Feuer,_Goodwin_-_Sampling_in_Digital_Signal_Processing_and_Control.pdf

Systems & Control: Foundations & Applications

Founding Editor

Christopher I. Byrnes, Washington University

Arie Feuer

Graham C. Goodwin

Sampling in

Digital Signal Processing

and Control

1996

Birkhauser

Boston • Basel • Berlin

Arie Feuer

Dept. of Electrical Engineering

Technion-Israel Institute of

Technology

Graham C. Goodwin

Faculty of Engineering

The University of Newcastle

Callaghan NSW 2308

Australia

Haifa 32000

Israel

Library of Congress Cataloging-in-Publication Data

Feuer, Arie, 1943-

Sampling, in digital signal processing and control / Arie Feuer,

Graham C. Goodwin.

p. cm. -- (Systems & control)

Includes bibliographical references.

ISBN-13: 978-1-4612-7546-6

e-ISBN-13: 978-1-4612-2460-0

DOl: 10.1007/978-1-4612-2460-0

1. Signal processing--Digital techniques. 2. Signal processing-

-Statistical methods. 3. Sampling (Statistics) 4. Control theory.

I. Goodwin, Graham C. (Graham Clifford), 1945-

II. Title.

III. Series.

TK5102.9.F48 1996

621.382'23--dc20

96-24284

CIP

Printed on acid-free paper

Softcover reprint of the hardcover 1st edition 1996

or transmitted, in any form orby any means, electronic, mechanical, photocopying, recording,

or otherwise, without prior permission of the copyright owner.

Permission to photocopy for internal or personal use of specific clients is granted by

Birkhauser Boston for libraries and other users registered with the Copyright Clearance

Center (CCC), provided that the base fee of$6.00 per copy, plus $0.20 per page is paid directly

to CCC, 222 Rosewood Drive, Danvers, MA 01923, U.S.A. Special requests should be

addressed directly to Birkhauser Boston, 675 Massachusetts Avenue, Cambridge, MA 02139,

U.S.A.

ISBN-13 :97 8-1-4612-7546-6

Typeset by the Authors in LATEX.

987 6 5 432 1

Contents

Preface ................................

xiii

Notation ...............................

xix

Fourier Analysis

Chapter 1

1.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.2

The Basic Transforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.2.1

Fourier Series ...................................

1.2.2 The Continuous-Time Fourier Transform . . . . . . . . . . . . . .

1.2.3

The Discrete-Time Fourier Transform (DTFT) . . . . . . . . . .

1.2.4

The Discrete Fourier Transform (DFT) . . . . . . . . . . . . . . . .

1.3

Properties of Continuous-Time Fourier Transforms. . . . . . . . . . . .

1.4

Properties of Discrete-Time Fourier Transforms ..............

1.5

The A - Impulse Stream . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.6

Inter-relating the Various Transforms . . . . . . . . . . . . . . . . . . . . . . .

1.6.1

Fourier Series Revisited ...........................

1.6.2 The Discrete-Time Fourier Transform Revisited ........

1.6.3

The Discrete Fourier Transform Revisited .............

1.6.4

Summary.......................................

1. 7

Special Topics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.7.1

Sampling of Sequences. . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.7.2 Irregular Sampling in Periodic Patterns ...............

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