,Digital Signal
Processing
Principles, ~ l ~ o r i t h mand
i , Applications
Third Edition
John G. Proakis
Northeastern University
Dimitris G . Manolakis
Boilon College
PRENTICE-HALLINTERNATIONAL, INC.
,This edition may be sold only in those countries to which it is consigned by Prentice-Hall International.
It is not to be reexported and it is not for sale in the U.S.A.. Mexico. or Canada.
@ 19% by Prentice-Hall, Inc.
Simon 8.: SchusterlA Viacom Company
Upper Saddle River. New Jersey 07458
All rights resewed. No part of this book may be
reproduced. in any form or by any means,
without permission in writing from the publisher.
The author and publisher of this book have used their best efforts in preparing t h ~ sbook. These
efforts include the development. research. and testing of the theories and programs to dcterminc thelr
effectiveness. The author and publisher make no warranty of any kind, expressed or implied. with
regard to these programs or the documentation conlained in this book. The author and publisher shall
not be liable in any event for incidental or consequential damages in connection with. or arlsing out
of. the furnishing. performance. or use of these programs.
Printed in the United Slates of America
Prentice-Hall International (UK) Limited. London
Prentice-Hall of Australia Pty. Limited. Sydney
Prentice-Hall Canada, Inc., Toronro
Prentice-Hall Hispanoamericana. S.A.. Mexico
Prentice-Hall of India Private Limited, New Delhi
Prentice-Hall of Japan. Inc., T o k y o
Simon & Schuster Asia Pte. Ltd,, Singapore
Editora Prentice-Hall do Brasil, Ltda., Rio de Janeiro
Prentice-Hall, Inc, Upper Saddle River, New Jersey
, PREFACE
1 INTRODUCTION
1.1 Signals, Systems. and Signal Processing 2
1.1.1 Basic Elements of a D~gitalSignal Processing System. 4
1.1.2 Advantages of Digital over Analog Signal Processing, 5
1.2 Classification of Signals 6
1.2.1 Multichannel and Multidimensional Signals. 7
1.2.2 Continuous-Time Versus Discrete-Tlme Signals. 8
1.2.3 Continuous-Valued Versus Discrete-Valued Signals. 10
1.2.4 Determinist~cVersus Random Signals. 11
1.3 T h e Concept of Frequency in Continuous-Time and
Discrete-Time Signals 14
1.3.1 Continuous-Time Sinusoidal Signals, 14
1.3.2 Discrete-Time Sinusoidal Signals. 16
1.3.3 Harmonically Related Complex Exponentials, 19
1.4 Analog-to-Digital and Digital-to-Analog Conversion 21
1.4.1 Sampling of Analog Signals, 23
1.4.2 The Sampling Theorem, 29
1.4.3 Quantization of Continuous-Amplitude Signals, 33
1.4.4 Quantization of Sinusoidal Signals. 36
1.4.5 Coding of Quantized Samples. 38
1.4.6 Digital-to-Analog Conversion, 38
1.4.7 Analysis of Digital Signals and Systems Versus Discrete-Time
Signals and Systems, 39
1.5 Summary and References 39
Problems 40
Processing
Principles, ~ l ~ o r i t h mand
i , Applications
Third Edition
John G. Proakis
Northeastern University
Dimitris G . Manolakis
Boilon College
PRENTICE-HALLINTERNATIONAL, INC.
,This edition may be sold only in those countries to which it is consigned by Prentice-Hall International.
It is not to be reexported and it is not for sale in the U.S.A.. Mexico. or Canada.
@ 19% by Prentice-Hall, Inc.
Simon 8.: SchusterlA Viacom Company
Upper Saddle River. New Jersey 07458
All rights resewed. No part of this book may be
reproduced. in any form or by any means,
without permission in writing from the publisher.
The author and publisher of this book have used their best efforts in preparing t h ~ sbook. These
efforts include the development. research. and testing of the theories and programs to dcterminc thelr
effectiveness. The author and publisher make no warranty of any kind, expressed or implied. with
regard to these programs or the documentation conlained in this book. The author and publisher shall
not be liable in any event for incidental or consequential damages in connection with. or arlsing out
of. the furnishing. performance. or use of these programs.
Printed in the United Slates of America
Prentice-Hall International (UK) Limited. London
Prentice-Hall of Australia Pty. Limited. Sydney
Prentice-Hall Canada, Inc., Toronro
Prentice-Hall Hispanoamericana. S.A.. Mexico
Prentice-Hall of India Private Limited, New Delhi
Prentice-Hall of Japan. Inc., T o k y o
Simon & Schuster Asia Pte. Ltd,, Singapore
Editora Prentice-Hall do Brasil, Ltda., Rio de Janeiro
Prentice-Hall, Inc, Upper Saddle River, New Jersey
, PREFACE
1 INTRODUCTION
1.1 Signals, Systems. and Signal Processing 2
1.1.1 Basic Elements of a D~gitalSignal Processing System. 4
1.1.2 Advantages of Digital over Analog Signal Processing, 5
1.2 Classification of Signals 6
1.2.1 Multichannel and Multidimensional Signals. 7
1.2.2 Continuous-Time Versus Discrete-Tlme Signals. 8
1.2.3 Continuous-Valued Versus Discrete-Valued Signals. 10
1.2.4 Determinist~cVersus Random Signals. 11
1.3 T h e Concept of Frequency in Continuous-Time and
Discrete-Time Signals 14
1.3.1 Continuous-Time Sinusoidal Signals, 14
1.3.2 Discrete-Time Sinusoidal Signals. 16
1.3.3 Harmonically Related Complex Exponentials, 19
1.4 Analog-to-Digital and Digital-to-Analog Conversion 21
1.4.1 Sampling of Analog Signals, 23
1.4.2 The Sampling Theorem, 29
1.4.3 Quantization of Continuous-Amplitude Signals, 33
1.4.4 Quantization of Sinusoidal Signals. 36
1.4.5 Coding of Quantized Samples. 38
1.4.6 Digital-to-Analog Conversion, 38
1.4.7 Analysis of Digital Signals and Systems Versus Discrete-Time
Signals and Systems, 39
1.5 Summary and References 39
Problems 40
