| Signals and Signal Processing in Manufacturing | p. 1 |
| Classification of Signals | p. 1 |
| Deterministic Signal | p. 1 |
| Nondeterministic Signal | p. 3 |
| Signals in Manufacturing | p. 5 |
| Role of Signal Processing for Manufacturing | p. 11 |
| References | p. 13 |
| From Fourier Transform to Wavelet Transform: A Historical Perspective | p. 17 |
| Fourier Transform | p. 18 |
| Short-Time Fourier Transform | p. 21 |
| Wavelet Transform | p. 26 |
| References | p. 31 |
| Continuous Wavelet Transform | p. 33 |
| Properties of Continuous Wavelet Transform | p. 35 |
| Superposition Property | p. 35 |
| Covariant Under Translation | p. 36 |
| Covariant Under Dilation | p. 36 |
| Moyal Principle | p. 37 |
| Inverse Continuous Wavelet Transform | p. 38 |
| Implementation of Continuous Wavelet Transform | p. 39 |
| Some Commonly Used Wavelets | p. 41 |
| Mexican Hat Wavelets | p. 41 |
| Morlet Wavelet | p. 41 |
| Gaussian Wavelet | p. 42 |
| Frequency B-Spline Wavelet | p. 43 |
| Shannon Wavelet | p. 43 |
| Harmonic Wavelet | p. 44 |
| CWT of Representative Signals | p. 45 |
| CWT of Sinusoidal Function | p. 45 |
| CWT of Gaussian Pulse Function | p. 46 |
| CWT of Chirp Function | p. 46 |
| Summary | p. 47 |
| References | p. 47 |
| Discrete Wavelet Transform | p. 49 |
| Discretization of Scale and Translation Parameters | p. 49 |
| Multiresolution Analysis and Orthogonal Wavelet Transform | p. 53 |
| Multiresolution Analysis | p. 53 |
| Orthogonal Wavelet Transform | p. 55 |
| Dual-Scale Equation and Multiresolution Filters | p. 56 |
| The Mallat Algorithm | p. 58 |
| Commonly Used Base Wavelets | p. 60 |
| Haar Wavelet | p. 61 |
| Daubechies Wavelet | p. 61 |
| Coiflet Wavelet | p. 62 |
| Symlet Wavelet | p. 63 |
| Biorthogonal and Reverse Biorthogonal Wavelets | p. 63 |
| Meyer Wavelet | p. 65 |
| Application of Discrete Wavelet Transform | p. 65 |
| Summary | p. 68 |
| References | p. 68 |
| Wavelet Packet Transform | p. 69 |
| Theoretical Basis of Wavelet Packet | p. 69 |
| Definition | p. 69 |
| Wavelet Packet Property | p. 72 |
| Recursive Algorithm | p. 73 |
| FFT-Bascd Harmonic Wavelet Packet Transform | p. 74 |
| Harmonic Wavelet Transform | p. 74 |
| Harmonic Wavelet Packet Algorithm | p. 75 |
| Application of Wavelet Packet Transform | p. 78 |
| Time-Frequency Analysis | p. 78 |
| Wavelet Packet for Denoising | p. 79 |
| Summary | p. 79 |
| References | p. 80 |
| Wavelet-Rased Multiscale Enveloping | p. 83 |
| Signal Enveloping Through Hilbert Transform | p. 83 |
| Multiscale Enveloping Using Complex-Valued Wavelet | p. 86 |
| Application of Multiscale Enveloping | p. 87 |
| Ultrasonic Pulse Differentiation for Pressure Measurement in Injection Molding | p. 87 |
| Bearing Defect Diagnosis in Rotary Machine | p. 93 |
| Summary | p. 99 |
| References | p. 100 |
| Wavelet Integrated with Fourier Transform: A Unified Technique | p. 103 |
| Generalized Signal Transformation Frame | p. 103 |
| Fourier Transform in the Generalized Frame | p. 106 |
| Wavelet Transform in the Generalized Frame | p. 107 |
| Wavelet Transform with Spectral Postprocessing | p. 109 |
| Fourier Transform of the Measure Function | p. 110 |
| Fourier Transform of Wavelet-Extracted Data Set | p. 112 |
| Application to Bearing Defect Diagnosis | p. 113 |
| Effectiveness in Defect Feature Extraction | p. 115 |
| Selection of Decomposition Level | p. 118 |
| Effect of Bearing Operation Conditions | p. 120 |
| Summary | p. 124 |
| References | p. 124 |
| Wavelet Packet-Transform for Defect Severity Classification | p. 125 |
| Subband Feature Extraction | p. 125 |
| Energy Feature | p. 126 |
| Kurtosis | p. 27 |
| Key Feature Selection | p. 128 |
| Fisher Linear Discriminant Analysis | p. 129 |
| Principal Component Analysis | p. 131 |
| Neural-Network Classifier | p. 134 |
| Formulation of WPT-Based Defect Severity Classification | p. 136 |
| Case Studies | p. 137 |
| Case Study I: Roller Bearing Defect Severity Evaluation | p. 137 |
| Case Study II: Ball Bearing Defect Severity Evaluation | p. 142 |
| Summary | p. 146 |
| References | p. 146 |
| Local Discriminant Bases for Signal Classification | p. 149 |
| Dissimilarity Measures | p. 149 |
| Relative Entropy | p. 150 |
| Energy Difference | p. 151 |
| Correlation Index | p. 151 |
| Nonstationarity | p. 152 |
| Local Discriminant Bases | p. 153 |
| Case Study | p. 155 |
| Application to Gearbox Defect Classification | p. 158 |
| Summary | p. 162 |
| References | p. 162 |
| Selection of Base Wavelet | p. 165 |
| Overview of Base Wavelet Selection | p. 165 |
| Qualitative Measure | p. 166 |
| Quantitative Measure | p. 168 |
| Wavelet Selection Criteria | p. 169 |
| Energy and Shannon Entropy | p. 170 |
| Information Theoretic Measure | p. 172 |
| Numerical Study on Base Wavelet Selection | p. 176 |
| Evaluation Using Real-Valued Wavelets | p. 176 |
| Evaluation Using Complex-Valued Wavelets | p. 179 |
| Base Wavelet Selection for Bearing Vibration Signal | p. 183 |
| Summary | p. 185 |
| References | p. 186 |
| Designing Your Own Wavelet | p. 189 |
| Overview of Wavelet Design | p. 189 |
| Construction of an Impulse Wavelet | p. 190 |
| Impulse Wavelet Application | p. 198 |
| Summary | p. 202 |
| References | p. 203 |
| Beyond Wavelets | p. 205 |
| Second Generation Wavelet Transform | p. 205 |
| Theoretical Basis of SGWT | p. 206 |
| Illustration of SGWT in Signal Processing | p. 208 |
| Ridgelet Transform | p. 210 |
| Theoretical Basis of Ridgelet Transform | p. 210 |
| Application of the Ridgelet Transform | p. 212 |
| Curvelct Transform | p. 214 |
| Curvelet Transform | p. 214 |
| Application of the Curvelet Transform | p. 217 |
| Summary | p. 218 |
| References | p. 219 |
| Index | p. 221 |
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