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Symmetries and Groups in Signal Processing: An Introduction deals with the subject of symmetry, and with its place and role in modern signal processing. In the sciences, symmetry considerations and related group theoretic techniques have had a place of central importance since the early twenties. In engineering, however, a matching recognition of their power is a relatively recent development. Despite that, the related literature, in the form of journal papers and research monographs, has grown enormously. A proper understanding of the concepts that have emerged in the process requires a mathematical background that goes beyond what is traditionally covered in an engineering undergraduate curriculum.
Admittedly, there is a wide selection of excellent introductory textbooks on the subject of symmetry and group theory. But they are all primarily addressed to students of the sciences and mathematics, or to students of courses in mathematics. Addressed to students with an engineering background, this book is meant to help bridge the gap.
List of contents
Signals and Signal Spaces: A Structural Viewpoint.- Algebraic Preliminaries.- Measurement, Modeling, and Metaphors.- Symmetries, Automorphisms and Groups.- Representations of Finite Groups.- Signal Processing and Representation Theory.
Summary
Symmetries and Groups in Signal Processing: An Introduction deals with the subject of symmetry, and with its place and role in modern signal processing. In the sciences, symmetry considerations and related group theoretic techniques have had a place of central importance since the early twenties. In engineering, however, a matching recognition of their power is a relatively recent development. Despite that, the related literature, in the form of journal papers and research monographs, has grown enormously. A proper understanding of the concepts that have emerged in the process requires a mathematical background that goes beyond what is traditionally covered in an engineering undergraduate curriculum.
Admittedly, there is a wide selection of excellent introductory textbooks on the subject of symmetry and group theory. But they are all primarily addressed to students of the sciences and mathematics, or to students of courses in mathematics. Addressed to students with an engineering background, this book is meant to help bridge the gap.
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From the reviews:
"This is an modern introduction to theoretical topics in field of signal processing, which is based on representation theory of groups. It is suitable for beginning graduate students and does not require from reader solid mathematical prerequisites. ... Abstract concepts are illustrated with their concrete engineering interpretations ... . this style makes the whole book very readable and suitable as textbook." (Jaak Henno, Zentralblatt MATH, Vol. 1205, 2011)
