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Dedication | ||
Acknowledgments | ||
Preface | ||
1 | Introduction | |
2 | Linear Filters | |
Filters in Time Domain | 16 | |
Filters in the Frequency Domain | 25 | |
Filters in Practice | 39 | |
3 | Optimum Linear Estimation | |
The Wiener Filter and Estimation | 54 | |
Recursive Filtering and the Kalman Filter | 63 | |
Prediction with the Kalman Filter | 71 | |
Vector Kalman Filter Estimation | 74 | |
Applications | 80 | |
4 | Discrete Wavelet Transforms | |
Properties of the Wavelet Transform | 101 | |
Discrete Wavelet Filters | 106 | |
The Discrete Wavelet Transform | 117 | |
The Maximal Overlap Discrete Wavelet Transform | 134 | |
Practical Issues in Implementation | 143 | |
Applications | 146 | |
5 | Wavelets and Stationary Processes | |
Wavelets and Long-Memory Processes | 162 | |
Generalizations of the DWT and MODWT | 176 | |
Wavelets and Seasonal Long Memory | 183 | |
Applications | 194 | |
6 | Wavelet Denoising | |
Nonlinear Denoising via Thresholding | 207 | |
Threshold Selection | 212 | |
Implementing Wavelet Denoising | 224 | |
Applications | 227 | |
7 | Wavelets for Variance-Covariance Estimation | |
The Wavelet Variance | 238 | |
Testing Homogeneity of Variance | 246 | |
The Wavelet Covariance and Cross-Covariance | 251 | |
The Wavelet Correlation and Cross-Correlation | 256 | |
Applications | 262 | |
Univariate and Bivariate Spectrum Analysis | 266 | |
8 | Artificial Neural Networks | |
Activation Functions | 276 | |
Feedforward Networks | 279 | |
Recurrent Networks | 290 | |
Network Selection | 294 | |
Adaptivity | 301 | |
Estimation of Recurrent Networks | 301 | |
Applications of Neural Network Models | 303 | |
Notations | 315 | |
Bibliography | 323 | |
Index | 349 |
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