WaveletPhi

WaveletPhi[wave,x]

gives the scaling function for the symbolic wavelet wave evaluated at x.

WaveletPhi[wave]

gives the scaling function as a pure function.

Details and Options

Examples

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Basic Examples  (2)

Haar scaling function:

Symlet scaling function:

Scope  (4)

Compute primal scaling function:

Dual scaling function:

Scaling function for HaarWavelet:

DaubechiesWavelet:

SymletWavelet:

CoifletWavelet:

BiorthogonalSplineWavelet:

ReverseBiorthogonalSplineWavelet:

CDFWavelet:

ShannonWavelet:

BattleLemarieWavelet:

MeyerWavelet:

Multivariate scaling and wavelet functions are products of univariate ones:

Options  (3)

MaxRecursion  (1)

Plot scaling function using different levels of recursion:

WorkingPrecision  (2)

By default WorkingPrecision->MachinePrecision is used:

Use higher-precision filter computation:

Properties & Relations  (4)

Scaling function integrates to unity :

In particular, :

satisfies the recursion equation :

Plot the components and the sum of the recursion:

Frequency response for is given by :

The filter is a lowpass filter:

Fourier transform of is given by :

Neat Examples  (1)

Plot translates and dilations of scaling function:

Wolfram Research (2010), WaveletPhi, Wolfram Language function, https://reference.wolfram.com/language/ref/WaveletPhi.html.

Text

Wolfram Research (2010), WaveletPhi, Wolfram Language function, https://reference.wolfram.com/language/ref/WaveletPhi.html.

BibTeX

@misc{reference.wolfram_2021_waveletphi, author="Wolfram Research", title="{WaveletPhi}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/WaveletPhi.html}", note=[Accessed: 24-October-2021 ]}

BibLaTeX

@online{reference.wolfram_2021_waveletphi, organization={Wolfram Research}, title={WaveletPhi}, year={2010}, url={https://reference.wolfram.com/language/ref/WaveletPhi.html}, note=[Accessed: 24-October-2021 ]}

CMS

Wolfram Language. 2010. "WaveletPhi." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/WaveletPhi.html.

APA

Wolfram Language. (2010). WaveletPhi. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/WaveletPhi.html