Franz Pichler

Dyadic (Walsh) analysis emerged as a new research area in applied mathematics and engineering in early seventies within attempts to provide answers to demands from practice related to application of spectral analysis of different classes of signals, including audio, video, sonar, and radar signals. In the meantime, it evolved in a mature mathematical discipline with fundamental results and important features providing basis for various applications. The book will provide fundamentals of the area through reprinting carefully selected earlier publications followed by overview of recent results concerning particular subjects in the area written by experts, most of them being founders of the field, and some of their followers. In this way, this first volume of the two volume book offers a rather complete coverage of the development of dyadic Walsh analysis, and provides a deep insight into its mathematical foundations necessary for consideration of generalizations and applications that are the subject of the second volume. The presented theory is quite sufficient to be a basis for further research in the subject area as well as to be applied in solving certain new problems or improving existing solutions for tasks in the areas which motivated development of the dyadic analysis.

The second volume of the two volumes book is dedicated to various extensions and generalizations of Dyadic (Walsh) analysis and related applications. Considered are dyadic derivatives on Vilenkin groups and various other Abelian and finite non-Abelian groups. Since some important results were developed in former Soviet Union and China, we provide overviews of former work in these countries. Further, we present translations of three papers that were initially published in Chinese. The presentation continues with chapters written by experts in the area presenting discussions of applications of these results in specific tasks in the area of signal processing and system theory. Efficient computing of related differential operators on contemporary hardware, including graphics processing units, is also considered, which makes the methods and techniques of dyadic analysis and generalizations computationally feasible. The volume 2 of the book ends with a chapter presenting open problems pointed out by several experts in the area.

Microtechnologies and their corresponding CAD tools have meanwhile reached alevel of sophistication that requires the application of theoretical means on all modelling levels of design and analysis. Also, there is a growing need for a scientific approach in modelling again. Many concepts provided by Systems Theory again turn out to be of major importance. This is especially valid for the design of "machines with intelligent behaviour". When dealing with complex systems, the engineering design has to be supported by CAD tools. Consequently, the methods of Systems Theory must also get computerized. The newly established field of "Computer Aided Systems Theory" (CAST) is a first effort in this direction. The goal of CAST research and development isto provide "Systems Theory Method Banks" which can be used in education and to provide a platform for the migration of CAST methods into existing CAD tools. This book, basing on different research and development projects in CAST, is written for engineers who are interested in using and developing CAST systems, particularly in thefield of Information and Systems Engineering.

Dieses Buch befaßt sich mit der Aufgabe, einen Grundrahmen für den Aufbau einer Methodenbank der Systemtheorie zu schaffen und die Anwendung desselben mittels einer konkreten Software-Implementierung zu demonstrieren. Als allgemeines Problemlösungsgerüst wird die sogenannte STIPS-Maschine eingeführt, mit der "Systemtypen" über "Systemtransformationen" abgeleitet und interaktiv "Systemalgorithmen" entwickelt werden können. Am Beispiel der speziellen Methodenbank CAST. FSM für die Behandlung von Problemstellungen der Automaten- und Schaltwerktheorie wird dieses Konzept demonstriert. Ziel ist es zu zeigen, welche Systematik heute bei der Sammlung von Methoden der Systemtheorie angewandt werden kann und wie es gelingt, eine solche Sammlung für die Entwicklung von Anwendungssoftware für den CAD-Bereich einzusetzen. Im Vordergrund stehen dabei die klassischen Anwendungsgebiete der Systemtheorie im Bereich des Entwurfs von komplexen Hardwaremoduln der Computertechnik und im Bereich der Signalverarbeitung. Das Buch zeigt, wie über die Entwicklung von Programmpaketen hinaus mit den heutigen Mitteln der Softwaretechnik mit Workstations leistungsfähig interaktive Methodenbanken für den Einsatz von systemtheoretischen Methoden in der Technik gebaut werden können.