WaveletPsi [wave,x]
gives the wavelet function for the symbolic wavelet wave evaluated at x.
WaveletPsi [wave]
gives the wavelet function as a pure function.
WaveletPsi
WaveletPsi [wave,x]
gives the wavelet function for the symbolic wavelet wave evaluated at x.
WaveletPsi [wave]
gives the wavelet function as a pure function.
Details and Options
- The wavelet function satisfies the recursion equation , where is the scaling function and are the high-pass filter coefficients.
- A discrete wavelet transform effectively represents a signal in terms of scaled and translated wavelet functions , where .
- WaveletPsi [wave,x,"Dual"] gives the dual wavelet function for biorthogonal wavelets such as BiorthogonalSplineWavelet and ReverseBiorthogonalSplineWavelet .
- The dual wavelet function satisfies the recursion equation , where are the dual high-pass filter coefficients.
- The following options can be used:
-
Examples
open all close allBasic Examples (3)
Haar wavelet function:
Daubechies wavelet function:
Mexican hat wavelet function:
Scope (5)
Compute primal wavelet function:
Dual wavelet function:
Wavelet function for discrete wavelets, including HaarWavelet :
ReverseBiorthogonalSplineWavelet :
Wavelet function for continuous wavelets, including DGaussianWavelet :
Multivariate scaling and wavelet functions are products of univariate ones:
Options (3)
MaxRecursion (1)
Plot wavelet function using different levels of recursion:
WorkingPrecision (2)
By default WorkingPrecision->MachinePrecision is used:
Use higher-precision filter computation:
Properties & Relations (4)
Wavelet function integrates to zero :
satisfies the recursion equation :
Plot the components and the sum of the recursion:
Frequency response for is given by :
The filter is a high-pass filter:
Fourier transform of is given by :
Neat Examples (1)
Plot translates and dilations of wavelet function:
Related Guides
History
Text
Wolfram Research (2010), WaveletPsi, Wolfram Language function, https://reference.wolfram.com/language/ref/WaveletPsi.html.
CMS
Wolfram Language. 2010. "WaveletPsi." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/WaveletPsi.html.
APA
Wolfram Language. (2010). WaveletPsi. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/WaveletPsi.html
BibTeX
@misc{reference.wolfram_2025_waveletpsi, author="Wolfram Research", title="{WaveletPsi}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/WaveletPsi.html}", note=[Accessed: 04-January-2026]}
BibLaTeX
@online{reference.wolfram_2025_waveletpsi, organization={Wolfram Research}, title={WaveletPsi}, year={2010}, url={https://reference.wolfram.com/language/ref/WaveletPsi.html}, note=[Accessed: 04-January-2026]}