This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# WaveletPsi

 WaveletPsigives the wavelet function for the symbolic wavelet wave evaluated at x. WaveletPsi[wave]gives the wavelet function as a pure function.
• 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 .
• 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
Haar wavelet function:
Daubechies wavelet function:
Mexican hat wavelet function:
Haar wavelet function:
 Out[1]=
 Out[2]=

Daubechies wavelet function:
 Out[1]=
 Out[2]=

Mexican hat wavelet function:
 Out[1]=
 Out[2]=
 Scope   (5)
Compute primal wavelet function:
Dual wavelet function:
Wavelet function for discrete wavelets, including HaarWavelet:
Wavelet function for continuous wavelets, including DGaussianWavelet:
Multivariate scaling and wavelet functions are products of univariate ones:
 Options   (3)
By default WorkingPrecision is used:
Use higher-precision filter computation:
Plot wavelet function using different levels of recursion:
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 :
Plot translates and dilations of wavelet function:
New in 8