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 allclose 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:
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