WaveletListPlot
WaveletListPlot[dwd]
plots wavelet transform coefficients in the DiscreteWaveletData dwd.
WaveletListPlot[dwd,wind]
plots wavelet transform coefficients corresponding to the wavelet index specification wind.
WaveletListPlot[dwd,wind,func]
applies func to coefficients before plotting.
WaveletListPlot[{dwd1,dwd2,…},…]
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:
-
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 - The following settings for PlotLayout can be used to display multiple sets of data:
-
"CommonXAxis" coefficients are plotted against a common axis
"CommonYAxis" coefficients are plotted using a common axis
- 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:
-
Automatic refinement level Full full wavelet index - With the setting Method->"InverseTransform", the inverse transform of each coefficient array will be plotted.
- WaveletListPlot returns a Graphics object.
Examples
open allclose allBasic Examples (1)
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:
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:
Fill plots of each coefficient:
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 (17)
The AxesOrigin option has special settings depending on the setting for PlotLayout:
With "CommonXAxis", AxesOrigin->{…,n} aligns the horizontal axis with the n plot:
With "CommonYAxis", AxesOrigin->{n,…} places the vertical axis after the n plot:
DataRange (1)
FrameTicks (1)
Method (5)
PlotLayout (1)
PlotStyle (1)
PlotTheme (1)
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:
Text
Wolfram Research (2010), WaveletListPlot, Wolfram Language function, https://reference.wolfram.com/language/ref/WaveletListPlot.html (updated 2014).
CMS
Wolfram Language. 2010. "WaveletListPlot." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2014. https://reference.wolfram.com/language/ref/WaveletListPlot.html.
APA
Wolfram Language. (2010). WaveletListPlot. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/WaveletListPlot.html