Symmetries and Groups in Signal Processing An Introduction
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 ce
- PDF / 1,875,692 Bytes
- 164 Pages / 439.37 x 666.141 pts Page_size
- 52 Downloads / 162 Views
For other titles published in this series, go to http://www.springer.com/series/4748
Virendra P. Sinha
Symmetries and Groups in Signal Processing An Introduction
123
Prof. Virendra P. Sinha Dhirubhai Ambani Institute of Information and Comm. Tech. Near Indroda Circle 382007 Gandhinagar, Gujarat, India vp [email protected]
ISBN 978-90-481-9433-9 e-ISBN 978-90-481-9434-6 DOI 10.1007/978-90-481-9434-6 Springer Dordrecht Heidelberg London New York Library of Congress Control Number: 2010931379 c Springer Science+Business Media B.V. 2010 No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Cover design: SPi Publisher Services Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
To my grandsons Rohan, Ishaan, and Shloak, for a whiff of algebra
Preface The field of signal processing, as it stands today, abounds in varied generalizations of system theoretic concepts that can be said to rest on the notion of symmetry, and on group theoretic methods of exploiting symmetries. A wide range of such generalizations and developments rely centrally on a transition from the classical Fourier theory to the modern theory of non-commutative harmonic analysis, with its roots in the representation theory of groups. In the framework that emerges through this transition, all the basic notions—transforms, convolutions, spectra, and so on, carry over in a form that allows a wide variety of interpretations, subsuming the old ones and admitting new ones. This book is an introductory treatment of a selection of topics that together serve to provide in my view a background for a proper understanding of the theoretical developments within this framework. Addressed primarily to beginning graduate students in electrical and communication engineering, it is meant to serve as a bridge between what they know from their undergraduate years, and what lies ahead for them in their graduate studies, be it in the area of signal processing, or in related areas such as image processing and image understanding, coding theory, fault diagnostics, and the theory of algorithms and computation. I assume that the reader is familiar with the theory of linear time–invariant continuous–time and discrete–time systems as it is generally taught in a basic undergraduate course on signals and systems. There are no mathematical prerequisites beyond what they would have learnt in their undergraduate years. Familiarity with rudiments of linear algebra would be helpful, but even that is not necessary; whatever of it is needed in the book, they can pick up on their own as they go along. A point about pedagogy. In teaching mathematical concepts to engineering students, a p
Data Loading...
