represents a Paul wavelet of order 4.
represents a Paul wavelet of order n.
- 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.
Examplesopen allclose all
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:
Wolfram Research (2010), PaulWavelet, Wolfram Language function, https://reference.wolfram.com/language/ref/PaulWavelet.html.
Wolfram Language. 2010. "PaulWavelet." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/PaulWavelet.html.
Wolfram Language. (2010). PaulWavelet. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/PaulWavelet.html