| Description |
1 online resource (xv, 507 pages) |
| Contents |
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 |
| Summary |
This book covers the theory of multidimensional signals and systems and related practical aspects. It extends the properties and mathematical tools of one-dimensional signals and systems to multiple dimensions and covers relevant timeless topics including multidimensional transformations, multidimensional sampling as well as discrete multidimensional systems. A special emphasis is placed on physical systems described by partial differential equations, the construction of suitable integral transformations and the implementation of the corresponding discrete-time algorithms. To this end, signal spaces and functional transformations are introduced at a mathematical level provided by undergraduate programs in engineering and science. The presentation takes a comprehensive, illustrative and educational approach without reference to a particular application field. Instead, the book builds a solid theoretical concept of multidimensional signals and systems and shows the application to various problems relevant for practical scenarios |
| Notes |
Description based upon print version of record |
| Subject |
Signal theory (Telecommunication)
|
|
System analysis.
|
|
systems analysis.
|
|
Signal theory (Telecommunication)
|
|
System analysis
|
| Form |
Electronic book
|
| Author |
Schäfer, Maximilian
|
| ISBN |
9783031265143 |
|
3031265149 |
|
