WaveletMatrixPlot

WaveletMatrixPlot[dwd]

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

WaveletMatrixPlot[dwd,r]

plots coefficients up to refinement level r.

WaveletMatrixPlot[dwd,r,func]

applies func to coefficients before plotting.

Details and Options

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[dwd,r] plots basis coefficients up to refinement level r when dwd comes from DiscreteWaveletTransform or LiftingWaveletTransform.
WaveletMatrixPlot[dwd,r] plots all coefficients at refinement level r when dwd comes from DiscreteWaveletPacketTransform.
In WaveletMatrixPlot[dwd,r,func], each func[coef_i,wind_i] should yield an array with the same dimensions as coef_i.
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

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->"InverseTransform", 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:

Scope (11)

Data (6)

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[dwd,r] 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:

"Grid" layout is used to plot coefficients from StationaryWaveletTransform:

Presentation (5)

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 (3)

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:

Use a theme with minimal styling:

Options (15)

Axes (1)

Plot with no axes:

ColorFunction (1)

Specify a function to determine the colors of coefficients:

Use a named color function:

Frame (1)

Include a frame:

FrameTicks (2)

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:

GridLines (1)

Plot without drawing grid lines separating coefficients:

Draw only horizontal grid lines:

GridLinesStyle (1)

Specify an overall style for grid lines separating wavelet coefficients:

Specify separate styles for horizontal and vertical grid lines:

Method (1)

Inverse transform each coefficient before plotting:

Inverse transform coefficients from stationary wavelet transform:

Inverse transform coefficients from lifting wavelet transform:

PlotLayout (1)

Show the plot in a pyramid layout:

Use a gridded layout instead:

PlotLegends (3)

Use legends for coefficient values:

Use BarLegend to add an overall legend label:

Use Placed to put legends above the plot:

PlotTheme (2)

Use a monochrome theme:

Change the grid lines style:

Ticks (1)

Draw ticks on the vertical axis only:

Properties & Relations (4)

WaveletMatrixPlot plots matrix wavelet coefficients in a hierarchical grid layout:

dwd[…,"MatrixPlot"] 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:

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WaveletMatrixPlot

Details and Options

Examples

Basic Examples (2)