| Wavelet Toolbox |
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- About the Authors
- Notes by Yves Meyer
- Notes by Ingrid Daubechies
- Acknowledgments
- What Is the Wavelet Toolbox?
- Using This Guide
- New Users
- Experienced Users
- All Users
- Caution
- For More Background
- Installing the Wavelet Toolbox
- System Recommendations
- Platform-Specific Details
- Typographical Conventions
- Related Products
- 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
- 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 Z
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
- 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
- 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
- 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
- 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
- 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
- Functions - By Category
- Graphical User Interface Tools
- General Wavelet Functions
- Wavelet Families
- Continuous Wavelet: One-Dimensional
- Discrete Wavelets: One-Dimensional
- Discrete Wavelets: Two-Dimensional
- Wavelet Packet Algorithms
- Discrete Stationary Wavelet Transform Algorithms
- De-Noising and Compression for Signals/ Images
- Tree Management Utilities
- General Utilities
- Miscellaneous Functions and Demos
- Obsolete Functions
- Functions - Alphabetical List
- General Features
- Color Coding
- Connection of Plots
- Using the Mouse
- Controlling the Colormap
- 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
- 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)
| | Preface | |