Preface
About the Authors
Notes by Yves Meyer
Notes by Ingrid Daubechies
Acknowledgements
What Is the Wavelet Toolbox?
Using This Guide
Caution
For More Background
Installing the Wavelet Toolbox
System Recommendations
Platform-Specific Details
Typographical Conventions
Related Products List
Wavelets: A New Tool for Signal Analysis
Wavelet Applications
Scale aspects
Time aspects
Wavelet Decomposition as a Whole
Fourier Analysis
Short-Time Fourier Analysis
Wavelet Analysis
What Can Wavelet Analysis Do?
What Is Wavelet Analysis?
Number of Dimensions
The Continuous Wavelet Transform
Scaling
Shifting
Five Easy Steps to a Continuous Wavelet Transform
Scale and Frequency
The Scale of Nature
What's Continuous About the Continuous Wavelet Transform?
The Discrete Wavelet Transform
One-Stage Filtering: Approximations and Details
Multiple-Level Decomposition
Wavelet Reconstruction
Reconstruction Filters
Reconstructing Approximations and Details
Relationship of Filters to Wavelet Shapes
Multistep Decomposition and Reconstruction
Wavelet Packet Analysis
History of Wavelets
An Introduction to the Wavelet Families
Haar
Daubechies
Biorthogonal
Coiflets
Symlets
Morlet
Mexican Hat
Meyer
Other Real Wavelets
Complex Wavelets
Using the Wavelet Toolbox
Using Wavelets
One-Dimensional Continuous Wavelet Analysis
Continuous Analysis Using the Command Line
Continuous Analysis Using the Graphical Interface
Importing and Exporting Information from the Graphical Interface
One-Dimensional Complex Continuous Wavelet Analysis
Complex Continuous Analysis Using the Command Line
Complex Continuous Analysis Using the Graphical Interface
Importing and Exporting Information from the Graphical Interface
One-Dimensional Discrete Wavelet Analysis
One-Dimensional Analysis Using the Command Line
One-Dimensional Analysis Using the Graphical Interface
Importing and Exporting Information from the Graphical Interface
Two-Dimensional Discrete Wavelet Analysis
Two-Dimensional Analysis Using the Command Line
Two-Dimensional Analysis Using the Graphical Interface
Importing and Exporting Information from the Graphical Interface
Wavelets: Working with Images
Understanding Images in MATLAB
Indexed Images
Wavelet Decomposition of Indexed Images
Other Images
Image Conversion
One-Dimensional Discrete Stationary Wavelet Analysis
One-Dimensional Analysis Using the Command Line
One-Dimensional Analysis for De-noising Using the Graphical Interface
Importing and Exporting Information from the Graphical Interface
Two-Dimensional Discrete Stationary Wavelet Analysis
Two-Dimensional Analysis Using the Command Line
Two-Dimensional Analysis for De-noising Using the Graphical Interface
Importing and Exporting Information from the Graphical Interface
One-Dimensional Wavelet Regression Estimation
One-Dimensional Estimation Using the GUI for Equally Spaced Observations (Fixed Design)
One-Dimensional Estimation Using the GUI for Randomly Spaced Observations (Stochastic Design)
Importing and Exporting Information from the Graphical Interface
One-Dimensional Wavelet Density Estimation
One-Dimensional Estimation Using the Graphical Interface
Importing and Exporting Information from the Graphical Interface
One-Dimensional Variance Adaptive Thresholding of Wavelet Coefficients
One-Dimensional Local Thresholding for De-noising Using the Graphical Interface
Importing and Exporting Information from the Graphical Interface
One-Dimensional Selection of Wavelet Coefficients Using the Graphical Interface
Two-Dimensional Selection of Wavelet Coefficients Using the Graphical Interface
One-Dimensional Extension
One-Dimensional Extension Using the Command Line
One-Dimensional Extension Using the Graphical Interface
Importing and Exporting Information from the Graphical Interface
Two-Dimensional Extension
Two-Dimensional Extension Using the Command Line
Two-Dimensional Extension Using the Graphical Interface
Importing and Exporting Information from the Graphical Interface
Wavelet Applications
Detecting Discontinuities and Breakdown Points I
Discussion
Detecting Discontinuities and Breakdown Points II
Discussion
Detecting Long-Term Evolution
Discussion
Detecting Self-Similarity
Wavelet Coefficients and Self-Similarity
Discussion
Identifying Pure Frequencies
Discussion
Suppressing Signals
Discussion
De-Noising Signals
Discussion
De-noising Images
Discussion
Compressing Images
Discussion
Fast Multiplication of Large Matrices
Wavelets in Action: Examples and Case Studies
Illustrated Examples
Advice to the Reader
Example 1: A Sum of Sines
Example 2: A Frequency Breakdown
Example 3: Uniform White Noise
Example 4: Colored AR(3) Noise
Example 5: Polynomial + White Noise
Example 6: A Step Signal
Example 7: Two Proximal Discontinuities
Example 8: A Second-Derivative Discontinuity
Example 9: A Ramp + White Noise
Example 10: A Ramp + Colored Noise
Example 11: A Sine + White Noise
Example 12: A Triangle + A Sine
Example 13: A Triangle + A Sine + Noise
Example 14: A Real Electricity Consumption Signal
Case Study: An Electrical Signal
Data and the External Information
Analysis of the Midday Period
Analysis of the End of the Night Period
Suggestions for Further Analysis
Using Wavelet Packets
About Wavelet Packet Analysis
One-Dimensional Wavelet Packet Analysis
Compressing a Signal Using Wavelet Packets
De-Noising a Signal Using Wavelet Packets
Two-Dimensional Wavelet Packet Analysis
Compressing an Image Using Wavelet Packets
Importing and Exporting from Graphical Tools
Saving Information to Disk
Loading Information into the Graphical Tools
Advanced Concepts
Mathematical Conventions
General Concepts
Wavelets: A New Tool for Signal Analysis
Wavelet Decomposition: A Hierarchical Organization
Finer and Coarser Resolutions
Wavelet Shapes
Wavelets and Associated Families
Wavelet Transforms: Continuous and Discrete
Local and Global Analysis
Synthesis: an Inverse Transform
Details and Approximations
The Fast Wavelet Transform (FWT) Algorithm
Filters Used to Calculate the DWT and IDWT
Algorithms
Why Does Such an Algorithm Exist?
One-Dimensional Wavelet Capabilities
Two-Dimensional Wavelet Capabilities
Dealing with Border Distortion
Signal Extensions: Zero-Padding, Symmetrization, and Smooth Padding
Discrete Stationary Wavelet Transform (SWT)
e-decimated DWT
How to Calculate the e-decimated DWT: SWT
Inverse Discrete Stationary Wavelet Transform (ISWT)
More about SWT
Frequently Asked Questions
Wavelet Families: Additional Discussion
Daubechies Wavelets: dbN
Symlet Wavelets: symN
Coiflet Wavelets: coifN
Biorthogonal Wavelet Pairs: biorNr.Nd
Meyer Wavelet: meyr
Battle-Lemarie Wavelets
Mexican Hat Wavelet: mexh
Morlet Wavelet: morl
Other Real Wavelets
Complex Wavelets
Summary of Wavelet Families and Associated Properties (Part 1)
Summary of Wavelet Families and Associated Properties (Part 2)
Wavelet Applications: More Detail
Suppressing Signals
Splitting Signal Components
Noise Processing
De-Noising
Data Compression
Function Estimation: Density and Regression
Available Methods for De-noising, Estimation and Compression Using GUI Tools
Wavelet Packets
From Wavelets to Wavelet Packets: Decomposing the Details
Wavelet Packets in Action: an Introduction
Building Wavelet Packets
Wavelet Packet Atoms
Organizing the Wavelet Packets
Choosing the Optimal Decomposition
Some Interesting Subtrees
Wavelet Packets 2-D Decomposition Structure
Wavelet Packets for Compression and De-Noising
References
Adding Your Own Wavelets
Preparing to Add a New Wavelet Family
Choose the Wavelet Family Full Name
Choose the Wavelet Family Short Name
Determine the Wavelet Type
Define the Orders of Wavelets Within the Given Family
Build a MAT-File or M-File
Define the Effective Support
Adding a New Wavelet Family
Example 1
Example 2
After Adding a New Wavelet Family
Reference
Reference
Functions by Category
allnodes
appcoef
appcoef2
bestlevt
besttree
biorfilt
biorwavf
centfrq
cgauwavf
cmorwavf
coifwavf
cwt
dbaux
dbwavf
ddencmp
depo2ind
detcoef
detcoef2
drawtree
dtree
dwt
dwt2
dwtmode
dyaddown
dyadup
entrupd
fbspwavf
gauswavf
get
idwt
idwt2
ind2depo
instdfft
intwave
isnode
istnode
iswt
iswt2
leaves
mexihat
meyer
meyeraux
morlet
nodeasc
nodedesc
nodejoin
nodepar
nodesplt
noleaves
nstdfft
ntnode
ntree
orthfilt
plot
qmf
rbiowavf
read
readtree
scal2frq
set
shanwavf
swt
swt2
symaux
symwavf
thselect
tnodes
treedpth
treeord
upcoef
upcoef2
upwlev
upwlev2
wavedec
wavedec2
wavedemo
wavefun
waveinfo
wavemenu
wavemngr
waverec
waverec2
wbmpen
wcodemat
wdcbm
wdcbm2
wden
wdencmp
wentropy
wextend
wfilters
wkeep
wmaxlev
wnoise
wnoisest
wp2wtree
wpbmpen
wpcoef
wpcutree
wpdec
wpdec2
wpdencmp
wpfun
wpjoin
wprcoef
wprec
wprec2
wpsplt
wpthcoef
wptree
wpviewcf
wrcoef
wrcoef2
wrev
write
wtbo
wthcoef
wthcoef2
wthresh
wthrmngr
Discrete Wavelet 1-D options.
Discrete Stationary Wavelet 1-D options.
Discrete Wavelet 2-D options.
Discrete Stationary Wavelet 2-D options.
Discrete Wavelet Packet 1-D options.
Discrete Wavelet Packet 2-D options.
wtreemgr
wvarchg
GUI Reference
General Features
Color Coding
Connectedness of Plots
Using the Mouse
Controlling the Colormap
Controlling the Number of Colors
Controlling the Coloration Mode
Using Menus
Using the View Axes Button
Using the Interval Dependent Threshold Settings Tool
Continuous Wavelet Tool Features
Wavelet 1-D Tool Features
Tree Mode
More Display Options
Wavelet 2-D Tool Features
Wavelet Packet Tool Features (1-D and 2-D)
Node Action Functionality
Wavelet Display Tool
Wavelet Packet Display Tool
Object-Oriented Programming
Short Description of Objects in the Toolbox
Simple Use of Objects Through Four Examples
Example 1: plot and wpviewcf
Example 2: drawtree and readtree
Example 3: A Funny One
Example 4: Thresholding Wavelet Packets
Detailed Description of Objects in the Toolbox
WTBO object
NTREE object
DTREE object
WPTREE object
Advanced Use of Objects
Example 1: Building a Wavelet Tree Object (WTREE)
Example 2: Building a Right Wavelet Tree Object (RWVTREE)
Example 3: Building a Wavelet Tree Object (WVTREE)
Example 4: Building a Wavelet Tree Object (EDWTTREE)
New Features Detailed Description
New Graphical User Interface Tools
New Wavelets
New Functions
Enhancements
Compatibility with Earlier Versions
Printable Documentation (PDF)
Product Page (Web)