Multidimensional Signals and Systems: Theory and Foundations

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.

本書涵蓋多維信號和系統的理論及相關實際應用。它將一維信號和系統的特性和數學工具擴展到多個維度，並涵蓋了相關的經典主題，包括多維轉換、多維取樣以及離散多維系統。特別強調了由偏微分方程描述的物理系統，適當積分變換的構建以及相應離散時間算法的實現。為此，引入了信號空間和功能變換，其數學水平適用於工程和科學的本科課程。

本書以全面、圖解和教育性的方式呈現，不涉及特定的應用領域。相反，本書建立了多維信號和系統的堅實理論概念，並展示了在實際情境中解決各種問題的應用。

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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.

Rudolf Rabenstein是德國弗萊堡-亞歷山大-紐倫堡大學（FAU）的退休教授。他在FAU和美國科羅拉多大學波德分校學習電機工程。他在FAU獲得電機工程的"Doktor-Ingenieur"學位和信號處理的"Habilitation"學位。他曾在德國西根大學物理系和FAU的多媒體通信和信號處理講座工作。他的研究興趣包括多維系統理論和多媒體信號處理。他是幾本關於信號和系統以及信號處理的教科書的合著者和合編者。

Maximilian Schäfer是德國弗萊堡-亞歷山大-紐倫堡大學（FAU）的博士後研究員。他在FAU學習電機工程，並獲得碩士學位和電機工程的"Doktor-Ingenieur"學位。他曾在FAU的多媒體通信和信號處理講座工作，現在在FAU的數字通信研究所工作。他的研究重點是多維系統理論和在聲音合成和分子通信中應用的分佈參數系統建模。