Advances in Electronics and Electron Physics (eBook)

Cover 1
Contents 6
Contributors 8
Preface 10
Chapter 1. Discrete Fast Fourier Transform Algorithms: A Tutorial Survey 14
I. Introduction 15
II. Tensor Product Formulation of Cooley–Tukey Algorithms 17
III. Multidimensional Algorithms 29
IV. Line Algorithm 39
V. Parallel Implementation of the Line Algorithm 51
VI. The Fourier Transform in X-ray Crystallography 53
VII. Symmetric Fourier Transforms 64
References 78
Chapter 2. Number Theoretic Techniques in Digital Signal Processing 82
I. Introduction 83
II. Discrete Fourier Transforms 88
III. Fast Fourier Transform (FFT) Algorithms 90
IV. Finite Algebras 93
V. Number Theoretic Transforms 97
VI. Residue Number Systems 134
VII. Implementation of NTTs using the RNS 144
VIII. VLSI Implementations of Finite Algebraic Systems 153
IX. Conclusions 172
Acknowledgments 173
References 173
Chapter 3. Information Energy and Its Applications 178
I. Introduction 179
II. Information Energy and Information Energy Gain for Discrete Random Variables 180
III. Information Energy and Information Energy Gain for Continuous Random Variables 189
IV. Statistical Aspects of Information Energy 201
V. Information Energy and Fuzzy Sets Theory 237
VI. Weighted Information Energy 247
Acknowledgments 251
References 252
Chapter 4. Recent Developments in Image Algebra 256
I. Introduction 256
II. Image Algebra 259
III. A Medley of Consequences 286
Acknowledgments 318
References 318
Chapter 5. Image Filtering and Analysis through the Wigner Distribution 322
I. Introduction 322
II. The Wigner Distribution 326
III. Wigner Distribution Representation of Images 339
IV. Image Filtering through the Wigner Distribution 357
V. Image Analysis through the Wigner Distribution 372
VI. Applications of the Space (Time)-Frequency Representations 385
VII. Conclusions 400
Acknowledgments 401
References 401
Index 412