plots wavelet transform coefficients in the DiscreteWaveletData dwd.


plots wavelet transform coefficients corresponding to the wavelet index specification wind.


applies func to coefficients before plotting.


plots wavelet transform coefficients from several DiscreteWaveletData objects dwd1, dwd2, .

Details and Options

  • WaveletListPlot works for DiscreteWaveletData coming from 1D array data.
  • The wavelet index specification wind is the same as used by DiscreteWaveletData.
  • WaveletListPlot[dwd] is equivalent to WaveletListPlot[dwd,Automatic].
  • WaveletListPlot has the same options as ListPlot, with the following additions and changes:
  • AspectRatioAutomaticratio of height to width
    JoinedTruewhether to join points
    MethodAutomaticwhat method to use
    PlotLayout"CommonXAxis"what layout to use for the plot
    PlotRangeAllrange of values to include
  • Possible settings for PlotLayout include: "CommonXAxis" and "CommonYAxis".
  • With the setting "CommonXAxis", coefficients are plotted against a common horizontal axis where the independent axes are separately scaled to occupy the same amount of vertical space.
  • With the setting "CommonYAxis", coefficients are plotted using a common vertical axis where the independent axes are separately scaled to occupy the same amount of horizontal space.
  • Ticks and FrameTicks have the following settings with special interpretations in the direction perpendicular to the common axis:
  • Automaticrefinement level
    Fullfull wavelet index
  • With the setting Method->"InverseTransform", the inverse transform of each coefficient array will be plotted.
  • WaveletListPlot returns a Graphics object.


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Basic Examples  (1)

Compute a discrete wavelet transform:

Plot the different wavelet transform coefficients:

Plot against a common vertical axis:

Scope  (16)

Data  (6)

Plot wavelet coefficients used by default in the inverse wavelet transform:

Specify which coefficients to plot:

Discrete wavelet transform coefficients are spaced so as to lie on the same horizontal axis:

Stationary wavelet transform coefficients are all the same length:

In the "CommonXAxis" layout, each coefficient is separately rescaled:

In the "CommonYAxis" layout, all coefficients are plotted on a common vertical scale:

Plot multiple DiscreteWaveletData objects together:

Using Filling to highlight the differences:

Apply a function to data before plotting:

Presentation  (10)

Lay out coefficients vertically or horizontally with a specified common axis:

Label coefficients by their refinement level using the full wavelet index as a tooltip:

Label coefficients by their full wavelet index:

Curves are automatically styled to appear distinct:

With multiple DiscreteWaveletData objects, each object is colored distinctly:

With a single DiscreteWaveletData object, each coefficient is colored distinctly:

Specify an overall style applying to every coefficient:

Provide explicit styling to each coefficient:

Add labels:

Draw a frame around the plot:

Fill plots of each coefficient:

Specify filling style:

Plot DiscreteWaveletPacketTransform coefficients:

Use plot theme:

Generalizations & Extensions  (1)

Plot wavelet coefficients from complex-valued data:

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

By default, Re is applied:

Options  (17)

AxesOrigin  (1)

The AxesOrigin option has special settings depending on the setting for PlotLayout:

With "CommonXAxis", AxesOrigin->{,n} aligns the horizontal axis with the n^(th) plot:

With "CommonYAxis", AxesOrigin->{n,} places the vertical axis after the n^(th) plot:

DataRange  (1)

Plot coefficients assuming the original data occupies the actual coordinate range {0,1}:

Filling  (1)

Fill plots to the axis:

Plot against common vertical axis with filling:

Frame  (1)

Plot coefficients with a frame:

FrameTicks  (1)

By default, coefficients are labeled with their refinement level:

Label with the full wavelet index:

Plot coefficients against a common vertical axis, labeling with the full wavelet index:

GridLines  (1)

Specify automatically placed grid lines:

Joined  (1)

Plot points are joined by default:

Plot without joining:

Method  (5)

Inverse transform each coefficient before plotting:

Control style of interior axes:

Draw no interior axes:

Choose which channel to plot in multichannel sound data:

Include original data (wavelet index {}) in plot:

PlotLayout  (1)

Plot coefficients over a common horizontal axis (default):

Plot against a common vertical axis:

PlotRange  (1)

Specify manual plot range:

PlotStyle  (1)

Specify an overall style for each wavelet coefficient:

Specify a single style for the whole plot:

PlotTheme  (1)

Use a theme with grid lines in a bright color scheme:

Add a feature theme with frame and full grid lines:

Change the color scheme:

Ticks  (1)

By default, coefficients are labeled with their refinement level:

Label with the full wavelet index on vertical axis:

Plot coefficients against a common vertical axis, labeling with the full wavelet index:

Applications  (4)

Feature Detection  (4)

Use PlotLayout->"CommonXAxis" to identify structure, such as edges in coefficients:

Detail coefficients {,1} are sensitive to edges:

Use PlotLayout->"CommonYAxis" to compare scale of coefficients:

Compare scale of constant and oscillatory parts:

Identify changing relative scale of coefficients:

Constant coefficient {,0} dominates early and first detail coefficient {1} dominates later:

Compare clean data with data plus noise with a nonzero mean:

Plot multiple sets of coefficients on the same WaveletListPlot:

Highpass coefficients {,1} are nearly the same, while lowpass coefficient {,0} is different:

Properties & Relations  (5)

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

dwd[,"ListPlot"] gives each coefficient as a separate list plot:

By default, WaveletListPlot shows the Automatic coefficients used in the inverse transform:

WaveletBestBasis selects a different default tree of coefficients:

WaveletScalogram plots vector coefficients with numerical magnitude indicated by color:

WaveletMatrixPlot plots matrix wavelet coefficients in a hierarchical grid:

WaveletImagePlot shows image wavelet coefficients in a hierarchical grid:

Neat Examples  (1)

Show stationary wavelet transform coefficients for data oscillating at different frequencies:

Introduced in 2010
Updated in 2014