BUILT-IN MATHEMATICA SYMBOL

WaveletListPlot

WaveletListPlot[dwd]
plots wavelet transform coefficients in the DiscreteWaveletData dwd.

WaveletListPlot

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

WaveletListPlot

applies func to coefficients before plotting.

WaveletListPlot

plots wavelet transform coefficients from several DiscreteWaveletData objects

,

, ....

MORE INFORMATION

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:

AspectRatio	Automatic	ratio of height to width
Joined	True	whether to join points
Method	Automatic	what method to use
PlotLayout	"CommonXAxis"	what layout to use for the plot
PlotRange	All	range of values to include

Possible settings for PlotLayout include: and .

With the setting , 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 , 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:

	Automatic	refinement level
	Full	full wavelet index

With the setting Method, the inverse transform of each coefficient array will be plotted.

WaveletListPlot returns a Graphics object.

EXAMPLES

CLOSE ALL

Basic Examples (1)

Compute a discrete wavelet transform:

Plot the different wavelet transform coefficients:

Plot against a common vertical axis:

Compute a discrete wavelet transform:

In[1]:=

In[2]:=

Out[2]=

Plot the different wavelet transform coefficients:

In[3]:=

Out[3]=

Plot against a common vertical axis:

In[4]:=

Out[4]=

Scope (15)

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

layout, each coefficient is separately rescaled:

In the

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:

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:

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 (16)

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

With

, AxesOrigin

aligns the horizontal axis with the n

plot:

With

, AxesOrigin

places the vertical axis after the n

plot:

Plot coefficients assuming the original data occupies the actual coordinate range

:

Fill plots to the axis:

Plot against common vertical axis with filling:

Plot coefficients with a frame:

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:

Specify automatically placed grid lines:

Plot points are joined by default:

Plot without joining:

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:

Plot coefficients over a common horizontal axis (default):

Plot against a common vertical axis:

Specify manual plot range:

Specify an overall style for each wavelet coefficient:

Specify a single style for the whole plot:

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)

Use PlotLayout

to identify structure, such as edges in coefficients:

Detail coefficients

are sensitive to edges:

Use PlotLayout

to compare scale of coefficients:

Compare scale of constant and oscillatory parts:

Identify changing relative scale of coefficients:

Constant coefficient

dominates early and first detail coefficient

dominates later:

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

Plot multiple sets of coefficients on the same WaveletListPlot:

High-pass coefficients

are nearly the same, while low-pass coefficient

is different:

Properties & Relations (5)

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

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: