Intro
Preface
Contents
Acronyms
1 Introduction
References
2 Overview on Multidimensional Signals
2.1 One-Dimensional Signals
2.1.1 One-Dimensional Time-Dependent Signals
2.1.2 One-Dimensional Space-Dependent Signals
2.2 Two-Dimensional Signals
2.2.1 Two-Dimensional Space-Dependent Signals
2.2.2 Two-Dimensional Space- and Time-Dependent Signals
2.3 Three-Dimensional Signals
2.3.1 Three-Dimensional Space-Dependent Signals
2.3.2 Three-Dimensional Space- and Time-Dependent Signals
2.4 Four-Dimensional Signals
2.5 Higher Dimensional Signals

2.6 Properties of Multidimensional Signals
2.7 Multidimensional Systems
2.7.1 Autonomous Systems and Input-Output-Systems
2.7.2 Linear, Time-, and Shift-Invariant Systems
2.7.3 Mathematical Formulation of Multidimensional Systems
2.7.3.1 Difference Equations
2.7.3.2 Differential Equations
2.8 Overview on the Next Chapters
2.9 Problems
References
3 Elements from One-Dimensional Signals and Systems
3.1 Convolution and Impulse Response
3.1.1 An Introductory Example
3.1.1.1 Integer Numbers
3.1.1.2 Sequences of Numbers
3.1.1.3 Continuous Functions

3.1.2 Delta Impulse
3.1.2.1 Classical Functions and Generalized Functions
3.1.2.2 Definition
3.1.2.3 Properties
3.1.2.4 Summary of the Properties of the Delta Impulse
3.1.3 Convolution
3.1.3.1 Derivation of Continuous-Time Convolution
3.1.3.2 Properties of Continuous-Time and Discrete-Time Convolution
3.1.3.3 Summary of the Properties of Continuous-Time and Discrete-Time Convolution
3.2 Fourier Transformation
3.2.1 Eigenfunctions of Linear and Time-Invariant Systems
3.2.2 Definition of the Fourier Transformation
3.2.3 Correspondences
3.2.4 Properties

3.2.5 Summary of Correspondences and Properties of the Fourier Transformation
3.3 Sampling
3.3.1 Sampling of Continuous-Time Functions
3.3.2 Spectrum of a Sampled Signal
3.4 Differential Equations and Transfer Functions
3.4.1 A Light Example
3.4.1.1 Circuit Analysis
3.4.1.2 Solution of the Homogeneous Differential Equation
3.4.1.3 Solution of the Inhomogeneous Differential Equation
3.4.1.4 Solution of the Initial Value Problem
3.4.2 State Space Systems
3.4.2.1 State Space Representation
3.4.2.2 Solution of the Homogeneous State Equation

3.4.2.3 Definition of the Propagator P P P P(t)
3.4.2.4 Properties of the Propagator P P P P(t)
3.4.2.5 Similarity Transformation
3.4.2.6 Interpretation of the State Transformation as a Signal Transformation
3.4.2.7 Propagator P P P P(t) in the Transform Domain
3.4.2.8 Laplace Transfer Function
3.4.2.9 Solution of the State Equations
3.4.2.10 Discrete-Time State Space Representation
3.4.3 Conclusion and Outlook
3.5 Problems
References
4 Signal Spaces
4.1 Foundations
4.1.1 Vectors, Functions, and Signals
4.1.2 Topics from Signal Processing