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

WaveletPhi
gives the scaling function for the symbolic wavelet wave evaluated at x.
WaveletPhi[wave]
gives the scaling function as a pure function.
  • The scaling function satisfies the recursion equation , where are the low-pass filter coefficients.
  • The dual scaling function satisfies the recursion equation , where are the dual low-pass filter coefficients.
  • The following options can be used:
MaxRecursion8number of recursive iterations to use
WorkingPrecisionMachinePrecisionprecision to use in internal computations
Haar scaling function:
Symlet scaling function:
Haar scaling function:
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Symlet scaling function:
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Compute primal scaling function:
Dual scaling function:
Scaling function for HaarWavelet:
Multivariate scaling and wavelet functions are products of univariate ones:
By default WorkingPrecision->MachinePrecision is used:
Use higher-precision filter computation:
Plot scaling function using different levels of recursion:
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 :
Plot translates and dilations of scaling function:
New in 8