1. Introduction to Signal Processing and Machine Learning Theory
Abstract
1.1 Introduction
1.2 Continuous-time signals and systems
1.3 Discrete-time signals and systems
1.4 Random signals and stochastic processes
1.5 Sampling and quantization
1.6 FIR and IIR filter design
1.7 Digital filter structures and implementations
1.8 Multirate signal processing
1.9 Filter banks and wavelets
1.10 Discrete multiscale and transforms
1.11 Frames
1.12 Parameter estimation
1.13 Adaptive filtering
1.14 Graph Signal Processing
1.15 Tensors
1.16 Non-convex Optimization
1.17 Dictionary Learning
1.18 Closing comments
References


2. Continuous-Time Signals and Systems
Abstract
Nomenclature
2.1 Introduction
2.2 Continuous-time systems
2.3 Differential equations
2.4 Laplace transform: definition and properties
2.5 Transfer function and stability
2.6 Frequency response
2.7 The Fourier series and the Fourier transform
2.8 Conclusion and future trends
2.9 Relevant Websites:
2.10 Supplementary data
2.11 Supplementary data
Glossary
References

3. Discrete-Time Signals and Systems
Abstract
3.1 Introduction
3.2 Discrete-time signals: sequences
3.3 Discrete-time systems
3.4 Linear time-invariant (LTI) systems
3.5 Discrete-time signals and systems with MATLAB
3.6 Conclusion
References

4. Random Signals and Stochastic Processes
Abstract
Acknowledgments
4.1 Introduction
4.2 Probability
4.3 Random variable
4.4 Random process
References

5. Sampling and Quantization
Abstract
5.1 Introduction
5.2 Preliminaries
5.3 Sampling of deterministic signals
5.4 Sampling of stochastic processes
5.5 Nonuniform sampling and generalizations
5.6 Quantization
5.7 Oversampling techniques
5.8 Discrete-time modeling of mixed-signal systems
References

6. Digital Filter Structures and Their Implementation
Abstract
6.1 Introduction
6.2 Digital FIR filters
6.3 The analog approximation problem
6.4 Doubly resistively terminated lossless networks
6.5 Ladder structures
6.6 Lattice structures
6.7 Wave digital filters
6.8 Frequency response masking (FRM) structure
6.9 Computational properties of filter algorithms
6.10 Architecture
6.11 Arithmetic operations
6.12 Sum-of-products (SOP)
6.13 Power reduction techniques
References

7. Multi-rate Signal Processing for Software Radio Architectures
Abstract
7.1 Introduction
7.2 The Sampling process and the “Resampling¿ process
7.3 Digital filters
7.4 Windowing
7.5 Basics on multirate filters
7.6 From single channel down converter to standard down converter channelizer
7.7 Modifications of the standard down converter channelizer—M:2 down converter channelizer
7.8 Preliminaries on software defined radios
7.9 Proposed architectures for software radios
7.10 Closing comments
Glossary
References

8. Modern Transform Design for Practical Audio/Image/Video Coding Applications
Abstract
8.1 Introduction
8.2 Background and fundamentals
8.3 Design strategy
8.4 Approximation approach via direct scaling
8.5 Approximation approach via structural design
8.6 Wavelet filters design via spectral factorization
8.7 Higher-order design approach via optimization
8.8 Conclusion
References

9. Discrete Multi-Scale Transforms in Signal Processing
Abstract
9.1 Introduction
9.2 Wavelets: a multiscale analysis tool
9.3 Curvelets and their applications
9.4 Contourlets and their applications
9.5 Shearlets and their applications
A Appendix
References

10. Frames in Signal Processing
Abstract
10.1 Introduction
10.2 Basic concepts
10.3 Relevant definitions
10.4 Some computational remarks
10.5 Construction of frames from a prototype signal
10.6 Some remarks and highlights on applications
10.7 Conclusion
References

11. Parametric Estimation
Abstract
11.1 Introduction
11.2 Deterministic and stochastic signals
11.3 Parametric models for signals and systems
References

12. Adaptive Filters
Abstract
Acknowledgment
12.1 Introduction
12.2 Optimum filtering
12.3 Stochastic algorithms
12.4 Statistical analysis
12.5 Extensions and current research
12.6 Supplementary data
References

13. Signal Processing over Graphs
Abstract
Acknowledgment
13.1 Introduction
13.6 Supplementary data
References

14. Tensors for Signal Processing and Machine Learning
Abstract
Acknowledgment
14.1 Introduction

15. Non-convex Optimization for Machine Learning

16. Dictionary Learning and Sparse Representation
Abstract