Signal Processing for Modern Informatics
Autor Vincenzo Dentamaroen Limba Engleză Hardback – 26 ian 2027
Leading machine learning architectures--CNNs, Transformers, Graph Neural Networks--are fundamentally signal-processing chains, yet most CS and AI curricula omit formal signal theory. Signal Processing for Modern Informatics: A Bridge between Theory and Modern Artificial Intelligence closes that gap. It re-examines discrete-time signal processing from sampling through filtering, then systematically places each concept within current AI practice and deep model design.
The book provides an integrated treatment tying Hilbert transforms, STFT, wavelets, Graph Fourier Transform, CNN filters, and attention heads together under a unified signal-processing framework. It compares model-based versus data-driven methods in depth, with guidance on constructing hybrid models. Coverage extends to empirical mode decomposition, singular spectrum analysis, and feature extraction for audio and image data.
Readers will also find:
- End-of-chapter code snippets executed on publicly available datasets, enabling immediate replication and experimentation with each technique
- Detailed treatment of graph signal processing and filtering methods applied to robotics and AI system design
- Coverage of sampling, quantization, and linear time-invariant systems grounded in their direct relevance to deep learning pipelines
- Practical examples demonstrating the Fourier Transform and FFT applied to real-world signal analysis and frequency-domain applications
- Analysis of how convolutional neural network architectures and transformer attention mechanisms relate directly to classical signal structures
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Specificații
Cuprins
About the Author i
Preface iii
1 Introduction 1
2 The Basics of the Digital World: Discrete Time Signals and Systems 9
2.1 Introduction: Discrete Signals Are Everywhere around Your Computer 9
2.2 What are Discrete-Time Signals? 10
2.2.1 Formal Definition and Notation 10
2.2.2 Graphical Representation 11
2.2.3 Basic Discrete Signals 11
2.3 From the Outside World to the Inside World: Sampling and Quantization 12
2.3.1 Sampling: Tracing out a Continuous Signal 12
2.3.2 [Advanced] Nyquist-Shannon Sampling Theorem 14
2.3.3 Quantization: Rounding Values 14
2.3.4 The Complete A/D Process 15
2.4 Signal Processing: Introduction to Discrete Systems 15
2.4.1 What is a Discrete System? 16
2.4.2 Fundamental Properties of Systems 16
2.4.3 Linearity and Time-Invariance: The Class of LTI Systems 16
2.5 Convolution: The "Recipe" for LTI Systems 17
2.5.1 Intuition: How Does An LTI System Respond? 17
2.5.2 The Convolution Sum 19
2.5.3 Interpretation and Properties of Convolution 20
2.5.4 Practical Calculation of Convolution 21
2.5.5 Analog Frequency vs. Digital Frequency and Aliasing 21
2.6 Examples 23
2.7 Common Errors and Misunderstandings 25
2.8 Applications in Modern Computing 26
2.9 Summary of Key Concepts 27
2.10 Example Code 28
2.11 References 28
3 Frequency Domain and Fast Fourier Transform (FFT) 31
3.1 Introduction and Motivation 31
3.2 The Fourier Transform in Simple Words 32
3.2.1 Continuous Signals (such as A Freehand Sketch) 32
3.2.2 Discrete Signals (like a Pixelated Image) 33
3.2.3 What is its purpose? 33
3.3 Theoretical Background: Signals and Systems 33
3.3.1 Intuition: Breaking Down into Sinusoidal Waves 34
3.3.2 The Continuous Fourier Transform (CFT) 35
3.3.3 The Discrete Fourier Transform (DFT) 36
3.3.4 Fundamental Properties of DFT 37
3.4 The Fast Fourier Transform (FFT): A Revolutionary Algorithm 38
3.4.1 The Computational Problem of the DFT 38
3.4.2 The Key Idea: Divide and Conquer 38
3.4.3 Radix-2 FFT Algorithm (Decimation-in-Time - Overview) 38
3.5 Spectral Analysis: Interpreting the FFT Result 39
3.5.1 Amplitude and Phase Spectrum 39
3.5.2 Power Spectral Density (PSD) 40
3.5.3 Frequency Resolution and Window [Advanced Concept] 40
3.5.4 Deciphering the DFT Output 41
3.6 Practical Examples 43
3.7 Common Errors and Misconceptions 47
3.8 Applications in Modern Technology 48
3.9 Sample Code 49
3.10 Summary of Key Concepts 52
3.11 References 52
4 Time-Frequency Analysis 53
4.1 Introduction and Motivations 53
4.2 Limits of Traditional Fourier Analysis: The Necessity of Time 54
4.3 The Short-Time Fourier Transform (STFT) 57
4.3.1 The Spectrogram 59
4.3.2 The Time-Frequency Compromise in STFT 60
4.3.3 Dissecting the STFT: Windows, Hops, and FFT 61
4.4 Wavelet Transform Explained Simply 62
4.4.1 Continuous Wavelet Transform (CWT) 62
4.4.2 Discrete Wavelet Transform (DWT) 63
4.4.3 What is it Used For? 63
4.5 The Wavelet Transform 63
4.5.1 The Mother Wavelet and its Characteristics 64
4.5.2 Scaling and Translation: Creating the Wavelet Family 64
4.5.3 Continuous Wavelet Transform (CWT) 65
4.5.4 Discrete Wavelet Transform (DWT) and Multi-Resolution Analysis 68
4.5.5 Intuition on Wavelets and Basis Choice 71
4.6 Other Time-Frequency Distributions [Advanced Section] 72
4.7 Practical Guided Examples 73
4.8 Common Errors and Misunderstandings 76
4.9 Applications in Modern Technology 77
4.10 Summary of Key Concepts 78
4.11 Example Code 79
4.12 References 83
5 Phase and Envelope: The Analytical Signal and the Hilbert Transform 85
5.1 Introduction and Motivation 85
5.2 The Hilbert Transform And The Analytic Signal Made Easy 87
5.2.1 What is the purpose of phase shifting? 87
5.2.2 In Brief 87
5.3 Review of Complex Signals and Complex Exponentials 88
5.4 The Hilbert transform 89
5.4.1 Definition and Intuition 89
5.4.2 Properties of the Hilbert transform 90
5.4.3 Numerical Implementation [Advanced Note] 90
5.5 The Analytic Signal 91
5.5.1 Definition 91
5.5.2 Instantaneous Envelope (Amplitude Envelope) 92
5.5.3 Instantaneous Phase 92
5.5.4 Polar Representation of the Analytic Signal 92
5.5.5 Instantaneous Frequency 92
5.5.6 The Analytical Signal: Construction, Meaning, and Practical Examples 93
5.6 Guided Practical Examples 96
5.7 Common Errors and Misunderstandings 99
5.8 Cutting Edge Technology 100
5.9 Summary of Key Concepts 102
5.10 Implementation Examples 102
5.11 References 105
6 Audio and Image Applications Specific Feature Extraction 107
6.1 Introductions and Objectives 107
6.2 Brief Description of MFCCs and Gabor Filters 108
6.3 Theoretical Background: What is Feature Extraction? 110
6.4 Performance Characteristics for Audio: MFCC 111
6.4.1 MFCC Fundamentals 111
6.4.2 Mathematical Foundations of MFCCs 112
6.4.3 Interpretation and Use 116
6.5 Image Specific Features: Gabor Filters 117
6.5.1 Gabor Filters Overview 117
6.5.2 Mathematical Foundations of Gabor Filters 117
6.5.3 Interpretation and Use 119
6.6 Illustrated Practical Prototypes 120
6.6.1 Prototype 1 (Fundamental): MFCC Calculation Overview for a Basic Audio Frame 120
6.6.2 Example 2 (Intermediate): A Case Study on MFCC Features for Basic Speech Recognition 121
6.6.3 Example 3 (Advanced): Applying Gabor Filters for Texture Analysis122
6.7 Common Errors and Misunderstandings 122
6.8 Applications in Modern Technology 124
6.9 Summary of Key Concepts 125
6.10 Sample Code 125
6.11 References 128
7 Decomposition and Alternate Signal Representations 129
7.1 Motivation and Introduction 129
7.2 Signal Processing Methods That Are Remarkably Original, But Understandable
130
7.2.1 Empirical Mode Decomposition (EMD) - Dividing into Basic Waves130
7.2.2 Singular Spectrum Analysis (SSA) - Discovering Concealed Patterns131
7.2.3 Recovery of Sparse Signals 135
7.2.4 Further Insights and Intuitions 138
7.3 Examples 143
7.4 Frequent Mistakes and Misinterpretations 145
7.5 Practices of Contemporary Technology 145
7.6 Summary of Key Points 146
7.7 Example Code 147
7.8 References 150
8 An Introductory Exploration of Traditional Machine Learning for the Processing of Signals 151
8.1 A Preamble and its Justification 151
8.2 The Theoretical Framework: Machine Learning 153
8.3 Supervised Learning 154
8.3.1 K-Nearest Neighbours (K-NN) 155
8.3.2 Decision Trees 157
8.3.3 Random Forests 161
8.3.4 Support Vector Machines (SVM) 163
8.4 Unsupervised Learning 168
8.4.1 Clustering with K-Means 169
8.4.2 Gaussian Mixture Models (GMM) 171
8.4.3 Principal Component Analysis (PCA) 177
8.4.4 t-Distributed Stochastic Neighbour Embedding (t-SNE) 182
8.5 Practical Examples 185
8.6 Typical Mistakes and Misconceptions 198
8.7 Uses in Current Signal Processing 201
8.8 Key Idea Summary 203
8.9 References 204
9 Deep Learning and Signal Processing: A Relationship Between Data and Knowledge 205
9.1 Introduction and Motivation 205
9.2 Essential Theoretical Background 206
9.2.1 Signals: Discrete and Continuous 206
9.2.2 Signal Processing (Basic Concepts) 207
9.2.3 Machine Learning and Deep Learning 207
9.3 Core Ideas and Their Corresponding Mathematical Frameworks 208
9.3.1 Backpropagation Algorithm 208
9.4 Use of Non-linearity Within Autoencoders and Noise Removal 210
9.4.1 Multi Layer Perceptron: Theory and Practice 210
9.4.2 The Importance of Non-Linearity: "Bending" the Space 211
9.4.3 Common Activation Functions: When and How to Use Them 213
9.4.4 Stacked Denoising Autoencoder (SDAE) 216
9.4.5 Applications of SDAEs in Signal Processing: 225
9.5 Convolutional Neural Networks (CNN) 225
9.5.1 Convolutional Neural Networks: Building Blocks 226
9.6 The Multiscale Learning Paradigm and CNNs 228
9.6.1 The Importance of Scale in Signals and Data 228
9.6.2 Principles of Multiscale Representation Learning 229
9.6.3 CNNs: An Implicit Multiscale Architecture 229
9.6.4 Advanced: Explicit Multiscale CNN Designs 231
9.7 Transformer Architectures 232
9.7.1 Motivations and Key Ideas 232
9.7.2 Fundamental Components (Transformer Encoder) 233
9.7.3 Multi-Headed Self-Attention (MHSA) and relationship with Signal Processing 235
9.7.4 Demystification of the Self-Attention Mechanism: Questions, Keys, and Values in Action 236
9.8 Multimodal Learning and Signal Processing 242
9.9 Parallelism between Convolutional Network Kernels and Transformers in Simple Pills 245
9.9.1 How Backpropagation Refines Kernels 245
9.9.2 Parallelism with Transforms (Fourier, Wavelet, etc.) 246
9.10 Worked Examples 246
9.11 Pitfalls and Misconceptions 250
9.12 Applications in Modern Technology 251
9.13 Summary of Key Points 252
9.14 Sample Code 253
9.15 References 260
10 Graph Signal Processing (GSP) 263
10.1 Why is it important in computer science? 263
10.2 Graph Signal Processing - GSP in a nutshell 264
10.3 Theoretical Background: Graph Theory Basics 265
10.3.1 Adjacency Matrix 265
10.3.2 Degree Matrix 265
10.4 Mathematical Foundations and Basic Concepts of GSP 265
10.4.1 Graph Signals 266
10.4.2 The Graph Shift Operator 266
10.4.3 The Graph Laplacian 267
10.4.4 Normalized Laplacians [Advanced] 268
10.4.5 Graph Fourier Transform (GFT) 269
10.4.6 Graph Filtering 270
10.4.7 Convolutional Graph Neural Networks (GCN) 271
10.5 Worked Examples 276
10.6 Applications in Modern Technology 281
10.7 Summary of Key Points 282
10.7.1 Example 1: Fourier Transform on Graphs and Filtering 283
10.7.2 Example 2: Graph Convolutional Network (GCN) for Node Classification - Drug Toxicity prediction 287
10.7.3 GSP Example Conclusions 295
10.8 References 295
11 Kalman Filters and Particle Filters for Artificial Intelligence and Robotics297
11.1 Kalman Filters and Particle Filters in a Nutshell 298
11.1.1 The Particle Filter (PF): The Sleuth with an Army of Assisting Experts 299
11.2 Theoretical Background: Dynamic Systems and Uncertainty 300
11.2.1 State-Space Models 300
11.2.2 Uncertainty and Probability 301
11.2.3 Gaussian Noise 302
11.3 The Kalman Filter (KF) 302
11.3.1 KF assumptions 302
11.3.2 The Kalman Filter Algorithm 303
11.3.3 Limitations of KF and Extended Kalman Filter (EKF) 304
11.4 Particle Filters (PF) 306
11.4.1 The Basic Concept: Sampling Representation 306
11.4.2 Base Algorithm: Sequential Importance Sampling (SIS) 308
11.4.3 The Degeneration Problem and Resampling 308
11.4.4 The Full Algorithm: Sampling Importance Resampling (SIR) 309
11.4.5 Advantages and Disadvantages of PF 310
11.5 Application Examples 311
11.6 Pitfalls and Misconceptions 314
11.7 Applications in Modern Technology 314
11.8 Summary of Key Points 316
11.9 Example Code 316
11.9.1 Example 1: Linear Kalman Filter 316
11.9.2 Example 2: Particle Filter 320
11.10 References 324
12 Conclusions 325
12.1 Summary of Contents 325
12.2 Contributions and Impact of the Integration between SP and Deep Learning326
12.3 Challenges and Future Prospects 327
12.4 Final Thoughts 327
Index
Preface iii
1 Introduction 1
2 The Basics of the Digital World: Discrete Time Signals and Systems 9
2.1 Introduction: Discrete Signals Are Everywhere around Your Computer 9
2.2 What are Discrete-Time Signals? 10
2.2.1 Formal Definition and Notation 10
2.2.2 Graphical Representation 11
2.2.3 Basic Discrete Signals 11
2.3 From the Outside World to the Inside World: Sampling and Quantization 12
2.3.1 Sampling: Tracing out a Continuous Signal 12
2.3.2 [Advanced] Nyquist-Shannon Sampling Theorem 14
2.3.3 Quantization: Rounding Values 14
2.3.4 The Complete A/D Process 15
2.4 Signal Processing: Introduction to Discrete Systems 15
2.4.1 What is a Discrete System? 16
2.4.2 Fundamental Properties of Systems 16
2.4.3 Linearity and Time-Invariance: The Class of LTI Systems 16
2.5 Convolution: The "Recipe" for LTI Systems 17
2.5.1 Intuition: How Does An LTI System Respond? 17
2.5.2 The Convolution Sum 19
2.5.3 Interpretation and Properties of Convolution 20
2.5.4 Practical Calculation of Convolution 21
2.5.5 Analog Frequency vs. Digital Frequency and Aliasing 21
2.6 Examples 23
2.7 Common Errors and Misunderstandings 25
2.8 Applications in Modern Computing 26
2.9 Summary of Key Concepts 27
2.10 Example Code 28
2.11 References 28
3 Frequency Domain and Fast Fourier Transform (FFT) 31
3.1 Introduction and Motivation 31
3.2 The Fourier Transform in Simple Words 32
3.2.1 Continuous Signals (such as A Freehand Sketch) 32
3.2.2 Discrete Signals (like a Pixelated Image) 33
3.2.3 What is its purpose? 33
3.3 Theoretical Background: Signals and Systems 33
3.3.1 Intuition: Breaking Down into Sinusoidal Waves 34
3.3.2 The Continuous Fourier Transform (CFT) 35
3.3.3 The Discrete Fourier Transform (DFT) 36
3.3.4 Fundamental Properties of DFT 37
3.4 The Fast Fourier Transform (FFT): A Revolutionary Algorithm 38
3.4.1 The Computational Problem of the DFT 38
3.4.2 The Key Idea: Divide and Conquer 38
3.4.3 Radix-2 FFT Algorithm (Decimation-in-Time - Overview) 38
3.5 Spectral Analysis: Interpreting the FFT Result 39
3.5.1 Amplitude and Phase Spectrum 39
3.5.2 Power Spectral Density (PSD) 40
3.5.3 Frequency Resolution and Window [Advanced Concept] 40
3.5.4 Deciphering the DFT Output 41
3.6 Practical Examples 43
3.7 Common Errors and Misconceptions 47
3.8 Applications in Modern Technology 48
3.9 Sample Code 49
3.10 Summary of Key Concepts 52
3.11 References 52
4 Time-Frequency Analysis 53
4.1 Introduction and Motivations 53
4.2 Limits of Traditional Fourier Analysis: The Necessity of Time 54
4.3 The Short-Time Fourier Transform (STFT) 57
4.3.1 The Spectrogram 59
4.3.2 The Time-Frequency Compromise in STFT 60
4.3.3 Dissecting the STFT: Windows, Hops, and FFT 61
4.4 Wavelet Transform Explained Simply 62
4.4.1 Continuous Wavelet Transform (CWT) 62
4.4.2 Discrete Wavelet Transform (DWT) 63
4.4.3 What is it Used For? 63
4.5 The Wavelet Transform 63
4.5.1 The Mother Wavelet and its Characteristics 64
4.5.2 Scaling and Translation: Creating the Wavelet Family 64
4.5.3 Continuous Wavelet Transform (CWT) 65
4.5.4 Discrete Wavelet Transform (DWT) and Multi-Resolution Analysis 68
4.5.5 Intuition on Wavelets and Basis Choice 71
4.6 Other Time-Frequency Distributions [Advanced Section] 72
4.7 Practical Guided Examples 73
4.8 Common Errors and Misunderstandings 76
4.9 Applications in Modern Technology 77
4.10 Summary of Key Concepts 78
4.11 Example Code 79
4.12 References 83
5 Phase and Envelope: The Analytical Signal and the Hilbert Transform 85
5.1 Introduction and Motivation 85
5.2 The Hilbert Transform And The Analytic Signal Made Easy 87
5.2.1 What is the purpose of phase shifting? 87
5.2.2 In Brief 87
5.3 Review of Complex Signals and Complex Exponentials 88
5.4 The Hilbert transform 89
5.4.1 Definition and Intuition 89
5.4.2 Properties of the Hilbert transform 90
5.4.3 Numerical Implementation [Advanced Note] 90
5.5 The Analytic Signal 91
5.5.1 Definition 91
5.5.2 Instantaneous Envelope (Amplitude Envelope) 92
5.5.3 Instantaneous Phase 92
5.5.4 Polar Representation of the Analytic Signal 92
5.5.5 Instantaneous Frequency 92
5.5.6 The Analytical Signal: Construction, Meaning, and Practical Examples 93
5.6 Guided Practical Examples 96
5.7 Common Errors and Misunderstandings 99
5.8 Cutting Edge Technology 100
5.9 Summary of Key Concepts 102
5.10 Implementation Examples 102
5.11 References 105
6 Audio and Image Applications Specific Feature Extraction 107
6.1 Introductions and Objectives 107
6.2 Brief Description of MFCCs and Gabor Filters 108
6.3 Theoretical Background: What is Feature Extraction? 110
6.4 Performance Characteristics for Audio: MFCC 111
6.4.1 MFCC Fundamentals 111
6.4.2 Mathematical Foundations of MFCCs 112
6.4.3 Interpretation and Use 116
6.5 Image Specific Features: Gabor Filters 117
6.5.1 Gabor Filters Overview 117
6.5.2 Mathematical Foundations of Gabor Filters 117
6.5.3 Interpretation and Use 119
6.6 Illustrated Practical Prototypes 120
6.6.1 Prototype 1 (Fundamental): MFCC Calculation Overview for a Basic Audio Frame 120
6.6.2 Example 2 (Intermediate): A Case Study on MFCC Features for Basic Speech Recognition 121
6.6.3 Example 3 (Advanced): Applying Gabor Filters for Texture Analysis122
6.7 Common Errors and Misunderstandings 122
6.8 Applications in Modern Technology 124
6.9 Summary of Key Concepts 125
6.10 Sample Code 125
6.11 References 128
7 Decomposition and Alternate Signal Representations 129
7.1 Motivation and Introduction 129
7.2 Signal Processing Methods That Are Remarkably Original, But Understandable
130
7.2.1 Empirical Mode Decomposition (EMD) - Dividing into Basic Waves130
7.2.2 Singular Spectrum Analysis (SSA) - Discovering Concealed Patterns131
7.2.3 Recovery of Sparse Signals 135
7.2.4 Further Insights and Intuitions 138
7.3 Examples 143
7.4 Frequent Mistakes and Misinterpretations 145
7.5 Practices of Contemporary Technology 145
7.6 Summary of Key Points 146
7.7 Example Code 147
7.8 References 150
8 An Introductory Exploration of Traditional Machine Learning for the Processing of Signals 151
8.1 A Preamble and its Justification 151
8.2 The Theoretical Framework: Machine Learning 153
8.3 Supervised Learning 154
8.3.1 K-Nearest Neighbours (K-NN) 155
8.3.2 Decision Trees 157
8.3.3 Random Forests 161
8.3.4 Support Vector Machines (SVM) 163
8.4 Unsupervised Learning 168
8.4.1 Clustering with K-Means 169
8.4.2 Gaussian Mixture Models (GMM) 171
8.4.3 Principal Component Analysis (PCA) 177
8.4.4 t-Distributed Stochastic Neighbour Embedding (t-SNE) 182
8.5 Practical Examples 185
8.6 Typical Mistakes and Misconceptions 198
8.7 Uses in Current Signal Processing 201
8.8 Key Idea Summary 203
8.9 References 204
9 Deep Learning and Signal Processing: A Relationship Between Data and Knowledge 205
9.1 Introduction and Motivation 205
9.2 Essential Theoretical Background 206
9.2.1 Signals: Discrete and Continuous 206
9.2.2 Signal Processing (Basic Concepts) 207
9.2.3 Machine Learning and Deep Learning 207
9.3 Core Ideas and Their Corresponding Mathematical Frameworks 208
9.3.1 Backpropagation Algorithm 208
9.4 Use of Non-linearity Within Autoencoders and Noise Removal 210
9.4.1 Multi Layer Perceptron: Theory and Practice 210
9.4.2 The Importance of Non-Linearity: "Bending" the Space 211
9.4.3 Common Activation Functions: When and How to Use Them 213
9.4.4 Stacked Denoising Autoencoder (SDAE) 216
9.4.5 Applications of SDAEs in Signal Processing: 225
9.5 Convolutional Neural Networks (CNN) 225
9.5.1 Convolutional Neural Networks: Building Blocks 226
9.6 The Multiscale Learning Paradigm and CNNs 228
9.6.1 The Importance of Scale in Signals and Data 228
9.6.2 Principles of Multiscale Representation Learning 229
9.6.3 CNNs: An Implicit Multiscale Architecture 229
9.6.4 Advanced: Explicit Multiscale CNN Designs 231
9.7 Transformer Architectures 232
9.7.1 Motivations and Key Ideas 232
9.7.2 Fundamental Components (Transformer Encoder) 233
9.7.3 Multi-Headed Self-Attention (MHSA) and relationship with Signal Processing 235
9.7.4 Demystification of the Self-Attention Mechanism: Questions, Keys, and Values in Action 236
9.8 Multimodal Learning and Signal Processing 242
9.9 Parallelism between Convolutional Network Kernels and Transformers in Simple Pills 245
9.9.1 How Backpropagation Refines Kernels 245
9.9.2 Parallelism with Transforms (Fourier, Wavelet, etc.) 246
9.10 Worked Examples 246
9.11 Pitfalls and Misconceptions 250
9.12 Applications in Modern Technology 251
9.13 Summary of Key Points 252
9.14 Sample Code 253
9.15 References 260
10 Graph Signal Processing (GSP) 263
10.1 Why is it important in computer science? 263
10.2 Graph Signal Processing - GSP in a nutshell 264
10.3 Theoretical Background: Graph Theory Basics 265
10.3.1 Adjacency Matrix 265
10.3.2 Degree Matrix 265
10.4 Mathematical Foundations and Basic Concepts of GSP 265
10.4.1 Graph Signals 266
10.4.2 The Graph Shift Operator 266
10.4.3 The Graph Laplacian 267
10.4.4 Normalized Laplacians [Advanced] 268
10.4.5 Graph Fourier Transform (GFT) 269
10.4.6 Graph Filtering 270
10.4.7 Convolutional Graph Neural Networks (GCN) 271
10.5 Worked Examples 276
10.6 Applications in Modern Technology 281
10.7 Summary of Key Points 282
10.7.1 Example 1: Fourier Transform on Graphs and Filtering 283
10.7.2 Example 2: Graph Convolutional Network (GCN) for Node Classification - Drug Toxicity prediction 287
10.7.3 GSP Example Conclusions 295
10.8 References 295
11 Kalman Filters and Particle Filters for Artificial Intelligence and Robotics297
11.1 Kalman Filters and Particle Filters in a Nutshell 298
11.1.1 The Particle Filter (PF): The Sleuth with an Army of Assisting Experts 299
11.2 Theoretical Background: Dynamic Systems and Uncertainty 300
11.2.1 State-Space Models 300
11.2.2 Uncertainty and Probability 301
11.2.3 Gaussian Noise 302
11.3 The Kalman Filter (KF) 302
11.3.1 KF assumptions 302
11.3.2 The Kalman Filter Algorithm 303
11.3.3 Limitations of KF and Extended Kalman Filter (EKF) 304
11.4 Particle Filters (PF) 306
11.4.1 The Basic Concept: Sampling Representation 306
11.4.2 Base Algorithm: Sequential Importance Sampling (SIS) 308
11.4.3 The Degeneration Problem and Resampling 308
11.4.4 The Full Algorithm: Sampling Importance Resampling (SIR) 309
11.4.5 Advantages and Disadvantages of PF 310
11.5 Application Examples 311
11.6 Pitfalls and Misconceptions 314
11.7 Applications in Modern Technology 314
11.8 Summary of Key Points 316
11.9 Example Code 316
11.9.1 Example 1: Linear Kalman Filter 316
11.9.2 Example 2: Particle Filter 320
11.10 References 324
12 Conclusions 325
12.1 Summary of Contents 325
12.2 Contributions and Impact of the Integration between SP and Deep Learning326
12.3 Challenges and Future Prospects 327
12.4 Final Thoughts 327
Index
Notă biografică
Vincenzo Dentamaro, PhD, is an Assistant Professor at the University of Bari and co-author of more than 50 peer-reviewed publications. His industrial collaborations include IBM, where he holds one patent, and the Italian AI start-up Nextome, which he co-founded. He is a co-founder of Geodesia.ai, an AI research lab based in San Francisco whose first product, G-1, provides real-time, model-agnostic validation and auditable evidence for enterprise deployments of large language models. He is a Member of IEEE, with research interests spanning machine learning for LLMs safety and auditability, healthcare signals, pattern recognition, and indoor positioning.