Multidimensional Signals and Systems

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.

Comprehensive introduction to multidimensional signals and systems with more than 70 problems with solutions From initial-boundary-value problems to discrete-time algorithms Includes examples from electrical and audio engineering, imaging, acoustics, numerical analysis, and diffusion

Autorentext
Rudolf Rabenstein is a retired professor at the Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU) in Germany. He studied Electrical Engineering at the FAU and at the University of Colorado at Boulder, USA. He received the degrees "Doktor-Ingenieur" in electrical engineering and "Habilitation" in signal processing from the FAU. He worked with the Physics Department of the University of Siegen, Germany, and with the chair of Multimedia Communication and Signal Processing at the FAU. His research interests include multidimensional systems theory and multimedia signal processing. He is co-author and co-editor of several textbooks on signals and systems and signal processing.

Maximilian Schäfer is a postdoctoral researcher at the Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU) in Germany. He studied Electrical Engineering at the FAU, where he received the degrees Master of Science and "Doktor-Ingenieur" in electrical engineering. He worked with the chair of Multimedia Communication and Signal Processing at the FAU, and now with the Institute of Digital Communications at the FAU. His research is focused on multidimensional systems theory and on the modeling of distributed parameter systems with applications in sound synthesis and molecular communications.

Inhalt

1. Introduction.- 2. Overview on Multidimensional Signals.- Part I: Theory.- 3. Elements from One-Dimensional Signals and Systems.- 4. Multidimensional Signals.- 5. Discrete Multidimensional Systems.- 6. Continuous Multidimensional Systems.- Part II Applications.- 7. Electrical Transmission Lines.- 8. Particle Diffusion.- 9. Sound Synthesis.- 10. Sound Propagation.- 11. Mathematical Derivations.- Solutions to Problems.