Wavelet Toolbox™ User's Guide R2022b.

✍ Scribed by Michel Misiti; Yves Misiti; Georges Oppenheim; Jean-Michel Poggi

• Publisher: The MathWorks, Inc.
• Year: 2022
• Tongue: English
• Leaves: 1214
• Category: Library

✦ Table of Contents

Acknowledgments
Acknowledgments
Wavelets, Scaling Functions, and Conjugate Quadrature Mirror Filters
Wavelet Families
Daubechies Wavelets: dbN
Symlet Wavelets: symN
Coiflet Wavelets: coifN
Biorthogonal Wavelet Pairs: biorNr.Nd
Meyer Wavelet: meyr
Gaussian Derivatives Family: gaus
Mexican Hat Wavelet: mexh
Morlet Wavelet: morl
Additional Real Wavelets
Complex Wavelets
Wavelet Families and Associated Properties — I
Wavelet Families and Associated Properties — II
Lifting Method for Constructing Wavelets
Lifting Background
Polyphase Representation
Split, Predict, and Update
Haar Wavelet Via Lifting
Bior2.2 Wavelet Via Lifting
Add Lifting Step To Haar Lifting Scheme
Integer-to-Integer Wavelet Transform
Orthogonal and Biorthogonal Filter Banks
Scaling Function and Wavelet
Lifting a Filter Bank
Add Quadrature Mirror and Biorthogonal Wavelet Filters
Least Asymmetric Wavelet and Phase
Continuous Wavelet Analysis
Using Wavelet Time-Frequency Analyzer App
1-D Continuous Wavelet Analysis
Morse Wavelets
What Are Morse Wavelets?
Morse Wavelet Parameters
Effect of Parameter Values on Morse Wavelet Shape
Relationship Between Analytic Morse Wavelet and Analytic Signal
Comparison of Analytic Wavelet Transform and Analytic Signal Coefficients
Recommended Morse Wavelet Settings for the CWT
References
Boundary Effects and the Cone of Influence
Time-Frequency Analysis and Continuous Wavelet Transform
Continuous Wavelet Analysis of Modulated Signals
Remove Time-Localized Frequency Components
Time-Varying Coherence
Continuous Wavelet Analysis of Cusp Signal
Two-Dimensional CWT of Noisy Pattern
2-D Continuous Wavelet Transform
Discrete Wavelet Analysis
Critically Sampled and Oversampled Wavelet Filter Banks
Double-Density Wavelet Transform
Dual-Tree Complex Wavelet Transform
Dual-Tree Double-Density Wavelet Transforms
1-D Decimated Wavelet Transforms
Analysis-Decomposition Functions
Synthesis-Reconstruction Functions
Decomposition Structure Utilities
Denoising and Compression
1-D Analysis Using the Command Line
1-D Analysis Using the Wavelet Analyzer App
Importing and Exporting Information from the Wavelet Analyzer App
Fast Wavelet Transform (FWT) Algorithm
Filters Used to Calculate the DWT and IDWT
Algorithms
Why Does Such an Algorithm Exist?
1-D Wavelet Capabilities
2-D Wavelet Capabilities
Border Effects
Signal Extensions: Zero-Padding, Symmetrization, and Smooth Padding
Practical Considerations
Arbitrary Extensions
Image Extensions
Nondecimated Discrete Stationary Wavelet Transforms (SWTs)
ε-Decimated DWT
How to Calculate the ε-Decimated DWT: SWT
Inverse Discrete Stationary Wavelet Transform (ISWT)
More About SWT
1-D Stationary Wavelet Transform
Analysis-Decomposition Functions
Synthesis-Reconstruction Functions
1-D Analysis
Wavelet Changepoint Detection
Scale-Localized Volatility and Correlation
R Wave Detection in the ECG
Wavelet Cross-Correlation for Lead-Lag Analysis
1-D Multisignal Analysis
1-D Multisignal Analysis
2-D Discrete Wavelet Analysis
Analysis-Decomposition Functions
Synthesis-Reconstruction Functions
Decomposition Structure Utilities
Denoising and Compression
Wavelet Image Analysis and Compression
2-D Stationary Wavelet Transform
Analysis-Decomposition Function
Synthesis-Reconstruction Function
2-D Analysis
Shearlet Systems
Shearlets
Transform Type
References
Dual-Tree Complex Wavelet Transforms
Analytic Wavelets Using the Dual-Tree Wavelet Transform
Multifractal Analysis
Time-Frequency Gallery
Time-Frequency Gallery
Short-Time Fourier Transform (Spectrogram)
Continuous Wavelet Transform (Scalogram)
Wigner-Ville Distribution
Reassignment and Synchrosqueezing
Constant-Q Gabor Transform
Data-Adaptive Methods and Multiresolution Analysis
Wavelet Packets
About Wavelet Packet Analysis
Wavelet Packets
From Wavelets to Wavelet Packets
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 Denoising
Introduction to Object-Oriented Features
Objects in the Wavelet Toolbox Software
Examples Using Wavelet Packet Tree Objects
plot and wpviewcf
Change Terminal Node Coefficients
Thresholding Wavelet Packets
Description of Objects in the Wavelet Toolbox Software
WTBO Object
NTREE Object
Private
DTREE Object
WPTREE Object
Build Wavelet Tree Objects
Building a Wavelet Tree Object (WTREE)
Working With Wavelet Tree Objects (WTREE)
Building a Right Wavelet Tree Object (RWVTREE)
Working With Right Wavelet Tree Objects (RWVTREE)
Building a Wavelet Tree Object (WVTREE)
Working With Wavelet Tree Objects (WVTREE)
Building a Wavelet Tree Object (EDWTTREE)
Working With Wavelet Tree Object (EDWTTREE)
Denoising, Nonparametric Function Estimation, and Compression
Wavelet Denoising and Nonparametric Function Estimation
Denoising Methods
Soft or Hard Thresholding
Dealing with Unscaled Noise and Nonwhite Noise
Wavelet Denoising in Action
Extension to Image Denoising
1-D Wavelet Variance Adaptive Thresholding
Wavelet Denoising Analysis Measurements
Wavelet Denoising
Denoise a Signal with the Wavelet Signal Denoiser
Translation Invariant Wavelet Denoising with Cycle Spinning
1-D Cycle Spinning
Multivariate Wavelet Denoising
Multivariate Wavelet Denoising — Command Line
Wavelet Multiscale Principal Components Analysis
Wavelet Data Compression
Compression Scores
Wavelet Compression for Images
Effects of Quantization
True Compression Methods
Quantitative and Perceptual Quality Measures
More Information on True Compression
2-D Wavelet Compression
Compression by Global Thresholding and Huffman Encoding
Uncompression
Compression by Progressive Methods
Handling Truecolor Images
Matching Pursuit
Matching Pursuit Algorithms
Redundant Dictionaries and Sparsity
Nonlinear Approximation in Dictionaries
Basic Matching Pursuit
Orthogonal Matching Pursuit
Weak Orthogonal Matching Pursuit
Matching Pursuit
Sensing Dictionary Creation and Visualization
Orthogonal Matching Pursuit on 1-D Signal
Electricity Consumption Analysis Using Matching Pursuit
Code Generation from MATLAB Support in Wavelet Toolbox
Code Generation Support, Usage Notes, and Limitations
Denoise Signal Using Generated C Code
Generate Code to Denoise a Signal
CUDA Code from CWT
Special Topics
Wavelet Scattering
Wavelet Scattering Transform
Invariance Scale
Quality Factors and Filter Banks
In Practice
Wavelet Scattering Invariance Scale and Oversampling
Empirical Wavelet Transform
Tunable Q-factor Wavelet Transform
Frequency-Domain Scaling
TQWT Algorithm
Redundancy and Q-factor
Example: MRA of Audio Signal
Featured Examples — Time-Frequency Analysis
Practical Introduction to Continuous Wavelet Analysis
CWT-Based Time-Frequency Analysis
Time-Frequency Reassignment and Mode Extraction with Synchrosqueezing
Frequency- and Time-Localized Reconstruction from the Continuous Wavelet Transform
Compare Time-Frequency Content in Signals with Wavelet Coherence
Continuous and Discrete Wavelet Analysis of Frequency Break
Wavelet Packets: Decomposing the Details
Wavelet Analysis of Physiologic Signals
Visualize and Recreate EWT Decomposition
Visualize and Recreate VMD Decomposition
Featured Examples — Discrete Multiresolution Analysis
Practical Introduction to Multiresolution Analysis
Wavelet Analysis for 3-D Data
Multisignal 1-D Wavelet Analysis
Detecting Discontinuities and Breakdown Points
Haar Transforms for Time Series Data and Images
Wavelet Analysis of Financial Data
Image Fusion
Boundary Effects in Real-Valued Bandlimited Shearlet Systems
Wavelet Packet Harmonic Interference Removal
Visualize and Recreate TQWT Decomposition
Featured Examples — Denoising and Compression
Denoising Signals and Images
Wavelet Interval-Dependent Denoising
Multivariate Wavelet Denoising
Multiscale Principal Components Analysis
Data Compression using 2-D Wavelet Analysis
Smoothing Nonuniformly Sampled Data
Two-Dimensional True Compression
Signal Deconvolution and Impulse Denoising Using Pursuit Methods
Featured Examples — Machine Learning and Deep Learning
Signal Classification Using Wavelet-Based Features and Support Vector Machines
Wavelet Time Scattering for ECG Signal Classification
Wavelet Time Scattering Classification of Phonocardiogram Data
Wavelet Time Scattering with GPU Acceleration — Spoken Digit Recognition
Spoken Digit Recognition with Wavelet Scattering and Deep Learning
Classify Time Series Using Wavelet Analysis and Deep Learning
Texture Classification with Wavelet Image Scattering
Digit Classification with Wavelet Scattering
Acoustic Scene Recognition Using Late Fusion
GPU Acceleration of Scalograms for Deep Learning
Deploy Signal Classifier Using Wavelets and Deep Learning on Raspberry Pi
Crack Identification from Accelerometer Data
Deploy Signal Classifier on NVIDIA Jetson Using Wavelet Analysis and Deep Learning
Code Generation for a Deep Learning Simulink Model to Classify ECG Signals
Modulation Classification Using Wavelet Analysis on NVIDIA Jetson
Parasite Classification Using Wavelet Scattering and Deep Learning
Air Compressor Fault Detection Using Wavelet Scattering
Fault Detection Using Wavelet Scattering and Recurrent Deep Networks
Anomaly Detection Using Autoencoder and Wavelets
Detect Anomalies Using Wavelet Scattering with Autoencoders
Classify ECG Signals Using DAG Network Deployed to FPGA
Human Health Monitoring Using Continuous Wave Radar and Deep Learning
Signal Recovery with Differentiable Scalograms and Spectrograms
Wavelet Analyzer Topics
Matching Pursuit Using Wavelet Analyzer App
Matching Pursuit 1-D Interactive Tool
Interactive Matching Pursuit of Electricity Consumption Data
1-D Wavelet Packet Analysis
Starting the Wavelet Packet 1-D Tool
Importing a Signal
Analyzing a Signal
Computing the Best Tree
Compressing a Signal Using Wavelet Packets
De-Noising a Signal Using Wavelet Packets
2-D Wavelet Packet Analysis
Starting the Wavelet Packet 2-D Tool
Compressing an Image Using Wavelet Packets
Importing and Exporting from Wavelet Analyzer App
Saving Information to Disk
Loading Information into the Graphical Tools
drawtree and readtree
2-D CWT App Example
Importing and Exporting Information
Loading Signals
Saving Wavelet Coefficients
1-D Adaptive Thresholding of Wavelet Coefficients
1-D Local Thresholding Using the Wavelet Analyzer App
Importing and Exporting Information from the Wavelet Analyzer App
Multiscale Principal Components Analysis Using the Wavelet Analyzer App
Importing and Exporting PCA from the Wavelet Analyzer App
2-D Wavelet Compression using the Wavelet Analyzer App
Importing and Exporting Compressed Image from the Wavelet Analyzer App
Univariate Wavelet Regression
Regression for Equally-Spaced Observations
Regression for Randomly-Spaced Observations
Importing and Exporting Information from the Wavelet Analyzer App
Multivariate Wavelet Denoising Using the Wavelet Analyzer App
Importing and Exporting Denoised Signal from the Wavelet Analyzer App
Interactive 1-D Stationary Wavelet Transform Denoising
Selecting a Thresholding Method
Importing and Exporting 1-D SWT Denoised Image from the Wavelet Analysis App
3-D Discrete Wavelet Analysis
Performing 3-D Analysis Using the Command Line
Performing 3-D Analysis Using the Wavelet Analyzer App
Importing and Exporting Information from the Wavelet Analyzer App
2-D Wavelet Analysis Using the Wavelet Analyzer App
Importing and Exporting 2-D Information from the Wavelet Analyzer App
Saving Information to Disk
Loading Information into the Wavelet 2-D Tool
Interactive 2-D Stationary Wavelet Transform Denoising
Importing and Exporting 2-D SWT Information from the Wavelet Analyzer App
Comparing 1-D Extension Differences
1-D Multisignal Analysis Using the Wavelet Analyzer App
Manual Threshold Tuning
Statistics on Signals
Clustering Signals
Partitions
More on Clustering
Importing and Exporting Multisignal Information from the Wavelet Analyzer App
Saving Information to Disk
Saving Decompositions
Loading Information into the Wavelet 1-D Multisignal Analysis Tool
Loading and Saving Partitions.
Generating MATLAB Code from Wavelet Toolbox Wavelet Analyzer App
Generate MATLAB Code for 1-D Decimated Wavelet Denoising and Compression
Wavelet 1-D Denoising
Generate MATLAB Code for 2-D Decimated Wavelet Denoising and Compression
2-D Decimated Discrete Wavelet Transform Denoising
2-D Decimated Discrete Wavelet Transform Compression
Generate MATLAB Code for 1-D Stationary Wavelet Denoising
1-D Stationary Wavelet Transform Denoising
Generate MATLAB Code for 2-D Stationary Wavelet Denoising
2-D Stationary Wavelet Transform Denoising
Generate MATLAB Code for 1-D Wavelet Packet Denoising and Compression
1-D Wavelet Packet Denoising
Generate MATLAB Code for 2-D Wavelet Packet Denoising and Compression
2-D Wavelet Packet Compression
Wavelet Analyzer App Features Summary
General Features
Color Coding
Connection of Plots
Using the Mouse
Controlling the Colormap
Using Menus
Using the View Axes Button
Wavelet 2-D Tool Features
Wavelet Packet Tool Features (1-D and 2-D)
Coefficients Coloration
Node Action
Node Label
Node Action Functionality