BUILT-IN MATHEMATICA SYMBOL

WaveletPsi

gives the wavelet function

for the symbolic wavelet wave evaluated at x.

WaveletPsi[wave]
gives the wavelet function as a pure function.

MORE INFORMATION

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 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:

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

EXAMPLES

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Basic Examples (3)

Haar wavelet function:

Daubechies wavelet function:

Mexican hat wavelet function:

Haar wavelet function:

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Daubechies wavelet function:

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Out[1]=

In[2]:=

Out[2]=

Mexican hat wavelet function:

In[1]:=

Out[1]=

In[2]:=

Out[2]=

Scope (5)

Compute primal wavelet function:

Dual wavelet function:

Wavelet function

for discrete wavelets, including HaarWavelet:

DaubechiesWavelet:

SymletWavelet:

CoifletWavelet:

BiorthogonalSplineWavelet:

ReverseBiorthogonalSplineWavelet:

CDFWavelet:

ShannonWavelet:

BattleLemarieWavelet:

MeyerWavelet:

Wavelet function

for continuous wavelets, including DGaussianWavelet:

Multivariate scaling and wavelet functions are products of univariate ones:

Options (3)

By default WorkingPrecision->MachinePrecision is used:

Use higher-precision filter computation:

Plot wavelet function using different levels of recursion:

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: