WaveletListPlot
✖
WaveletListPlot
plots wavelet transform coefficients corresponding to the wavelet index specification wind.
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 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.
-
AlignmentPoint Center the default point in the graphic to align with AspectRatio Automatic ratio of height to width Axes True whether to draw axes AxesLabel None axes labels AxesOrigin Automatic where axes should cross AxesStyle {} style specifications for the axes Background None background color for the plot BaselinePosition Automatic how to align with a surrounding text baseline BaseStyle {} base style specifications for the graphic ContentSelectable Automatic whether to allow contents to be selected CoordinatesToolOptions Automatic detailed behavior of the coordinates tool DataRange Automatic the range of x values to assume for data Epilog {} primitives rendered after the main plot Filling None how to fill in stems for each point FillingStyle Automatic style to use for filling FormatType TraditionalForm the default format type for text Frame False whether to put a frame around the plot FrameLabel None frame labels FrameStyle {} style specifications for the frame FrameTicks Automatic frame ticks FrameTicksStyle {} style specifications for frame ticks GridLines None grid lines to draw GridLinesStyle {} style specifications for grid lines ImageMargins 0. the margins to leave around the graphic ImagePadding All what extra padding to allow for labels etc. ImageSize Automatic the absolute size at which to render the graphic IntervalMarkers Automatic how to render uncertainty IntervalMarkersStyle Automatic style for uncertainty elements Joined True whether to join points LabelingFunction Automatic how to label points LabelingSize Automatic maximum size of callouts and labels LabelStyle {} style specifications for labels Method Automatic what method to use MultiaxisArrangement None how to arrange multiple axes for data PerformanceGoal $PerformanceGoal aspects of performance to try to optimize PlotHighlighting Automatic highlighting effect for curves PlotLabel None overall label for the plot PlotLabels None labels for data PlotLayout "CommonXAxis" what layout to use for the plot PlotLegends None legends for data PlotMarkers None markers to use to indicate each point PlotRange All range of values to include PlotRangeClipping True whether to clip at the plot range PlotRangePadding Automatic how much to pad the range of values PlotRegion Automatic the final display region to be filled PlotStyle Automatic graphics directives to determine styles of points PlotTheme $PlotTheme overall theme for the plot PreserveImageOptions Automatic whether to preserve image options when displaying new versions of the same graphic Prolog {} primitives rendered before the main plot RotateLabel True whether to rotate y labels on the frame ScalingFunctions None how to scale individual coordinates TargetUnits Automatic units to display in the plot Ticks Automatic axes ticks TicksStyle {} style specifications for axes ticks
List of all options




Examples
open allclose allBasic Examples (1)Summary of the most common use cases
Compute a discrete wavelet transform:

https://wolfram.com/xid/0cpt410ym573i6-p8r1i8

https://wolfram.com/xid/0cpt410ym573i6-d6bzga

Plot the different wavelet transform coefficients:

https://wolfram.com/xid/0cpt410ym573i6-m4gs1v

Plot against a common vertical axis:

https://wolfram.com/xid/0cpt410ym573i6-b85hbx

Scope (16)Survey of the scope of standard use cases
Data (6)
Plot wavelet coefficients used by default in the inverse wavelet transform:

https://wolfram.com/xid/0cpt410ym573i6-qwfi5

https://wolfram.com/xid/0cpt410ym573i6-cjr0wt

Specify which coefficients to plot:

https://wolfram.com/xid/0cpt410ym573i6-bl9dxz

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

https://wolfram.com/xid/0cpt410ym573i6-g6dz7y

https://wolfram.com/xid/0cpt410ym573i6-ci78mh

Stationary wavelet transform coefficients are all the same length:

https://wolfram.com/xid/0cpt410ym573i6-dbdaj

https://wolfram.com/xid/0cpt410ym573i6-b428a6

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

https://wolfram.com/xid/0cpt410ym573i6-isofsj

https://wolfram.com/xid/0cpt410ym573i6-bm9ade

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

https://wolfram.com/xid/0cpt410ym573i6-gi4jr8

Plot multiple DiscreteWaveletData objects together:

https://wolfram.com/xid/0cpt410ym573i6-epl9mc

https://wolfram.com/xid/0cpt410ym573i6-kbyj1k

https://wolfram.com/xid/0cpt410ym573i6-dea9u2
Using Filling to highlight the differences:

https://wolfram.com/xid/0cpt410ym573i6-ctdznt

Apply a function to data before plotting:

https://wolfram.com/xid/0cpt410ym573i6-dr0dbr

https://wolfram.com/xid/0cpt410ym573i6-ec3sck

Presentation (10)
Lay out coefficients vertically or horizontally with a specified common axis:

https://wolfram.com/xid/0cpt410ym573i6-gwj84z

https://wolfram.com/xid/0cpt410ym573i6-donm6p

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

https://wolfram.com/xid/0cpt410ym573i6-hphaca

https://wolfram.com/xid/0cpt410ym573i6-b1dglr

Label coefficients by their full wavelet index:

https://wolfram.com/xid/0cpt410ym573i6-cghrlq

Curves are automatically styled to appear distinct:

https://wolfram.com/xid/0cpt410ym573i6-i3nn32

https://wolfram.com/xid/0cpt410ym573i6-jigmf2

https://wolfram.com/xid/0cpt410ym573i6-nrjs47

https://wolfram.com/xid/0cpt410ym573i6-xok8j
With multiple DiscreteWaveletData objects, each object is colored distinctly:

https://wolfram.com/xid/0cpt410ym573i6-ce5v13

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

https://wolfram.com/xid/0cpt410ym573i6-gbjf6h

Specify an overall style applying to every coefficient:

https://wolfram.com/xid/0cpt410ym573i6-gtm156

https://wolfram.com/xid/0cpt410ym573i6-l6qgw5

Provide explicit styling to each coefficient:

https://wolfram.com/xid/0cpt410ym573i6-euxfhi


https://wolfram.com/xid/0cpt410ym573i6-r4dg

https://wolfram.com/xid/0cpt410ym573i6-cc9z1j


https://wolfram.com/xid/0cpt410ym573i6-g1bq8f

https://wolfram.com/xid/0cpt410ym573i6-gzc02

Fill plots of each coefficient:

https://wolfram.com/xid/0cpt410ym573i6-mnpcsa

https://wolfram.com/xid/0cpt410ym573i6-c3xt2u


https://wolfram.com/xid/0cpt410ym573i6-3lbbhv

https://wolfram.com/xid/0cpt410ym573i6-xuubj5

https://wolfram.com/xid/0cpt410ym573i6-kt05zw


https://wolfram.com/xid/0cpt410ym573i6-syu9c5

https://wolfram.com/xid/0cpt410ym573i6-2cnzux

Plot DiscreteWaveletPacketTransform coefficients:

https://wolfram.com/xid/0cpt410ym573i6-pct0lz

https://wolfram.com/xid/0cpt410ym573i6-76xuh8

https://wolfram.com/xid/0cpt410ym573i6-4x7opd


https://wolfram.com/xid/0cpt410ym573i6-cf1d4n


https://wolfram.com/xid/0cpt410ym573i6-lgjns3


https://wolfram.com/xid/0cpt410ym573i6-0tjp6c

https://wolfram.com/xid/0cpt410ym573i6-0poe6y

Generalizations & Extensions (1)Generalized and extended use cases
Plot wavelet coefficients from complex-valued data:

https://wolfram.com/xid/0cpt410ym573i6-c9r4rv

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

https://wolfram.com/xid/0cpt410ym573i6-hppopy

By default, Re is applied:

https://wolfram.com/xid/0cpt410ym573i6-br4gb

Options (16)Common values & functionality for each option
DataRange (1)
Filling (1)
Frame (1)
FrameTicks (1)
By default, coefficients are labeled with their refinement level:

https://wolfram.com/xid/0cpt410ym573i6-b29r4x

https://wolfram.com/xid/0cpt410ym573i6-u32tx

https://wolfram.com/xid/0cpt410ym573i6-gktifg

Label with the full wavelet index:

https://wolfram.com/xid/0cpt410ym573i6-c1ldx5

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

https://wolfram.com/xid/0cpt410ym573i6-fcexo1

GridLines (1)
Joined (1)
Method (5)
Inverse transform each coefficient before plotting:

https://wolfram.com/xid/0cpt410ym573i6-cv9b4p

https://wolfram.com/xid/0cpt410ym573i6-d2854h

Control style of interior axes:

https://wolfram.com/xid/0cpt410ym573i6-eib72l

https://wolfram.com/xid/0cpt410ym573i6-ctmc3


https://wolfram.com/xid/0cpt410ym573i6-l3c3a9

https://wolfram.com/xid/0cpt410ym573i6-c9qa4

Choose which channel to plot in multichannel sound data:

https://wolfram.com/xid/0cpt410ym573i6-dikyxz

https://wolfram.com/xid/0cpt410ym573i6-cxjq8e

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

https://wolfram.com/xid/0cpt410ym573i6-b782u2

https://wolfram.com/xid/0cpt410ym573i6-djvwal

PlotLayout (1)
Plot coefficients over a common horizontal axis (default):

https://wolfram.com/xid/0cpt410ym573i6-esbohd

https://wolfram.com/xid/0cpt410ym573i6-cssokh

https://wolfram.com/xid/0cpt410ym573i6-eqq65w

Plot against a common vertical axis:

https://wolfram.com/xid/0cpt410ym573i6-o1k6b

PlotRange (1)
PlotStyle (1)
Specify an overall style for each wavelet coefficient:

https://wolfram.com/xid/0cpt410ym573i6-1bg73

https://wolfram.com/xid/0cpt410ym573i6-jzpkk5

https://wolfram.com/xid/0cpt410ym573i6-k21ap

Specify a single style for the whole plot:

https://wolfram.com/xid/0cpt410ym573i6-fwjr0n

PlotTheme (1)
Use a theme with grid lines in a bright color scheme:

https://wolfram.com/xid/0cpt410ym573i6-m2lcao

https://wolfram.com/xid/0cpt410ym573i6-29v5q7

Add a feature theme with frame and full grid lines:

https://wolfram.com/xid/0cpt410ym573i6-jz76qa

https://wolfram.com/xid/0cpt410ym573i6-ddd8ei


https://wolfram.com/xid/0cpt410ym573i6-joajh8

Ticks (1)
By default, coefficients are labeled with their refinement level:

https://wolfram.com/xid/0cpt410ym573i6-fxdzh

https://wolfram.com/xid/0cpt410ym573i6-h17pso

https://wolfram.com/xid/0cpt410ym573i6-c9tc3j

Label with the full wavelet index on vertical axis:

https://wolfram.com/xid/0cpt410ym573i6-nj8jw

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

https://wolfram.com/xid/0cpt410ym573i6-c2i8b8

Applications (4)Sample problems that can be solved with this function
Feature Detection (4)
Use PlotLayout->"CommonXAxis" to identify structure, such as edges in coefficients:

https://wolfram.com/xid/0cpt410ym573i6-c51qrn

https://wolfram.com/xid/0cpt410ym573i6-r46l9

Detail coefficients {…,1} are sensitive to edges:

https://wolfram.com/xid/0cpt410ym573i6-c4rs4x

https://wolfram.com/xid/0cpt410ym573i6-eyycn

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

https://wolfram.com/xid/0cpt410ym573i6-fcfy02

https://wolfram.com/xid/0cpt410ym573i6-fvkre9

Compare scale of constant and oscillatory parts:

https://wolfram.com/xid/0cpt410ym573i6-rzcx7

https://wolfram.com/xid/0cpt410ym573i6-e6tim1

Identify changing relative scale of coefficients:

https://wolfram.com/xid/0cpt410ym573i6-ddcpsh

https://wolfram.com/xid/0cpt410ym573i6-fcxh3s

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

https://wolfram.com/xid/0cpt410ym573i6-ge6otz

https://wolfram.com/xid/0cpt410ym573i6-bbpplh

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

https://wolfram.com/xid/0cpt410ym573i6-dqzpxi

https://wolfram.com/xid/0cpt410ym573i6-k8fh7b
Plot multiple sets of coefficients on the same WaveletListPlot:

https://wolfram.com/xid/0cpt410ym573i6-ed6g2m

https://wolfram.com/xid/0cpt410ym573i6-eax270

https://wolfram.com/xid/0cpt410ym573i6-bdv26f

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

https://wolfram.com/xid/0cpt410ym573i6-hmtbdp

Properties & Relations (5)Properties of the function, and connections to other functions
WaveletListPlot plots vector wavelet coefficients with a common horizontal or vertical axis:

https://wolfram.com/xid/0cpt410ym573i6-qhg65

https://wolfram.com/xid/0cpt410ym573i6-dnxltq

https://wolfram.com/xid/0cpt410ym573i6-dd00aq

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

https://wolfram.com/xid/0cpt410ym573i6-ekeg6

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

https://wolfram.com/xid/0cpt410ym573i6-f6up9i

https://wolfram.com/xid/0cpt410ym573i6-imlz62


https://wolfram.com/xid/0cpt410ym573i6-iroa21

WaveletBestBasis selects a different default tree of coefficients:

https://wolfram.com/xid/0cpt410ym573i6-ndabl8

https://wolfram.com/xid/0cpt410ym573i6-c58h50


https://wolfram.com/xid/0cpt410ym573i6-o2jz22

WaveletScalogram plots vector coefficients with numerical magnitude indicated by color:

https://wolfram.com/xid/0cpt410ym573i6-i7b594

https://wolfram.com/xid/0cpt410ym573i6-e10aos

https://wolfram.com/xid/0cpt410ym573i6-nbuq3

WaveletMatrixPlot plots matrix wavelet coefficients in a hierarchical grid:

https://wolfram.com/xid/0cpt410ym573i6-dd59u4

https://wolfram.com/xid/0cpt410ym573i6-bgp78f

https://wolfram.com/xid/0cpt410ym573i6-eb14aw

WaveletImagePlot shows image wavelet coefficients in a hierarchical grid:

https://wolfram.com/xid/0cpt410ym573i6-b7f69

https://wolfram.com/xid/0cpt410ym573i6-gpuis

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).
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.
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
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: 01-April-2025
]}
BibLaTeX
@online{reference.wolfram_2025_waveletlistplot, organization={Wolfram Research}, title={WaveletListPlot}, year={2014}, url={https://reference.wolfram.com/language/ref/WaveletListPlot.html}, note=[Accessed: 01-April-2025
]}