BUILT-IN MATHEMATICA SYMBOL

WaveletMatrixPlot

WaveletMatrixPlot[dwd]
plots the basis tree of wavelet matrix coefficients in the DiscreteWaveletData dwd.

WaveletMatrixPlot

plots coefficients up to refinement level r.

WaveletMatrixPlot

applies func to coefficients before plotting.

MORE INFORMATION

WaveletMatrixPlot generates a single plot using a pyramid of matrix plots.

WaveletMatrixPlot[dwd] is equivalent to WaveletMatrixPlot[dwd, Automatic], corresponding to the basis of coefficients used in the InverseWaveletTransform.

The wavelet indices used in the Automatic setting are given by dwd["BasisIndex"].

The dwd should be generated from matrix data and produced by DiscreteWaveletTransform, DiscreteWaveletPacketTransform, or LiftingWaveletTransform.

WaveletMatrixPlot plots basis coefficients up to refinement level r when dwd comes from DiscreteWaveletTransform or LiftingWaveletTransform.

WaveletMatrixPlot plots all coefficients at refinement level r when dwd comes from DiscreteWaveletPacketTransform.

In WaveletMatrixPlot, each should yield an array with the same dimensions as .

WaveletMatrixPlot has the same options as MatrixPlot, with the following additions and changes:

Axes	True	whether to draw axes
Frame	None	whether to draw a frame
FrameTicks	Automatic	where to draw frame ticks
GridLines	Automatic	whether to draw grid lines
PerformanceGoal	$PerformanceGoal	aspects of performance to try to optimize
PlotLayout	Automatic	what layout to use for the plot

Possible settings for PlotLayout include: and .

With the setting GridLines->Automatic, grid lines are drawn between adjacent coefficient matrices.

The Automatic setting for Ticks and FrameTicks draws ticks corresponding to refinement levels.

With the setting Method, the inverse transform of each coefficient array will be plotted.

WaveletMatrixPlot returns a Graphics object.

EXAMPLES

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Basic Examples (2)

Plot wavelet matrix coefficients in a pyramid layout:

Plot wavelet matrix coefficients in a grid layout:

Plot a full tree of wavelet packet coefficients at different refinement levels:

Plot wavelet matrix coefficients in a pyramid layout:

In[1]:=

In[2]:=

Out[2]=

Plot wavelet matrix coefficients in a grid layout:

In[3]:=

Out[3]=

Plot a full tree of wavelet packet coefficients at different refinement levels:

In[1]:=

In[2]:=

Out[2]=

Scope (11)

DiscreteWaveletTransform of matrix data:

Plot matrix wavelet coefficients in a hierarchical grid with wavelet index as a tooltip:

The plotted coefficients are the Automatic coefficients used in the inverse transform:

Use WaveletMatrixPlot

to plot coefficients only up to refinement level r:

The hierarchical layout corresponds to the tree structure of the wavelet coefficients:

DiscreteWaveletPacketTransform of matrix data:

The DiscreteWaveletData object contains a full tree of coefficients at each level:

Default Automatic coefficients for packet transform correspond to the highest refinement level:

WaveletBestBasis computes a different Automatic tree of coefficients:

Specify a function f to apply to wavelet coefficients before plotting:

layout is used to plot coefficients from StationaryWaveletTransform:

Add labels:

Use a named color gradient:

Include a frame:

Place ticks indicating refinement level on all sides:

Specify an overall style for grid lines separating wavelet coefficients:

Generalizations & Extensions (2)

Data need not be square:

Plot rectangular coefficients in a hierarchical grid layout:

DiscreteWaveletTransform of complex data:

Specify a real-valued function to apply to complex data before plotting:

By default, Re is applied:

Options (9)

Plot with no axes:

Specify a function to determine the colors of coefficients:

Use a named color function:

Include a frame:

Draw no frame ticks:

Draw frame ticks indicating refinement level on all sides:

Draw frame ticks only on the specified sides:

Draw tick marks at the specified positions:

Draw tick marks at the specified positions with the specified labels:

Plot without drawing grid lines separating coefficients:

Draw only horizontal grid lines:

Specify an overall style for grid lines separating wavelet coefficients:

Specify separate styles for horizontal and vertical grid lines:

Draw no ticks on axes:

Draw ticks on the vertical axis only:

Draw tick marks at the specified positions with the specified labels:

Inverse transform each coefficient before plotting:

Inverse transform coefficients from stationary wavelet transform:

Inverse transform coefficients from lifting wavelet transform:

Properties & Relations (4)

WaveletMatrixPlot plots matrix wavelet coefficients in a hierarchical grid layout:

gives each coefficient as a separate matrix plot:

WaveletMatrixPlot plots the Automatic coefficients used in the inverse transform:

WaveletBestBasis selects a different default tree of coefficients:

WaveletImagePlot shows image wavelet coefficients in a hierarchical grid:

WaveletScalogram plots vector coefficients with numerical magnitude indicated by color:

WaveletListPlot plots vector coefficients with a common horizontal or vertical axis:

Possible Issues (2)

Wavelet coefficients from stationary wavelet transform cannot be plotted using pyramid layout:

Pyramid layout cannot be constructed for inverse transformed wavelet coefficients: