# WaveletScalogram

WaveletScalogram[wd]

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

WaveletScalogram[wd,wind]

plots wavelet coefficients corresponding to the wavelet index specification wind.

WaveletScalogram[wd,wind,func]

applies func to coefficients before plotting.

# Details and Options • 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 .
• 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:

## Scope(10)

### DiscreteWaveletData(6)

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:

### ContinuousWaveletData(4)

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)

### Axes(3)

Draw no axes:

Draw the axis but no axis:

Specify the style for each axis using AxesStyle:

### AxesOrigin(2)

The Automatic setting for AxesOrigin is set to {0,0}:

Coordinates for vertical axes start from 0 at the bottom:

Put the axis origin at and , which is indicated by the 5 refinement level:

### ColorFunction(3)

Blend two colors:

Reverse a color function:

Color by scaled coordinate:

### ColorFunctionScaling(2)

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

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

### Frame(3)

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:

### FrameTicks(3)

Place frame ticks on all the edges:

Use Full ticks to draw labels indicating octaves and voices {oct,voc} on the vertical axis:

Label frame ticks to indicate octaves:

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

### GridLines(3)

Put grid lines across the scalogram:

Specify location for grid lines:

Specify overall grid lines style:

### Method(2)

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)

indicates refinement level for DiscreteWaveletData on the vertical axis:

indicates wavelet index specification:

indicates refinement level for ContinuousWaveletData on the vertical axis:

indicates wavelet octave and voice specification:

## Neat Examples(2)

Draw contours over WaveletScalogram:

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