Products
  • Wolfram|One

    The definitive Wolfram Language and notebook experience

  • Mathematica

    The original technical computing environment

  • Notebook Assistant + LLM Kit

    All-in-one AI assistance for your Wolfram experience

  • Compute Services
  • System Modeler
  • Finance Platform
  • Wolfram|Alpha Notebook Edition
  • Application Server
  • Enterprise Private Cloud
  • Wolfram Engine
  • Wolfram Player
  • Wolfram Cloud App
  • Wolfram Player App

More mobile apps

Core Technologies of Wolfram Products

  • Wolfram Language
  • Computable Data
  • Wolfram Notebooks
  • AI & Linguistic Understanding

Deployment Options

  • Wolfram Cloud
  • wolframscript
  • Wolfram Engine Community Edition
  • Wolfram LLM API
  • WSTPServer
  • Wolfram|Alpha APIs

From the Community

  • Function Repository
  • Community Paclet Repository
  • Example Repository
  • Neural Net Repository
  • Prompt Repository
  • Wolfram Demonstrations
  • Data Repository
  • Group & Organizational Licensing
  • All Products
Consulting & Solutions

We deliver solutions for the AI era—combining symbolic computation, data-driven insights and deep technical expertise

  • Data & Computational Intelligence
  • Model-Based Design
  • Algorithm Development
  • Wolfram|Alpha for Business
  • Blockchain Technology
  • Education Technology
  • Quantum Computation

Wolfram Consulting

Wolfram Solutions

  • Data Science
  • Artificial Intelligence
  • Biosciences
  • Healthcare Intelligence
  • Sustainable Energy
  • Control Systems
  • Enterprise Wolfram|Alpha
  • Blockchain Labs

More Wolfram Solutions

Wolfram Solutions For Education

  • Research Universities
  • Colleges & Teaching Universities
  • Junior & Community Colleges
  • High Schools
  • Educational Technology
  • Computer-Based Math

More Solutions for Education

  • Contact Us
Learning & Support

Get Started

  • Wolfram Language Introduction
  • Fast Intro for Programmers
  • Fast Intro for Math Students
  • Wolfram Language Documentation

More Learning

  • Highlighted Core Areas
  • Demonstrations
  • YouTube
  • Daily Study Groups
  • Wolfram Schools and Programs
  • Books

Grow Your Skills

  • Wolfram U

    Courses in computing, science, life and more

  • Community

    Learn, solve problems and share ideas.

  • Blog

    News, views and insights from Wolfram

  • Resources for

    Software Developers

Tech Support

  • Contact Us
  • Support FAQs
  • Support FAQs
  • Contact Us
Company
  • About Wolfram
  • Career Center
  • All Sites & Resources
  • Connect & Follow
  • Contact Us

Work with Us

  • Student Ambassador Initiative
  • Wolfram for Startups
  • Student Opportunities
  • Jobs Using Wolfram Language

Educational Programs for Adults

  • Summer School
  • Winter School

Educational Programs for Youth

  • Middle School Camp
  • High School Research Program
  • Computational Adventures

Read

  • Stephen Wolfram's Writings
  • Wolfram Blog
  • Wolfram Tech | Books
  • Wolfram Media
  • Complex Systems

Educational Resources

  • Wolfram MathWorld
  • Wolfram in STEM/STEAM
  • Wolfram Challenges
  • Wolfram Problem Generator

Wolfram Initiatives

  • Wolfram Science
  • Wolfram Foundation
  • History of Mathematics Project

Events

  • Stephen Wolfram Livestreams
  • Online & In-Person Events
  • Contact Us
  • Connect & Follow
Wolfram|Alpha
  • Your Account
  • User Portal
  • Wolfram Cloud
  • Products
    • Wolfram|One
    • Mathematica
    • Notebook Assistant + LLM Kit
    • Compute Services
    • System Modeler
    • Finance Platform
    • Wolfram|Alpha Notebook Edition
    • Application Server
    • Enterprise Private Cloud
    • Wolfram Engine
    • Wolfram Player
    • Wolfram Cloud App
    • Wolfram Player App

    More mobile apps

    • Core Technologies
      • Wolfram Language
      • Computable Data
      • Wolfram Notebooks
      • AI & Linguistic Understanding
    • Deployment Options
      • Wolfram Cloud
      • wolframscript
      • Wolfram Engine Community Edition
      • Wolfram LLM API
      • WSTPServer
      • Wolfram|Alpha APIs
    • From the Community
      • Function Repository
      • Community Paclet Repository
      • Example Repository
      • Neural Net Repository
      • Prompt Repository
      • Wolfram Demonstrations
      • Data Repository
    • Group & Organizational Licensing
    • All Products
  • Consulting & Solutions

    We deliver solutions for the AI era—combining symbolic computation, data-driven insights and deep technical expertise

    WolframConsulting.com

    Wolfram Solutions

    • Data Science
    • Artificial Intelligence
    • Biosciences
    • Healthcare Intelligence
    • Sustainable Energy
    • Control Systems
    • Enterprise Wolfram|Alpha
    • Blockchain Labs

    More Wolfram Solutions

    Wolfram Solutions For Education

    • Research Universities
    • Colleges & Teaching Universities
    • Junior & Community Colleges
    • High Schools
    • Educational Technology
    • Computer-Based Math

    More Solutions for Education

    • Contact Us
  • Learning & Support

    Get Started

    • Wolfram Language Introduction
    • Fast Intro for Programmers
    • Fast Intro for Math Students
    • Wolfram Language Documentation

    Grow Your Skills

    • Wolfram U

      Courses in computing, science, life and more

    • Community

      Learn, solve problems and share ideas.

    • Blog

      News, views and insights from Wolfram

    • Resources for

      Software Developers
    • Tech Support
      • Contact Us
      • Support FAQs
    • More Learning
      • Highlighted Core Areas
      • Demonstrations
      • YouTube
      • Daily Study Groups
      • Wolfram Schools and Programs
      • Books
    • Support FAQs
    • Contact Us
  • Company
    • About Wolfram
    • Career Center
    • All Sites & Resources
    • Connect & Follow
    • Contact Us

    Work with Us

    • Student Ambassador Initiative
    • Wolfram for Startups
    • Student Opportunities
    • Jobs Using Wolfram Language

    Educational Programs for Adults

    • Summer School
    • Winter School

    Educational Programs for Youth

    • Middle School Camp
    • High School Research Program
    • Computational Adventures

    Read

    • Stephen Wolfram's Writings
    • Wolfram Blog
    • Wolfram Tech | Books
    • Wolfram Media
    • Complex Systems
    • Educational Resources
      • Wolfram MathWorld
      • Wolfram in STEM/STEAM
      • Wolfram Challenges
      • Wolfram Problem Generator
    • Wolfram Initiatives
      • Wolfram Science
      • Wolfram Foundation
      • History of Mathematics Project
    • Events
      • Stephen Wolfram Livestreams
      • Online & In-Person Events
    • Contact Us
    • Connect & Follow
  • Wolfram|Alpha
  • Wolfram Cloud
  • Your Account
  • User Portal
Wolfram Language & System Documentation Center
WaveletListPlot
  • See Also
    • ListPlot
    • DiscreteWaveletData
    • WaveletMatrixPlot
    • DiscreteWaveletTransform
    • LiftingWaveletTransform
    • StationaryWaveletTransform
    • DiscreteWaveletPacketTransform
    • StationaryWaveletPacketTransform
  • Related Guides
    • Wavelet Analysis
    • Data Visualization
    • Signal Visualization & Analysis
    • See Also
      • ListPlot
      • DiscreteWaveletData
      • WaveletMatrixPlot
      • DiscreteWaveletTransform
      • LiftingWaveletTransform
      • StationaryWaveletTransform
      • DiscreteWaveletPacketTransform
      • StationaryWaveletPacketTransform
    • Related Guides
      • Wavelet Analysis
      • Data Visualization
      • Signal Visualization & Analysis

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
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Data  
Presentation  
Generalizations & Extensions  
Options  
AspectRatio  
Axes  
AxesLabel  
Show More Show More
AxesOrigin  
AxesStyle  
DataRange  
Filling  
Frame  
FrameTicks  
GridLines  
ImageSize  
Joined  
Method  
PlotLayout  
PlotRange  
PlotStyle  
PlotTheme  
Ticks  
Applications  
Feature Detection  
Properties & Relations  
Neat Examples  
See Also
Related Guides
History
Cite this Page
BUILT-IN SYMBOL
  • See Also
    • ListPlot
    • DiscreteWaveletData
    • WaveletMatrixPlot
    • DiscreteWaveletTransform
    • LiftingWaveletTransform
    • StationaryWaveletTransform
    • DiscreteWaveletPacketTransform
    • StationaryWaveletPacketTransform
  • Related Guides
    • Wavelet Analysis
    • Data Visualization
    • Signal Visualization & Analysis
    • See Also
      • ListPlot
      • DiscreteWaveletData
      • WaveletMatrixPlot
      • DiscreteWaveletTransform
      • LiftingWaveletTransform
      • StationaryWaveletTransform
      • DiscreteWaveletPacketTransform
      • StationaryWaveletPacketTransform
    • Related Guides
      • Wavelet Analysis
      • Data Visualization
      • Signal Visualization & Analysis

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: [List of all options]
  • AspectRatio Automaticratio 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
  • ColorData["DefaultPlotColors"] gives the default sequence of colors used by PlotStyle.
  • 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.
  • List of all options

    • AlignmentPointCenterthe default point in the graphic to align with
      AspectRatioAutomaticratio of height to width
      AxesTruewhether to draw axes
      AxesLabelNoneaxes labels
      AxesOriginAutomaticwhere axes should cross
      AxesStyle{}style specifications for the axes
      BackgroundNonebackground color for the plot
      BaselinePositionAutomatichow to align with a surrounding text baseline
      BaseStyle{}base style specifications for the graphic
      ContentSelectableAutomaticwhether to allow contents to be selected
      CoordinatesToolOptionsAutomaticdetailed behavior of the coordinates tool
      DataRangeAutomaticthe range of x values to assume for data
      Epilog{}primitives rendered after the main plot
      FillingNonehow to fill in stems for each point
      FillingStyleAutomaticstyle to use for filling
      FormatTypeTraditionalFormthe default format type for text
      FrameFalsewhether to put a frame around the plot
      FrameLabelNoneframe labels
      FrameStyle{}style specifications for the frame
      FrameTicksAutomaticframe ticks
      FrameTicksStyle{}style specifications for frame ticks
      GridLinesNonegrid lines to draw
      GridLinesStyle{}style specifications for grid lines
      ImageMargins0.the margins to leave around the graphic
      ImagePaddingAllwhat extra padding to allow for labels etc.
      ImageSizeAutomaticthe absolute size at which to render the graphic
      IntervalMarkersAutomatichow to render uncertainty
      IntervalMarkersStyleAutomaticstyle for uncertainty elements
      JoinedTruewhether to join points
      LabelingFunctionAutomatichow to label points
      LabelingSizeAutomaticmaximum size of callouts and labels
      LabelStyle{}style specifications for labels
      MethodAutomaticwhat method to use
      MultiaxisArrangementNonehow to arrange multiple axes for data
      PerformanceGoal$PerformanceGoalaspects of performance to try to optimize
      PlotHighlightingAutomatichighlighting effect for curves
      PlotLabelNoneoverall label for the plot
      PlotLabelsNonelabels for data
      PlotLayout"CommonXAxis"what layout to use for the plot
      PlotLegendsNonelegends for data
      PlotMarkersNonemarkers to use to indicate each point
      PlotRangeAllrange of values to include
      PlotRangeClippingTruewhether to clip at the plot range
      PlotRangePaddingAutomatichow much to pad the range of values
      PlotRegionAutomaticthe final display region to be filled
      PlotStyleAutomaticgraphics directives to determine styles of points
      PlotTheme$PlotThemeoverall theme for the plot
      PreserveImageOptionsAutomaticwhether to preserve image options when displaying new versions of the same graphic
      Prolog{}primitives rendered before the main plot
      RotateLabelTruewhether to rotate y labels on the frame
      ScalingFunctionsNonehow to scale individual coordinates
      TargetUnitsAutomaticunits to display in the plot
      TicksAutomaticaxes ticks
      TicksStyle{}style specifications for axes ticks

Examples

open all close all

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  (37)

AspectRatio  (1)

By default, the ratio of the height to width for the plot is determined automatically:

Make the height the same as the width with AspectRatio1:

Use numerical value to specify the height-to-width ratio:

AspectRatioFull adjusts the height and width to tightly fit inside other constructs:

Axes  (3)

By default, Axes are drawn:

Use AxesFalse to turn off axes:

Turn each axis on individually:

AxesLabel  (3)

No axes labels are drawn by default:

Place a label on the axis:

Specify axes labels:

AxesOrigin  (3)

The position of the axes is determined automatically:

Specify an explicit origin for the axes:

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:

AxesStyle  (4)

Change the style for the axes:

Specify the style of each axis:

Use different styles for the ticks and the axes:

Use different styles for the labels and the axes:

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:

ImageSize  (7)

Use named sizes such as Tiny, Small, Medium and Large:

Specify the width of the plot:

Specify the height of the plot:

Allow the width and height to be up to a certain size:

Specify the width and height for a graphic, padding with space if necessary:

Setting AspectRatioFull will fill the available space:

Use maximum sizes for the width and height:

Use ImageSizeFull to fill the available space in an object:

Specify the image size as a fraction of the available space:

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:

See Also

ListPlot  DiscreteWaveletData  WaveletMatrixPlot  DiscreteWaveletTransform  LiftingWaveletTransform  StationaryWaveletTransform  DiscreteWaveletPacketTransform  StationaryWaveletPacketTransform

Related Guides

    ▪
  • Wavelet Analysis
  • ▪
  • Data Visualization
  • ▪
  • Signal Visualization & Analysis

History

Introduced in 2010 (8.0) | Updated in 2014 (10.0)

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_2025_waveletlistplot, author="Wolfram Research", title="{WaveletListPlot}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/WaveletListPlot.html}", note=[Accessed: 04-February-2026]}

BibLaTeX

@online{reference.wolfram_2025_waveletlistplot, organization={Wolfram Research}, title={WaveletListPlot}, year={2014}, url={https://reference.wolfram.com/language/ref/WaveletListPlot.html}, note=[Accessed: 04-February-2026]}

Top
Introduction for Programmers
Introductory Book
Wolfram Function Repository | Wolfram Data Repository | Wolfram Data Drop | Wolfram Language Products
Top
  • Products
  • Wolfram|One
  • Mathematica
  • Notebook Assistant + LLM Kit
  • Compute Services
  • System Modeler

  • Wolfram|Alpha Notebook Edition
  • Wolfram|Alpha Pro
  • Mobile Apps

  • Wolfram Engine
  • Wolfram Player

  • Volume & Site Licensing
  • Server Deployment Options
  • Consulting
  • Wolfram Consulting
  • Repositories
  • Data Repository
  • Function Repository
  • Community Paclet Repository
  • Neural Net Repository
  • Prompt Repository

  • Wolfram Language Example Repository
  • Notebook Archive
  • Wolfram GitHub
  • Learning
  • Wolfram U
  • Wolfram Language Documentation
  • Webinars & Training
  • Educational Programs

  • Wolfram Language Introduction
  • Fast Introduction for Programmers
  • Fast Introduction for Math Students
  • Books

  • Wolfram Community
  • Wolfram Blog
  • Public Resources
  • Wolfram|Alpha
  • Wolfram Problem Generator
  • Wolfram Challenges

  • Computer-Based Math
  • Computational Thinking
  • Computational Adventures

  • Demonstrations Project
  • Wolfram Data Drop
  • MathWorld
  • Wolfram Science
  • Wolfram Media Publishing
  • Customer Resources
  • Store
  • Product Downloads
  • User Portal
  • Your Account
  • Organization Access

  • Support FAQ
  • Contact Support
  • Company
  • About Wolfram
  • Careers
  • Contact
  • Events
Wolfram Community Wolfram Blog
Legal & Privacy Policy
WolframAlpha.com | WolframCloud.com
© 2026 Wolfram
© 2026 Wolfram | Legal & Privacy Policy |
English