gives the discrete wavelet packet transform (DWPT) of an array of data.
gives the discrete wavelet packet transform using the wavelet wave.
gives the discrete wavelet packet transform using r levels of refinement.
gives the discrete wavelet packet transform of an image.
gives the discrete wavelet packet transform of sampled sound.
Details and Options
- DiscreteWaveletPacketTransform gives a DiscreteWaveletData object.
- Properties of the DiscreteWaveletData dwd can be found using dwd["prop"], and a list of available properties can be found using dwd["Properties"].
- DiscreteWaveletPacketTransform is a generalization of DiscreteWaveletTransform where the full tree of wavelet coefficients is computed.
- The data can be a rectangular array of any depth.
- By default, input image is converted to an image of type "Real".
- The resulting wavelet coefficients are arrays of the same depth as the input data.
- The possible wavelet 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.
- With refinement level Full, r is given by .
- 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 available in ArrayPad.
- InverseWaveletTransform gives the inverse transform.
- By default, InverseWaveletTransform uses coefficients represented by dwd["BasisIndex"] for reconstruction. Use WaveletBestBasis to compute and set an optimal basis.
Examplesopen allclose all
Basic Examples (3)
The resulting DiscreteWaveletData represents a full tree of wavelet coefficients:
Transform an Image object:
Transform a sampled Sound object: