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:
  • AspectRatioAutomaticratio of height to width
    Joined Truewhether to join points
    Method Automaticwhat method to use
    PlotLayout "CommonXAxis"what layout to use for the plot
    PlotRange Allrange 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:
  • 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.

Examples

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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)

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:

Wolfram Research (2010), WaveletListPlot, Wolfram Language function, https://reference.wolfram.com/language/ref/WaveletListPlot.html (updated 2014).

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

BibTeX

@misc{reference.wolfram_2022_waveletlistplot, author="Wolfram Research", title="{WaveletListPlot}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/WaveletListPlot.html}", note=[Accessed: 20-March-2023 ]}

BibLaTeX

@online{reference.wolfram_2022_waveletlistplot, organization={Wolfram Research}, title={WaveletListPlot}, year={2014}, url={https://reference.wolfram.com/language/ref/WaveletListPlot.html}, note=[Accessed: 20-March-2023 ]}