Multidimensional Signals and Systems [electronic resource] : Theory and Foundations /

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.

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.