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WaveletPsi

WaveletPsi
gives 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:
MaxRecursion8number of recursive iterations to use
WorkingPrecisionMachinePrecisionprecision to use in internal computations
Haar wavelet function:
Daubechies wavelet function:
Mexican hat wavelet function:
Haar wavelet function:
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Daubechies wavelet function:
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Mexican hat wavelet function:
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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:
By default WorkingPrecision->MachinePrecision 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:
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