gives the discrete wavelet transform (DWT) of an array of data.
gives the discrete wavelet transform using the wavelet wave.
gives the discrete wavelet transform using r levels of refinement.
Details and Options
- DiscreteWaveletTransform gives a DiscreteWaveletData object representing a tree of wavelet coefficient arrays.
- Properties of the DiscreteWaveletData dwd can be found using dwd["prop"], and a list of available properties can be found using dwd["Properties"].
- The data can be any of the following:
list arbitrary-rank numerical array image arbitrary Image object audio an Audio or sampled Sound object
- The resulting wavelet coefficients are arrays of the same depth as the input data.
- The possible wavelets wave include:
BattleLemarieWavelet[…] Battle–Lemarié wavelets based on B-spline BiorthogonalSplineWavelet[…] B-spline-based wavelet CoifletWavelet[…] symmetric variant of Daubechies wavelets DaubechiesWavelet[…] the Daubechies wavelets HaarWavelet[…] classic Haar wavelet MeyerWavelet[…] wavelet defined in the frequency domain ReverseBiorthogonalSplineWavelet[…] B-spline-based wavelet (reverse dual and primal) ShannonWavelet[…] sinc function-based wavelet SymletWavelet[…] least asymmetric orthogonal wavelet
- The default wave is HaarWavelet.
- With higher settings for the refinement level r, larger-scale features are resolved.
- The default refinement level r is given by , where is the minimum dimension of data. »
- The tree of wavelet coefficients at level consists of coarse coefficients and detail coefficients , with representing the input data.
- The forward transform is given by and . »
- The inverse transform is given by . »
- The are lowpass filter coefficients and are highpass filter coefficients that are defined for each wavelet family.
- The dimensions of and are given by , where is the input data dimension and fl is the filter length for the corresponding wspec. »
- The following options can be given:
Method Automatic method to use Padding "Periodic" how to extend data beyond boundaries WorkingPrecision MachinePrecision precision to use in internal computations
- The settings for Padding are the same as those available in ArrayPad.
- InverseWaveletTransform gives the inverse transform.
Examplesopen allclose all
Basic Examples (3)
Compute a discrete wavelet transform using the HaarWavelet:
Use Normal to view all coefficients:
Transform an Image object: