Wavelets and Wavelet Transform Systems and Their Applications - A Digital Signal Processing Approach

Description

This textbook is unique because of its in-depth treatment of the applications of wavelets and wavelet transforms to many areas, across many disciplines. The book is written to serve the needs of a one or two semester course at either the undergraduate or graduate level. The author uses a very simplified, accessible approach that de-emphasizes mathematical rigor. The presentation includes many diagrams to illustrate points being discussed and uses MATLAB for all of application code. The author reinforces concepts introduced in the book with easy to grasp review questions and problems, tailored to each specific chapter for better mastery of the subject matter. This book enables students to understand the fundamental concepts of wavelets and wavelet transforms, as well as how to use them for problem solutions in digital signal and image processing, mixed-signal testing, space applications, aerospace applications, biomedical, cyber security, homeland security and many other application areas. Provides textbook coverage of Wavelets and applications, suitable for one and two semester courses, either at the undergraduate or graduate level; Discusses many types of wavelets and their applications across many disciplines; Includes MATLAB code illustrations to simplify the understanding of the various applications; Uses many illustrations, figures, tables, and visual comparisons to simplify and clarify the various concepts of wavelets, wavelet transforms and the various application areas; Ends each chapter with review questions/answers, as well as exercises to reinforce and test concepts introduced; Solutions manual and PowerPoint slides for each chapter available for instructors. Cajetan M. Akujuobi received his O.N.D. from Institute of Management and Technology Enugu, Nigeria in 1974, the B.S. degree from Southern University, Baton Rouge, Louisiana, in 1980, the M.S. degree from Tuskegee University, Alabama, in 1982, all in electrical & electronics engineering. He received the M.B.A. degree from Hampton University, Hampton, Virginia, in 1987. In 1995, he received the Ph.D. degree from George Mason University, Fairfax, Virginia, in electrical engineering with specialization in signal/image/video processing & communication systems. He is a full Professor in the Department of Electrical & Computer Engineering and the former Vice President for Research, Innovation and Sponsored Programs at Prairie View A&M University (PVAMU). He served as Dean in two different Universities - the Dean for Graduate Studies at PVAMU and founding STEM Dean at Alabama State University (ASU). He is the founder and the Executive Director of the Center of Excellence for Communication Systems Technology Research (CECSTR), a Texas A&M Board of Regents approved center where he has been able to attract research-funding exceeding over $25 Million. He is the founder and the Principal Investigator for the SECURE Cybersecurity Center of Excellence at PVAMU where he has received over $7 Million research award. Under his leadership as the Vice President for Research, Innovation and Sponsored Programs at Prairie View A&M University (PVAMU), he was instrumental in bringing to PVAMU five new Chancellors’ Research Initiative (CRI) research centers worth about $35 Million. He has worked in such corporations as Texas Instruments, Advanced Hardware Architecture, Schlumberger, Data Race Corporation, Spectrum Engineering, Intelsat and Bell Laboratories. Prof. Akujuobi developed and taught the Wavelets and Their Applications course at PVAMU for over 20 years. His research interests are in Wavelets and Wavelet transform Analysis and Applications, Cybersecurity, Smart & Connected Cities and DSP Solutions. In addition, his research interests include Communication Systems, Compressive Sensing, Signal/Image/Video Processing, Broadband Communication Systems, and Mixed Signal Systems. He was a participant and collaborative member of the ANSI TIEI.4 Working Group that had the technical responsibility of developing the T1.413, Issue 2 ADSL standard. He has received several professional and community related honors in teaching, research and service and has published extensively including writing books and book Chapters. Two of the books he published with Dr. M. N. O. Sadiku, are “Introduction to Broadband Communication Systems”, and “Solutions Manual for Introduction to Broadband Communication Systems”, both published by Chapman & Hall/CRC and Sci-Tech Publication, Boca Raton, Florida. Prof. Akujuobi is the current Chair of the IEEE Houston Section Life Members Group. He is also a Life Senior Member of the Institute of Electrical and Electronic Engineers (IEEE), Senior Member of Instrument Society of America (ISA), Member of American Society for Engineering Education (ASEE), Sigma XI, the Scientific Research Society, and the Texas Society for Biomedical Research (TSBR) Board of Directors. He is a licensed Professional Engineer in the State of Texas, USA. Preface Overview Acknowledgments Contents About the Author Abbreviations Chapter 1: Fundamental Concepts 1.1 Introduction 1.2 Fourier Transform and Analysis 1.3 Short-Time Fourier Transform 1.4 The Wavelet Transform Idea 1.5 Types of Wavelet Transforms 1.5.1 The Continuous Wavelet Transform (CWT) 1.5.2 The Discrete Wavelet Transform (DWT) 1.6 Wavelet Frames and Bases 1.7 Constructing Orthonormal Wavelet Bases with Compact Support 1.8 Similarities Between Wavelets and Fourier Transforms 1.9 Dissimilarities Between Wavelets and Fourier Transforms References Part I: Wavelets, Wavelet Transforms and Generations of Wavelets Chapter 2: Wavelets 2.1 Introduction 2.2 What Are Wavelets and Why Do We Look at Wavelets? 2.3 Types of Wavelets 2.3.1 The Haar Wavelet 2.3.2 The Daubechies Wavelet 2.3.3 The Morlet Wavelet 2.3.4 The Meyer Wavelet 2.3.5 The Mexican Hat Wavelet 2.3.6 The Berlage Wavelet 2.3.7 The Biorthogonal Wavelets 2.3.8 The Shannon Wavelet 2.3.9 The Symlet Wavelet 2.3.10 The Coiflet Wavelet 2.3.11 The Spline Wavelet 2.3.12 The Gabor Wavelet 2.3.13 The Lemarie-Battle Wavelet 2.3.14 The Mallat Wavelet Multiresolution Analysis 2.3.15 The Poisson Wavelet 2.3.16 Mathieu Wavelets 2.3.17 Strömberg Wavelet 2.3.18 Legendre Wavelet 2.3.19 Beta Wavelet References Chapter 3: Generations of Wavelets 3.1 Introduction 3.2 Brief History of Wavelets 3.3 First-Generation Wavelets 3.4 Second-Generation Wavelets 3.5 The Shortcomings with the First and Second Generations of the Wavelet Models 3.6 Third Generation of Wavelets 3.7 Next-Generation Wavelets 3.8 Comparisons of the Different Generations of Wavelets References Chapter 4: Wavelet Transforms 4.1 Introduction 4.2 The Multiscale Wavelet Transform 4.3 One-Dimensional Wavelet Transform 4.3.1 Relationship Between the High-Pass and the Low-Pass Coefficients 4.3.2 Multiple Stage Decomposition and Reconstruction Idea 4.3.3 Determination of the Number of Stages for Decomposition and Reconstruction 4.4 Two-Dimensional Wavelet Transform References Chapter 5: Similarities Between Wavelets and Fractals 5.1 Introduction 5.2 The Self-Similarity Idea in Wavelets and Fractals 5.3 Fractal Dimension Idea 5.4 Iterated Function System Code 5.5 Types of Fractals 5.5.1 Random Fractals 5.5.2 Scaling Fractals 5.5.3 The Koch Fractal 5.5.4 The Sierpinski Fractal 5.5.5 The Cantor Fractal 5.6 Areas of Similarities Between Wavelets and Fractals Based on Their Properties 5.6.1 Self-Similarity 5.6.2 Scaling Function 5.6.3 Affine Transforms 5.7 Areas of Similarities Between Wavelets and Fractals Based on Their Application Areas 5.7.1 Application to Modeling and Seismic Studies 5.7.2 Construction and Reconstruction of Images 5.7.3 Graphical, Storage, and Communication Applications 5.7.4 Image Compression 5.7.5 Texture Segmentation 5.7.6 Edge Detection of Images 5.7.7 Geometrical Objects Representation 5.7.8 The Multiscale Analysis and Representation of Signals References Part II: Wavelet and Wavelet Transform Applications to Mixed Signal Systems Chapter 6: Test Point Selection Using Wavelet Transforms for Digital-to-Analog Converters 6.1 Introduction 6.2 The Stenbakken and Souders Algorithm 6.3 Wavelet Transform Test Point Selection Algorithm 6.3.1 Circuit Model 6.3.2 Three Basic Model Types 6.3.3 Circuit Model by Wavelet Transforms 6.3.4 Choosing Test Points by QR Factorization 6.4 Implementation of the Test Method in Programming 6.4.1 Measured INL Data of 8-Bit DAC 6.4.2 Selection of a Set of Maximally Independent INL 6.4.3 Multiresolution Decomposition 6.4.4 Selection of the Independent Signatures (Coefficients) 6.4.5 Generation of a Reduced Matrix Ar from Q and R Matrices 6.4.6 Estimation of the Matrix Parameters of the Device 6.4.7 Generation of the Predicted INL ypk for all M Candidate Test Points 6.4.8 Getting the Root-Mean-Square for the Device k 6.4.9 Plotting the Measured INL, Predicted INL, and RMS Figures References Chapter 7: Wavelet-Based Dynamic Test of ADCS 7.1 Introduction 7.2 Measuring ENOB Using the Conventional Method 7.2.1 Measuring the ENOB Using FFT Method 7.2.2 Computing SNR Through FFT 7.2.3 Computing ENOB Through SNR 7.3 Measuring DNL Using Sinusoidal Histogram 7.3.1 Differential and Integral Nonlinearity 7.3.2 Sinusoidal Histogram Measurement 7.3.3 Measuring ENOB and DNL of ADC Using Discrete Wavelet Transform 7.3.4 Measuring the Instantaneous ENOB and DNL Using Haar Wavelet Transform 7.3.5 Measuring the Instantaneous ENOB 7.3.6 Measuring the Instantaneous DNL 7.4 Measuring ENOB and DNL of ADC Using Daubechies-4 Wavelet Transform 7.4.1 Daubechies-4 Wavelet Transform Using MATLAB 7.4.2 Measuring the ADC Instantaneous ENOB and DNL Using Daubechies-4 Wavelets 7.5 Extensions of the Wavelet-Based ADC Dynamic Test Algorithms and Key Observations 7.5.1 Hilbert Transform Implementation 7.5.2 The Range of |z[n]| 7.5.3 Using Different Formulations of the Haar Wavelet Coefficients in the Algorithm 7.6 Comparative Analysis of the Measurements for ADC 7.6.1 ENOB Measurements 7.6.2 DNL Measurements 7.7 The MATLAB Program for the ENOB and DNL Measurements 7.8 Differences Between Wavelet Transform Techniques and the Conventional Techniques in a Tabular Format References Chapter 8: Wavelet-Based Static Test of ADCs 8.1 Introduction 8.2 Static Testing of ADCs by Transfer Curve 8.2.1 ADC Transfer Curve 8.2.2 Testing for ADC Errors Using the DNL 8.3 Wavelet Transform-Based Static Testing of an ADC 8.3.1 The ADC Static Testing Method and Choice of Wavelet Transforms 8.3.2 Simulation of the ADC Testing Using Wavelet Transform 8.3.3 MATLAB Program for Measuring and Plotting some of the Wavelet-Based Static Testing of ADCs References Chapter 9: Mixed Signal Systems Testing Automation Using Discrete Wavelet Transform-Based Techniques 9.1 Introduction 9.2 Noise and Quantization Error 9.3 Worst-Case Effective Number of Bits (ENOB) 9.4 Instantaneous Differential Nonlinearity (DNL) 9.5 Instantaneous Integral Nonlinearity (INL) 9.6 Automation Testing Setup with LabVIEW and DWT 9.7 Testing Automation Programming Process 9.7.1 NI PXI-1042 Chassis 9.7.2 Power Supplies 9.7.3 HSDIO Card PXI-6552: Arbitrary Digital Waveform Generator 9.7.4 Scope Card PXI-5922 9.8 ADC Testing Setup and LabVIEW VIs 9.8.1 HSDIO Card PXI-6552 9.8.2 Waveform Generator NI PXI-5421 9.9 The GUI (Graphic User Interface) 9.10 Implementation of an Automated DWT-Based Algorithm for the Testing of ADCS 9.11 A Comparative Tabular Summary of the Automated ADC Testing Using DWTs 9.12 Implementation of an Automated DWT-Based Algorithm for the Testing of DACs 9.13 Cost Analysis in Terms of Test Duration Reduction References Part III: Wavelets and Wavelet Transform Application to Compression Chapter 10: Wavelet-Based Compression Using Nonorthogonal and Orthogonally Compensated W-Matrices 10.1 Introduction 10.2 Orthogonality Condition 10.3 W-Transform and W-Matrix 10.4 The Orthogonality Compensation Process 10.5 Compression Algorithms for the Nonorthogonal and Orthogonally Compensated Cases 10.6 Simulation Examples 10.7 Performance Evaluation for the Simulation Examples 10.8 The Simulation Example Results and Discussions References Chapter 11: Wavelet Application to Image and Data Compression 11.1 Introduction 11.2 Compression Ideas 11.2.1 Irrelevant Information Redundancy 11.2.2 Spatial and Temporal Redundancy 11.2.3 Coding Redundancy 11.3 Justification for Compression 11.4 The Different Modes of Compression 11.4.1 Lossless Compression Mode 11.4.2 Lossy Compression Mode 11.4.3 Predictive Compression Mode 11.4.4 Transform Coding Compression Mode 11.5 The Different Compression Techniques 11.5.1 JPEG/DCT Compression Technique 11.5.2 Vector Quantization (VQ) Compression Technique 11.5.3 Fractal Image Compression Technique 11.5.4 Wavelet Image Compression Technique 11.6 The Compression and Decompression of an Image/Data Using Wavelet Transform 11.7 The EZWT Algorithm 11.8 The SPIHT Algorithm 11.9 The EBCOT Algorithm 11.10 The WDR Algorithm 11.11 The ASWDR Algorithm 11.12 Usefulness of Wavelet-Based Compression References Chapter 12: Application of Wavelets to Video Compression 12.1 Introduction 12.2 Video Compression Quality and the Metrics 12.3 Video Compression Errors 12.3.1 Blocking Artifacts 12.3.2 Blurriness 12.3.3 Motion Estimation Errors 12.4 Transmission Errors: Packet Loss 12.5 Justification for Wavelet-Based Video Compression 12.6 The Basic Principles of the Wavelet-Based Technique to SVC 12.7 Wavelet-Based Three-Dimensional Video Compression 12.8 The Basic Image and Video Compression Standards 12.8.1 The Joint Pictures Experts Group (JPEG) 12.8.2 The Joint Pictures Experts Group (JPEG) 2000 12.8.3 The H.261 Video Compression Standard 12.8.4 The H.263 Video Compression Standard 12.8.5 The H.264 Video Compression Standard 12.8.6 The MPEG-1 Video Compression Standard 12.8.7 The MPEG-2 Video Compression Standard 12.8.8 The MPEG-4 Video Compression Standard 12.8.9 The MPEG-7 Video Compression Standard References Part IV: Wavelets and Wavelet Transforms to Medical Application Chapter 13: Wavelet Application to an Electrocardiogram (ECG) Medical Signal 13.1 Introduction 13.2 Description of an ECG Signal 13.3 Discrete Wavelet Transform Application to ECG Signals 13.3.1 One-Level DWT Decomposition and Reconstruction of the ECG Process 13.3.2 Extension to Five Levels of Decomposition and Reconstruction of the ECG Signals 13.3.3 The DWT Noise Removal Technique Using ECG Signals 13.4 Metrics for Performance Evaluation 13.4.1 Signal-to-Noise Ratio (SNR) 13.4.2 Peak Signal-to-Noise Ratio (PSNR) 13.4.3 Mean Squared Error (MSE) 13.4.4 Maximum Squared Error (MAXERR) 13.5 Evaluations of the Performance Measures References Part V: Wavelet and Wavelet Transform Application to Segmentation Chapter 14: Application of Wavelets to Image Segmentation 14.1 Introduction 14.2 Image Segmentation Idea 14.3 Thresholding Technique 14.3.1 Local Thresholding 14.3.2 Adaptive Thresholding 14.3.3 Global Thresholding 14.4 Implementation of the Region-Based Technique 14.4.1 Growing the Region 14.4.2 Region Splitting and Merging 14.5 Watershed Segmentation Technique 14.5.1 Watershed Segmentation Algorithm 14.5.2 Gradient of the Image 14.6 K-Means Clustering 14.7 Template Matching Segmentation Technique 14.7.1 The Definition and Method Template Matching 14.7.2 The bi-Level Image Template Matching 14.7.3 Gray-Level Image Template Matching 14.8 Contour-Based Segmentation Technique 14.8.1 Internal Energy 14.8.2 External Energy 14.9 Wavelet-Based Segmentation Technique 14.9.1 Image Feature Extraction 14.9.2 Pixel Differences 14.9.3 Circular Averaging Filtering 14.9.4 Thresholding References Chapter 15: Hybrid Wavelet- and Fractal-Based Segmentation 15.1 Introduction 15.2 The Hybrid Wavelet- and Fractal-Based Segmentation Model 15.3 Computation of Wavelet-Based Analysis Image Data for the Hybrid Segmentation Process 15.3.1 Wavelet-Based Analysis Image Data Computation Process for Segmentation 15.3.2 Algorithm for the Computation of the Wavelet-Based Analysis Image Data for Segmentation 15.4 Computation of Fractal-Based Analysis Image Data for the Hybrid Segmentation Process 15.4.1 The Fractal-Based Analysis Image Data Computation Process 15.4.2 Algorithm for the Computation of the Fractal-Based Analysis Image Data for Segmentation 15.5 Formalizing the Notion of Segmentation 15.6 The Segmentation Model Process 15.6.1 Classification Theory Formulation 15.6.2 The Segmentation (Classification) Model Algorithm 15.7 Example of Simulation Results and Discussions 15.8 Performance Complexity Evaluation References Part VI: Wavelet and Wavelet Transform Application to Cybersecurity Systems Chapter 16: Wavelet-Based Application to Information Security 16.1 Introduction 16.2 Information Security Schemes 16.2.1 Confidentiality 16.2.2 Integrity 16.2.3 Availability 16.3 Wavelet Application Analysis to Information Security 16.4 Detection Methods 16.5 Detection Schemes 16.6 Information Network Security Data Analysis Using Wavelet Transforms 16.6.1 Data Collection and Information Network Security Database (INSD) Segment 16.6.2 The Wavelet Transform Application Including the Denoised Segment 16.7 MATLAB Implementation of the Wavelet Transform-Based Analysis Algorithms 16.8 Wavelet Transforms and Cryptography in Information Security 16.8.1 AES Algorithm 16.8.2 Description of the Ciphers 16.8.3 Non-Uniform Block Adaptive Segmentation on Information (NUBASI) 16.8.4 Randomized Secret Sharing (RSS) 16.9 Cryptographic Symmetric and Asymmetric Systems 16.9.1 Substitution Permutation Cipher References Chapter 17: Application of Wavelets to Biometrics 17.1 Introduction 17.2 Biometric Characteristics 17.3 Biometric System 17.3.1 Enrollment Mode 17.3.2 Verification Mode 17.3.3 Identification Mode 17.4 Basics of Fingerprint Recognition 17.5 Classification of Fingerprints 17.5.1 Loops 17.5.2 Whorls 17.5.3 Arches 17.6 Fingerprint Matching Techniques 17.6.1 Ridge Feature-Based Matching 17.6.2 Correlation-Based Matching 17.6.3 Minutiae-Based Matching 17.7 The Fingerprinting Minutiae Matching System Algorithm Using Wavelet Transform 17.7.1 Partial Image Enhancement 17.7.2 Minutiae Extraction 17.7.3 Fingerprint Image Post-Processing 17.7.4 Procedure for Validating a Candidate Ridge Ending Point 17.7.5 Procedure for Validating a Candidate Bifurcation Point 17.8 Methodology 17.8.1 Performance Metrics 17.9 MATLAB Simulation Examples 17.10 Matching Indices for Different Wavelets References Chapter 18: Wavelet Application to Blockchain Technology Systems 18.1 Introduction 18.2 Capabilities and Limitations of Blockchain 18.2.1 Capabilities of Blockchain Technology 18.2.2 Limitations of Blockchain Technology 18.3 Blockchain-Based Strategies 18.4 How Blockchain Powers Applications Such as Bitcoin and Other Token-Based Initiatives 18.5 Different Types of Blockchain Models 18.5.1 Hyperledger 18.5.2 Fabric 18.5.3 Ethereum 18.6 Wavelet Transform Analysis 18.7 Wavelet Transform Analysis of Blockchain Systems 18.8 Wavelets and Bitcoin 18.9 Main Drivers of the Bitcoin Price as Evidenced from Wavelet Coherence Analysis 18.10 Advantages of Using Wavelets in Blockchain Systems 18.11 Disadvantages of Using Wavelets in Blockchain Systems References Part VII: Wavelet and Wavelet Transform Application to Detection, Discrimination and Estimation Chapter 19: Wavelet-Based Signal Detection, Identification, Discrimination, and Estimation 19.1 Introduction 19.2 Wavelet Transform 19.2.1 Haar Wavelet Characteristics 19.2.2 Morlet Wavelet Characteristics 19.3 Overview of the Wavelet-Based Signal Detection 19.3.1 Chirp Signal 19.3.2 Frequency-Shift Keying (FSK) Signals 19.3.3 Phase-Shift Keying (PSK) Signals 19.3.4 Quadrature Amplitude Modulation (QAM) Signals 19.4 Overall Detection System Model 19.5 Chirp Signal Detection 19.6 PSK, FSK, and QAM Interclass Detection 19.7 PSK and FSK Intraclass Detection, Estimation, and Identification 19.7.1 M-ary PSK Identification, Estimation, and Detection 19.7.2 M-ary FSK Identification, Estimation, and Detection 19.8 Overview of the GUI-Based Simulation Interface References Chapter 20: Wavelet-Based Identification, Discrimination, Detection, and Parameter Estimation of Radar Signals 20.1 Introduction 20.2 AMRTDS 20.3 Wavelet-Based Detection of Signals Using Pattern Recognition 20.3.1 Wavelet Transform Algorithm 20.3.2 Discrimination of Signals Using Signal Pattern Recognition 20.4 Wavelet-Based Detection of Signals Using Bayes´ Theorem 20.4.1 Signal Detection Using Bayes´ Theorem and Wavelet Transform 20.5 Calculation Examples 20.6 Receiver Operating Characteristic (ROC) Curve 20.7 Estimation Parameter and Theory 20.7.1 Frequency and Power Estimation 20.8 Frequency Modulation 20.9 Channel-to-Channel Phase Estimation 20.10 Important Issues to Note References Chapter 21: Application of Wavelets to Vibration Detection in an Aeroelastic System 21.1 Introduction 21.2 Overview of Wavelet Analysis for the Aeroelastic Systems 21.2.1 The Wavelet Transform 21.2.2 The Vibration Signal Analysis Techniques 21.3 Development of a Vibration Model: An Example 21.4 Wavelet Families Used for Vibration Detection 21.5 Development of the Vibration Detection Algorithm 21.5.1 Initial Consideration: Decomposition Level 21.5.2 Initial Consideration: Threshold 21.5.3 Vibration Detection Algorithm: An Example of the Procedure 21.6 Simulation Examples of the Vibration Model 21.7 Threshold Experimentation 21.7.1 Global Thresholding 21.7.2 Per-Level Thresholding 21.8 Application of the PLT Algorithm on an Aeroelastic Vibration Data for Verification 21.9 Remarks on the Wavelets Used for the Vibration Signal Detection References Appendices Appendix A: Wavelet Coefficients Appendix B: Riesz Basis Appendix C: The QR Factorization (QRF) Appendix D: Signal Power: Parseval´s Relation to Fast Fourier Transform Appendix E: Automation Process Testing GUIs Operation Manual for Mixed Signal Systems Using DWT Appendix F: 12-Bit and 14-Bit ADCs DWT Testing Results (Figs. F1, F2, F3, and F4) Appendix G: TLC876, ADS5410, and ADS5423 Data Sheet Manual Appendix H: 12-Bit and 14-Bit DWT DACs Testing (Figs. H1, H2, H3, H4, and H5) Appendix I: DAC2900, DAC2902, and DAC2904 Data Sheet Manual Appendix J: Samples of Fingerprint Images Appendix K: MATLAB Program Listings for Fingerprint Minutiae Processing Using Six Different Types of Wavelets Appendix K1: Program to Create Database of Statistical Parameters for 80 Fingerprint Images Appendix K2: Program to Verify a Test Image Appendix L: Instruction for MATLAB Programs Execution for Fingerprint Minutiae Processing of Appendix K Appendix M: MATLAB Programs for Chap. 19 Appendix N: MATLAB Programs for Chap. 20 Appendix O: MATLAB Programs for Chap. 21 Appendix O_1 of N Using Haar Wavelet Appendix O_2 of O Using Daubechies-4 Wavelet Appendix O_3 of O Using Morlet Wavelet Appendix O_4 of O Programs Using the Vibration Model and PLT Appendix O_4 of O Using Daubechies-14 Wavelet Appendix O_5 of O Programs Using Flight Research Data Index