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 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
open allclose allScope (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:
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 (18)
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:
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)
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)
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)
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:
Text
Wolfram Research (2010), WaveletScalogram, Wolfram Language function, https://reference.wolfram.com/language/ref/WaveletScalogram.html.
CMS
Wolfram Language. 2010. "WaveletScalogram." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/WaveletScalogram.html.
APA
Wolfram Language. (2010). WaveletScalogram. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/WaveletScalogram.html