero; :
Wavelet function and its Fourier transform:
PaulWavelet does not have a scaling function:
See Also
Related Guides
History
Text
Wolfram Research (2010), PaulWavelet, Wolfram Language function, https://reference.wolfram.com/language/ref/PaulWavelet.html.
CMS
Wolfram Language. 2010. "PaulWavelet." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/PaulWavelet.html.
APA
Wolfram Language. (2010). PaulWavelet. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/PaulWavelet.html
BibTeX
@misc{reference.wolfram_2025_paulwavelet, author="Wolfram Research", title="{PaulWavelet}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/PaulWavelet.html}", note=[Accessed: 10-August-2025]}
BibLaTeX
@online{reference.wolfram_2025_paulwavelet, organization={Wolfram Research}, title={PaulWavelet}, year={2010}, url={https://reference.wolfram.com/language/ref/PaulWavelet.html}, note=[Accessed: 10-August-2025]}