INTRODUCTION TO DIGITAL AUDIO CODING AND STANDARDS THE KLUWER INTERNATIONAL SERIES IN ENGINEERING AND COMPUTER SCIENCE INTRODUCTION TO DIGITAL AUDIO CODING AND STANDARDS Marina Bosi Stanford University Richard E. Goldberg The Brattle Group SPRINGER SCIENCE+BUSINESS MEDIA, LLC Library of Congress Cataloging-in-Publication Data Bosi, Marina Introduction to Digital Audio Coding and Standards/by Marina Bosi, Richard E. Goldberg, p. cm. -(The Kluwer international series in engineering and computer science; SECS 721 Includes bibliographical references and index. ISBN 978-1-4613-5022-4 ISBN 978-1-4615-0327-9 (eBook) DOI 10.1007/978-1-4615-0327-9 1. Sound—Recording and reproducing—Digital techniques—Standards. 2. Data compression (Computer science) I. Goldberg, Richard E. II. Title. III. Series. TK7881.4 .B59 2002 621.38932—<Jc21 2002040686 Copyright © 2003 by Springer Science+Business Media New York Originally published by Kluwer Academic Publishers in 2003 Softcover reprint of the hardcover 1st edition 2003 All rights reserved. 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 the 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. Printed on acid-free paper. Contents FOREWORD ................................................................................................ xiii PREFACE .................................................................................................... xvii PART I: AUDIO CODING METHODS Chapter I. INTRODUCTION 1. Representation of Audio Signals ................................................ 3 2. Whatis a Digital Audio Coder? ................................................. 4 3. Audio Coding Goals ................................................................... 5 4. The Simplest Coder - PCM ....................................................... 7 5. The Compact Disk ..................................................................... 8 6. Potential Coding Errors .............................................................. 9 7. A More Complex Coder. .......................................................... 10 8. References ................................................................................ 12 9. Exercises .................................................................................. 12 Chapter 2. QUANTIZATION I. Introduction .............................................................................. 13 2. Binary Numbers ....................................................................... 14 3. Quantization ............................................................................. 20 4. Quantization Errors .................................................................. 34 5. Entropy Coding ........................................................................ 38 6. Summary .................................................................................. 43 7. References ................................................................................ 44 8. Exercises .................................................................................. 44 Chapter 3. REPRESENTATION OF AUDIO SIGNALS 1. Introduction .............................................................................. 47 2. Notation .................................................................................... 48 3. Dirac Delta ............................................................................... 49 . 4. The Fourier Transform ............................................................. 51 5. Summary Properties of Audio Signals ..................................... 53 6. The Fourier Series .................................................................... 59 7. The Sampling Theorem ............................................................ 61 8. Prediction ................................................................................. 63 9. Summary .................................................................................. 68 10. Appendix - Exact Reconstruction of a Band-Limited, Periodic Signal from Samples within One Period .................... 68 11. References ................................................................................ 69 12. Exercises .................................................................................. 70 Chapter 4. TIME TO FREQUENCY MAPPING PART I: THE PQMF 1. Introduction .............................................................................. 75 2. The Z Transform ...................................................................... 77 3. Two-Channel Perfect Reconstruction Filter Banks .................. 84 4. The Pseudo-QMF Filter Bank, PQMF ..................................... 90 5. Summary .................................................................................. 99 6. References .............................................................................. 100 7. Exercises ................................................................................ 101 Chapter 5. TIME TO FREQUENCY MAPPING PART II: THE MDCT 1. Introduction ............................................................................ 103 2. The Discrete Fourier Transform ............................................. 104 3. The Overlap-and-Add Technique .......................................... 113 4. The Modified Discrete Cosine Transform, MDCT ................ 124 5. Summary ................................................................................ 143 6. References .............................................................................. 144 7. Exercises ................................................................................ 146 Chapter 6. INTRODUCTION TO PSYCHOACOUSTICS 1. Introduction ............................................................................ 149 2. Sound Pressure Levels ........................................................... 150 3. Loudness ................................................................................ 150 4. Hearing Range ........................................................................ 151 5. Hearing Threshold .................................................................. 153 6. The Masking Phenomenon ..................................................... 156 7. Measuring Masking Curves ................................................... 160 8. Critical Bandwidths ................................................................ 164 9. How Hearing Works .............................................................. 168 vi 10. Summary ................................................................................ 174 11. References .............................................................................. 175 12. Exercises ................................................................................ 177 Chapter 7. PSYCHOACOUSTIC MODELS FOR AUDIO CODING 1. Introduction ............................................................................ 179 2. Excitation Patterns and Masking Models ............................... 180 3. The Bark Scale ....................................................................... 182 4. Models for the Spreading of Masking .................................... 183 5. Masking Curves ..................................................................... 190 6. "Addition" of Masking ........................................................... 192 7. Modeling the Effects of Non-Simultaneous (Temporal) Masking .................................................................................. 195 8. Perceptual Entropy ................................................................. 196 9. Masked Thresholds and Allocation of the Bit Pool ............... 197 10. Summary ................................................................................ 198 11. References .............................................................................. 198 12. Exercises ................................................................................ 200 Chapter 8. BIT ALLOCATION STRATEGIES 1. Introduction ............................................................................ 201 2. Coding Data Rates ................................................................. 202 3. A Simple Allocation of the Bit Pool ...................................... 204 4. Optimal Bit Allocation ........................................................... 205 5. Time-Domain Distortion ........................................................ 214 6. Optimal Bit Allocation and Perceptual Models ..................... 216 7. Summary ................................................................................ 218 8. References .............................................................................. 219 9. Exercises ................................................................................ 219 Chapter 9. BUILDING A PERCEPTUAL AUDIO CODER 1. Introduction ............................................................................ 221 2. Overview of the Coder Building Blocks ................................ 221 3. Computing Masking Curves .................................................. 223 4. Bitstream Format. ................................................................... 230 5. Business Models and Coding Secrets ....................................