BUILT-IN MATHEMATICA SYMBOL

WaveletPhi

gives the scaling function

for the symbolic wavelet wave evaluated at x.

WaveletPhi[wave]
gives the scaling function as a pure function.

MORE INFORMATION

The scaling function satisfies the recursion equation , where are the low-pass filter coefficients.

WaveletPhi gives the dual scaling function for biorthogonal wavelets such as BiorthogonalSplineWavelet and ReverseBiorthogonalSplineWavelet.

The dual scaling function satisfies the recursion equation , where are the dual low-pass filter coefficients.

The following options can be used:

	MaxRecursion	8	number of recursive iterations to use
	WorkingPrecision	MachinePrecision	precision to use in internal computations

EXAMPLES

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Basic Examples (2)

Haar scaling function:

Symlet scaling function:

Haar scaling function:

In[1]:=

Out[1]=

In[2]:=

Out[2]=

Symlet scaling function:

In[1]:=

Out[1]=

In[2]:=

Out[2]=

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)

By default WorkingPrecision->MachinePrecision is used:

Use higher-precision filter computation:

Plot scaling function using different levels of recursion:

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 low-pass filter:

Fourier transform of

is given by

:

Neat Examples (1)

Plot translates and dilations of scaling function: