Mathematical Summary for Digital Signal Processing Applications with Matlab
Mathematical summary for Digital Signal Processing Applications with Matlab consists of Mathematics which is not usually dealt in the DSP core subject, but used in DSP applications. Matlab programs with illustrations are given for the selective topics suc
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E.S. Gopi
Mathematical Summary for Digital Signal Processing Applications with Matlab
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E.S. Gopi National Institute of Technology, Trichy Dept. Electronics & Communication Engineering 67 Tanjore Main Road Tiruchirappalli-620015 National Highway India [email protected]
ISBN 978-90-481-3746-6 e-ISBN 978-90-481-3747-3 DOI 10.1007/978-90-481-3747-3 Springer Dordrecht Heidelberg London New York Library of Congress Control Number: 2009944069 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: eStudio Calamar S.L. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Dedicated to my son G.V. Vasig and my wife G. Viji
Preface
The book titled “Mathematical summary for Digital Signal Processing Applications with Matlab” consists of Mathematics which is not usually dealt in the DSP core subject, but used in the DSP applications. Matlab Illustrations for the selective topics such as generation of Multivariate Gaussian distributed sample outcomes, Optimization using Bacterial Foraging etc. are given exclusively as the separate chapter for better understanding. The book is written in such a way that it is suitable for Nonmathematical readers and is very much suitable for the beginners who are doing research in Digital Signal Processing. E.S. Gopi
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Acknowledgements
I am extremely happy to express my thanks to Prof. K.M.M. Prabhu, Indian Institute of Technology Madras for his constant encouragement. I also thank the Director Prof. M. Chidambaram, Prof. B. Venkataramani and Prof. S. Raghavan National Institute of Technology Trichy for their support. I thank those who directly or indirectly involved in bringing up this Book. Special thanks to my parents Mr. E. Sankarasubbu and Mrs. E.S. Meena.
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Contents
1
Matrices .. . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . 1.1 Properties of Vectors.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . 1.2 Properties of Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . 1.3 LDU Decomposition of the Matrix . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . 1.4 PLDU Decomposition of an Arbitrary Matrix . . . . . . . . . . . . . .. . . . . . . . . . . 1.5 Vector Space and Its Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . 1.6 Linear Independence, Span, Basis and the Dimension of the Vector Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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