Adaptive digital processing of multidimensional signals with applications Adaptive digital processing of multidimensional signals with applications In this monograph, the novel promising trs in adaptive digal processing of multidimensional 1D-3D signals wh different applications to radio physics, radio engineering, and medicine are considered. The monograph consists of three parts. The first part (chapters 1-4) is devoted to the atomic functions (AF) and their applications, such as the novel wavelet systems (WA). This part includes the definion of the atomic functions, their properties, possible applications in signal and image processing, and the construction of novel wavelets based on the AF. The synthesis of novel weighting functions (windows) based on the AF and applications of the novel windows are discussed in the next chapters. In chapter 4, the basic principles of the wavelet analysis are considered in detail. Here, the Kotelnikov-Shannon and the Meyer wavelets as well as the wavelets based on the atomic functions are discussed. The second part of the book (chapters 5-9) is devoted to the multidimensional signal enhancement. Models of the image-and-noise and objective-and-subjective creria are discussed in the fifth chapter. Chapter 6 introduces different types of statistical estimators (M, R, L, and RM) and their properties. Chapter 7 gives a review of the linear and nonlinear filtering techniques. Some commonly used models of multichannel (color) images are presented there. A novel approach of the vectorial order statistics to multichannel and video processing is presented in chapter 8. The vector median ordering and filtering, the adaptive multichannel non-filtering, the Vector Directional filter wh a double window, etc. are explained. Elements of fuzzy logics theory and novel filtering techniques, such as 3D ultrasound, 3D vector, and fuzzy 3D vectorial filters, are discussed there. Chapter 9 exposes different implementations of processing techniques on the DSP and FPGA platforms. Some important problems are resolved: applications of the AF and wavelets based on the AF (WA) for compression-windowing in radar systems, compression algorhms for medical applications, and neural-network classification procedures in the mammography analysis. The analysis of the transversal FIR filter structure along wh some of s most widely used adaptive algorhms is presented in the tenth chapter. In chapter 11, the fast Fourier transform is used for performing the convolution and correlation required in applications reducing the computational complexy. The adaptive infine impulse response can provide the computational complexy wh a much smaller number of filter coefficients. Some problems such as slow convergence, possible filter instabily, and error function wh multiple local minima, are discussed in chapter 12. The echo canceling procedures are described in chapter 13. The inter symbol interference reduction applying efficient equalizer algorhms are discussed in the final, fourteenth chapter of this book. The monograph is recommed for scientists, engineers, students, and post-graduates specializing in radio physics, radio engineering, computational mathematics, computational physics, and medicine applications. Физматлит 978-5-9221-1170-6
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In this monograph, the novel promising trs in adaptive digal processing of multidimensional 1D-3D signals wh different applications to radio physics, radio engineering, and medicine are considered. The monograph consists of three parts. The first part (chapters 1-4) is devoted to the atomic functions (AF) and their applications, such as the novel wavelet systems (WA). This part includes the definion of the atomic functions, their properties, possible applications in signal and image processing, and the construction of novel wavelets based on the AF. The synthesis of novel weighting functions (windows) based on the AF and applications of the novel windows are discussed in the next chapters. In chapter 4, the basic principles of the wavelet analysis are considered in detail. Here, the Kotelnikov-Shannon and the Meyer wavelets as well as the wavelets based on the atomic functions are discussed. The second part of the book (chapters 5-9) is devoted to the multidimensional signal enhancement. Models of the image-and-noise and objective-and-subjective creria are discussed in the fifth chapter. Chapter 6 introduces different types of statistical estimators (M, R, L, and RM) and their properties. Chapter 7 gives a review of the linear and nonlinear filtering techniques. Some commonly used models of multichannel (color) images are presented there. A novel approach of the vectorial order statistics to multichannel and video processing is presented in chapter 8. The vector median ordering and filtering, the adaptive multichannel non-filtering, the Vector Directional filter wh a double window, etc. are explained. Elements of fuzzy logics theory and novel filtering techniques, such as 3D ultrasound, 3D vector, and fuzzy 3D vectorial filters, are discussed there. Chapter 9 exposes different implementations of processing techniques on the DSP and FPGA platforms. Some important problems are resolved: applications of the AF and wavelets based on the AF (WA) for compression-windowing in radar systems, compression algorhms for medical applications, and neural-network classification procedures in the mammography analysis. The analysis of the transversal FIR filter structure along wh some of s most widely used adaptive algorhms is presented in the tenth chapter. In chapter 11, the fast Fourier transform is used for performing the convolution and correlation required in applications reducing the computational complexy. The adaptive infine impulse response can provide the computational complexy wh a much smaller number of filter coefficients. Some problems such as slow convergence, possible filter instabily, and error function wh multiple local minima, are discussed in chapter 12. The echo canceling procedures are described in chapter 13. The inter symbol interference reduction applying efficient equalizer algorhms are discussed in the final, fourteenth chapter of this book. The monograph is recommed for scientists, engineers, students, and post-graduates specializing in radio physics, radio engineering, computational mathematics, computational physics, and medicine applications.
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Preface
The first part of this book (Chapters 1–4) is devoted to the atomic functions (AF)
and their applications, such as novel wavelet (WA) systems. The theory of atomic
functions goes back to 1971, when the function up (x) was first constructed and studies.
Subsequently, the AF theory was considered in detail in different works initiated by
the book by V. L. Rvachev and V.A. Rvachev «Non-classical Methods of Approximation
Theory in Boundary-Value Problems», Kiev: Naukova Dumka, 1979. In the last
years, several books concerning the AF theory have been published: V.F.Kravchenko
«Lectures on the Theory of Atomic Functions and Their Some Applications», Moscow,
Radiotekhnika, 2003; V. F. Kravchenko and M.A. Basarab «Boolean Algebra and
Approximation Methods in Boundary Value Problems of Electrodynamics», Moscow,
Fizmatlit, 2004; V. F. Kravchenko and V. L. Rvachev «Logic Algebra, Atomic Functions
and Wavelets in Physical Applications», Moscow, Fizmatlit, 2006; «Digital Signal and
Image Processing in Radio Physical Applications», Ed. by V. F. Kravchenko, Moscow,
Fizmatlit, 2007.
The first part of this book presents an introduction to the atomic functions, their
properties, possible applications in signal and image processing, and the design of novel
wavelets based on the AF. The synthesis of novel weighting functions (windows) based
on the AF and applications of the novel windows in the digital radar, electroencephalog-
raphy, SAR, etc., are discussed in next chapters of the first part. In chapter 4, the basic
principles of the wavelet analysis are considered in detail and different wavelets, such
as the Kotelnikov–Shannon and Meyer wavelets, as well as the wavelets based on the
atomic functions (WA), are discussed.
Chapters 5–9 are devoted to the multidimensional signal enhancement. Models of
image and noise (additive, speckle, and impulsive) are discussed in chapter 5. Also, the
objective and subjective criteria of evaluating the quality of filtering are presented there.
Chapter 6 introduces different types of statistical estimators: the maximum likelihood
and the M, R, and L estimators along with their properties. The theory of novel RM
estimators is discussed there too. Chapter 7 gives a review of the linear and nonlinear
filtering techniques. It offers explanation of the trimmed mean filters, the KNN, L

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Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Chapter 1. The Theory of Atomic Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.1. Introduction to the Theory of Atomic Functions . . . . . . . . . . . . . . . . . . . . . . . . 9
1.2. The «Mother» Atomic Function up (x) and Its Main Properties . . . . . . . . . . . . . . 10
1.3. Functions fup N(x) and Their Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.4. Atomic Functions ha(x) and Their Properties . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.5. Interpolation of Signals by ha(x) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.6. An Example of Evaluating ha(x) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
1.7. Atomic Functions n(x). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
1.8. Atomic Functions gk,h(x) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
1.9. Definition and the Main Properties of Functions upm(x) . . . . . . . . . . . . . . . . . . 27
1.10.Moments and Values of Functions upm(x). . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
1.11. Atomic Functions m(x) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Chapter 2. Spectral Properties of Atomic Functions and Novel Windows. . . . . . . . . 33
2.1. Synthesis of Novel Weighting Functions (Windows) . . . . . . . . . . . . . . . . . . . . . . 33
2.2. Application of New Weighting Functions in Problems of Speech Synthesis . . . . . . . 36
2.3. AF up (x), fup N(x), n(x) and Their Combinations Used in Digital Signal Processing 40
2.4. Convolution Operation in Synthesis of New Windows . . . . . . . . . . . . . . . . . . . . . 40
2.5. Numerical Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.6. Spectral Properties of New Weighting Functions Used in Digital Signal Processing 44
2.7. Atomic Function fup N(x) and Methods for Its Evaluation. . . . . . . . . . . . . . . . . . 45
2.8. New Synthesized Windows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
2.9. Signal Filtration Using the New Windows . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
2.10. Time-Domain Dilation of the New Synthesized Kravchenko Windows. . . . . . . . . . . 54
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
Chapter 3. Synthesis of Digital Filters on the Basis of the Atomic Functions and Its
Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.1. Synthesis of Digital Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.2. Kravchenko–Rvachev Windows Used in Digital Radar . . . . . . . . . . . . . . . . . . . . 62
3.3. The Use of the New Types of Windows in Electroencephalography . . . . . . . . . . . . 65
3.4. Approximation of a Given Function by Entire Functions of Exponential Type . . . . . . 69
3.5. The Use of Weighting Windows Based on the AF in SAR Digital Signal Processing 71
3.6. Synthesis of Two-Dimensional Window Functions on the Basis of Atomic Functions 74
3.7. Synthesis of Two-Dimensional FIR-Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
Chapter 4. Wavelet Systems and Atomic Functions . . . . . . . . . . . . . . . . . . . . . . . . 84
4.1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
4.2. Basic Principles of Wavelet Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
4.3.W-systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
4.4. Examples of W-systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
4.5.Methods for Constructing Orthogonal Bases. . . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.6.Wavelets based on Hermitian Splines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
4.7.Meyer Wavelets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
4.8. Kotelnikov–Shannon Wavelets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
4.9.WE-systems with Arbitrary Number of Continuous Derivatives . . . . . . . . . . . . . . 105
4.10.Wavelets Systems based on Atomic Functions . . . . . . . . . . . . . . . . . . . . . . . . . . 108
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
Chapter 5. Models of Image and Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
5.1. Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
5.2. Additive Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
5.3. Speckle Image Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
5.4. Impulsive Image Noise. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
5.5.Mathematical Solutions Applied in Noise Models . . . . . . . . . . . . . . . . . . . . . . . . 115
5.6. Objective and Subjective Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
Chapter 6. Types of Statistical Estimators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
6.1.Maximum Likelihood and M estimators. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
6.2. R and L Estimators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
6.3. Robust Properties of Estimators. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
6.4. RM Estimators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
Chapter 7. Linear and Nonlinear Filtering Techniques . . . . . . . . . . . . . . . . . . . . . 127
7.1. Trimmed Mean Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
7.2. L Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
7.3.Weighted Median and Order Statistics Filters . . . . . . . . . . . . . . . . . . . . . . . . . . 130
7.4. Examples of Data-Dependent Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
7.5. RM Filtering Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
7.6.Model of Multichannel (Color) Image . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
7.7.Wavelet Functions in Multidimensional Signal Processing . . . . . . . . . . . . . . . . . . 146
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
Chapter 8. Vector Order Statistics in Multichannel and Video Processing . . . . . . . . 157
8.1. Vector Order Statistics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
8.2. Kernel Density Estimation Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
8.3. Fuzzy Logic Definitions and Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
8.4. Fuzzy Generalization of Some Classical Filters . . . . . . . . . . . . . . . . . . . . . . . . . 167
8.5.Multidimensional and/or 3D Video Processing Algorithms . . . . . . . . . . . . . . . . . 170
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
Chapter 9. Processing of Multidimensional Signals Using DSP and FPGA Platforms 205
9.1. Platforms for Real Time Processing: DSP vs FPGA . . . . . . . . . . . . . . . . . . . . . 205
9.2. Compression-Windowing Procedures Applicable in Radar Systems. . . . . . . . . . . . . 206
9.3. Runtime Analysis of 2D-3D Filtering Algorithms . . . . . . . . . . . . . . . . . . . . . . . 215
9.4. Compression-Recognition Techniques Using Wavelet Transform . . . . . . . . . . . . . . 219
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235
Chapter 10. Transversal Adaptive Filters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238
10.1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238
10.2.Mean Square Error Surface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
10.3. Recursive Least-Square Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241
10.4. Least-Mean-Square Algorithm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244
10.5. Normalized LMS Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250
10.6. Time Varying Step Size LMS Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259
Chapter 11. Frequency Domain Adaptive Filters Based on Subband Decomposition 261
11.1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261
11.2. FIR Adaptive Filter Structure Based on Subband Decomposition Approach . . . . . . . 262
11.3. Short Delay Fast LMS Algorithm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273
Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274
Chapter 12. IIR Adaptive Filter Algorithms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276
12.1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276
12.2. Adaptive Filters Based on Equation Error Method . . . . . . . . . . . . . . . . . . . . . . . 277
12.3. Adaptive Filters Based on the Output Error Method. . . . . . . . . . . . . . . . . . . . . . 278
12.4. Orthogonalized IIR Adaptive Filter Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . 280
12.5. Cascade Lattice IIR Adaptive Filter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284
12.6. Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299
Chapter 13. Active Noise Cancelling Using the Discrete Cosine Transform . . . . . . . 301
13.1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301
13.2. ANC Structures Based on Subband Decomposition Approach . . . . . . . . . . . . . . . . 304
13.3. Computer Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318
Chapter 14. Adaptive Equalizers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320
14.1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320
14.2. Channel Model for Land Mobile Communication . . . . . . . . . . . . . . . . . . . . . . . . 322
14.3. Interference Cancellation in Wire Data Communication Systems . . . . . . . . . . . . . . 323
14.4. Analog Equalizer Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326
14.5. Fuzzy Equalizer Structure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336
14.6. Blind Equalizer Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 340
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 350
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351
About Authors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354
Штрихкод:   9785922111706
Аудитория:   Для специалистов
Бумага:   Офсет
Масса:   420 г
Размеры:   217x 145x 18 мм
Оформление:   Тиснение цветное
Тираж:   100
Литературная форма:   Монография
Тип иллюстраций:   Без иллюстраций
Язык:   Английский
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