BUILT-IN MATHEMATICA SYMBOL

WaveletScalogram

WaveletScalogram[wd]
plots wavelet vector coefficients in a DiscreteWaveletData or ContinuousWaveletData object wd.

WaveletScalogram

plots wavelet coefficients corresponding to the wavelet index specification wind.

WaveletScalogram

applies func to coefficients before plotting.

MORE INFORMATION

WaveletScalogram plots the transform coefficients as rows of colorized rectangles, in which large absolute values are shown darker and each subsequent row corresponds to different wavelet index specifications.

The wavelet index specification wind is the same as used by DiscreteWaveletData or ContinuousWaveletData.

WaveletScalogram[wd] is equivalent to WaveletScalogram[wd, Automatic].

The following special values can be used for func:

	"AbsoluteGlobal"	absolute value divided by the maximal coefficient
	"AbsoluteLevel"	absolute value divided by the maximal level coefficient

WaveletScalogram has the same options as Graphics, with the following additions and changes:

	ColorFunction	Automatic	how to color the wavelet coefficients
	ColorFunctionScaling	True	whether to scale the arguments to ColorFunction

WaveletScalogram returns a Graphics object.

EXAMPLES

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Basic Examples (2)

Plot a discrete wavelet scalogram:

Plot a continuous wavelet scalogram:

Plot a discrete wavelet scalogram:

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Plot a continuous wavelet scalogram:

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Scope (10)

Plot a discrete wavelet scalogram:

The vertical axis represents refinement level and the horizontal axis represents time:

Use Full ticks to expand the labels on the vertical axis:

Specify wavelet indices to plot:

Show wavelet transform as a tree:

The second argument is used to specify wavelet indices:

Scale wavelet coefficients before plotting:

The third argument is used to specify a scaling function:

A scalogram gives a visual representation of a wavelet transform:

Perform a wavelet transform:

Darker colors indicate larger coefficients and lighter colors indicate smaller coefficients:

Use WaveletListPlot to complement a scalogram:

Color variations in the scalogram can be better visualized using WaveletListPlot:

WaveletScalogram works on DiscreteWaveletData generated from any transform:

Plot a scalogram for DiscreteWaveletTransform and DiscreteWaveletPacketTransform:

Plot a scalogram for StationaryWaveletTransform and StationaryWaveletPacketTransform:

Plot a continuous wavelet scalogram:

The vertical axis represents scales and the horizontal axis represents time:

Use Full ticks to expand the labels on the vertical axis:

Specify wavelet indices to plot:

The second argument is used to specify wavelet indices:

Scale wavelet coefficients before plotting:

The third argument is used to specify a scaling function:

A single frequency shows up as a horizontal band at the equivalent scale:

Multiple frequencies show up as multiple bands at the equivalent scales:

Options (21)

Draw no axes:

Draw the

axis but no

axis:

Specify the style for each axis using AxesStyle:

The Automatic setting for AxesOrigin is set to

:

Coordinates for vertical axes start from 0 at the bottom:

Put the axis origin at

and

, which is indicated by the 5

refinement level:

Blend two colors:

Reverse a color function:

Color by scaled

coordinate:

No argument scaling on the left; automatic scaling on the right:

To use ColorFunction with a wider range, set ColorFunctionScaling to False:

Draw a frame around a plot:

Put a frame on specific edges:

Put a frame on left and right edges:

Put a frame on bottom and top edges:

Specify overall frame style, including the frame, frame ticks, and frame tick labels:

Place frame ticks on all the edges:

Use Full ticks to draw labels indicating octaves and voices

on the vertical axis:

Label frame ticks to indicate octaves:

Specify overall frame ticks style, including frame tick labels, using FrameTicksStyle:

Put grid lines across the scalogram:

Specify location for grid lines:

Specify overall grid lines style:

Use a nonlinear raster function as used by MatrixPlot:

Invert wavelet coefficients of DiscreteWaveletData:

Applications (2)

WaveletScalogram can be used to visualize discontinuities:

Plot scalogram for only detail coefficients:

Visualize time scale representation of multiple frequencies:

Higher frequencies are resolved at lower octaves and lower frequencies at higher octaves:

Properties & Relations (2)

Ticks->Automatic indicates refinement level for DiscreteWaveletData on the vertical axis:

Ticks->Full indicates wavelet index specification:

Ticks->Automatic indicates refinement level for ContinuousWaveletData on the vertical axis:

Ticks->Full indicates wavelet octave and voice specification:

Neat Examples (2)

Draw contours over WaveletScalogram:

Use ListPlot3D to visualize a wavelet scalogram in three-dimensional space: