gives the wavelet function for the symbolic wavelet wave evaluated at x.
gives the wavelet function as a pure function.
Details and Options
- 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[wave,x,"Dual"] 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
Examplesopen allclose all
Basic Examples (3)
Compute primal 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:
Properties & Relations (4)
Wolfram Research (2010), WaveletPsi, Wolfram Language function, https://reference.wolfram.com/language/ref/WaveletPsi.html.
Wolfram Language. 2010. "WaveletPsi." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/WaveletPsi.html.
Wolfram Language. (2010). WaveletPsi. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/WaveletPsi.html