Get a DiscreteWaveletData from wavelet transforms such as DiscreteWaveletTransform:

Show the computed wavelet coefficients in a tree layout:

Get the coefficient arrays as a list of rules:

InverseWaveletTransform operates on DiscreteWaveletData:

For orthogonal wavelets such as HaarWavelet[], the inverse transform is exact:

Extract coefficients corresponding to a wavelet index specification:

Coefficients are given as a list of rules:

Extract all coefficients corresponding to wavelet indexes of the form {0,_}:

Extract a list of the coefficient arrays instead of a list of rules:

Extract as simple list plots:

Extract properties of the wavelet transform data:

Discrete forward transform, number of refinement levels, and wavelet used:

Dimensions of each wavelet coefficient:

All available properties:

Use DiscreteWaveletData in other wavelet functions:

Inverse transform:

Wavelet visualization functions:

Transform DiscreteWaveletData using wavelet functions:

Apply thresholding operation to coefficients:

Apply an arbitrary function to each coefficient:

Plot coefficients in each wavelet data object:

Construct a DiscreteWaveletData from a list of rules giving coefficient arrays:

The result represents a tree of wavelet coefficients including the specified coefficients:

The other coefficients are assumed to be zero:

Construct a DiscreteWaveletData using a specified wavelet and forward transform:

The specified wavelet and forward transform are used in the inverse transform:

Find out which coefficients are available:

Show all coefficients in a tree layout:

Different wavelet index specifications to extract coefficient arrays from DiscreteWaveletData:

Extract a single coefficient array:

Coefficients corresponding to a list of indexes:

All coefficients whose wavelet index matches a pattern:

A list of indexes and patterns:

Coefficients used by default in the inverse wavelet transform:

All coefficients:

Get coefficient arrays in different forms:

Get as a list of rules:

Get values only:

Get coefficients as small list plots:

Get inverse transform of each coefficient array:

Combine forms:

Get matrix wavelet coefficients as small matrix plots:

Inverse transform of individual coefficients as small matrix plots:

Get image wavelet coefficients as Image objects with ImageAdjust applied by default:

Get images without color levels adjusted:

By default, image wavelet coefficients are given as arrays of pixel values for each color channel:

Get audio wavelet coefficients as Audio objects:

Inverse transform of an individual coefficient as an Audio object:

Get sound wavelet coefficients as Sound objects:

Inverse transform of individual coefficients as Sound objects:

Construct a DiscreteWaveletData for List input:

For List coefficients, input a list of rules wrules of the type {wind₁->coef₁,…}:

Perform an InverseWaveletTransform:

Image input:

For Image coefficients, input a list of rules irules of the type {wind₁->icoef₁,…}:

Perform an InverseWaveletTransform:

Sound input:

For Sound coefficients, input a list of rules srules of the type {wind₁->scoef₁,…}:

Perform an InverseWaveletTransform:

By default, parameter wavelet transform wtrans is computed automatically:

Specify parameter wavelet transform wtrans:

By default, data dimensions {d₁,…} are computed automatically:

Specify data dimensions:

Perform simple edge detection:

Get properties of the wavelet transform:

Forward transform, wavelet, and padding method used:

Number of levels of refinement, corresponding to longest wavelet index:

Properties of wavelet coefficients:

Wavelet indexes for all available coefficients:

Tree view of all coefficients with different layouts:

Dimensions of each coefficient array as a list of rules:

Properties related to wavelet basis:

Wavelet indexes in basis:

Show wavelet basis highlighted in a tree view or block grid of all coefficients:

Distribution of signal energy among basis coefficients:

Cost values of each coefficient array for bases computed by WaveletBestBasis:

Properties related to input data:

Data dimensions and number of audio or color channels:

Wrapper function that is automatically applied to the result of an inverse transform:

The settings for Method are the same as the methods for wavelet transforms:

Generate DiscreteWaveletData to perform "IntegerLifting":

The settings for Padding are the same as the methods for ArrayPad, including "Periodic":

"Reversed":

"ReversedNegation":

"Reflected":

"ReflectedDifferences":

"ReversedDifferences":

"Extrapolated":

By default, Padding->"Periodic" option is used:

For Sound input, SampleRate is automatically computed:

By default SampleRate is extracted from the first coefficient rule:

Specify SampleRate explicitly:

By default, WorkingPrecision->MachinePrecision is used:

Use higher-precision computation:

With numbers close to zero, accuracy is the better indicator of the number of correct digits:

Use WorkingPrecision->∞ for exact computation: