Handbook of SignalProcessing in Acoustics

Volume 1

Edited by

David Havelock

National Research Council, Canada

Sonoko Kuwano

Osaka University, Japan

Michael Vorlander

RWTH Aachen University, Germany

Handbook ofSignal Processingin AcousticsVolume 1

123

EditorsDavid Havelock Sonoko KuwanoNational Research Council Osaka UniversityInstitute for Microstructural Graduate School of Human

Sciences SciencesAcoustics and Signal Department of Environmental

Processing Group Psychology1200 Montreal Road 1-2 Yamadaok SuitaOttawa ON K1A 0R6 OsakaCanada Japan

Michael VorlanderRWTH Aachen UniversityInstitute of Technical AcousticsAachenGermany

ISBN: 978-0-387-77698-9 e-ISBN: 978-0-387-30441-0

Library of Congress Control Number: 2008923573

© 2008 Springer Science+Business Media, LLCAll rights reserved. This work may not be translated or copied in whole or inpart without the written permission of the publisher (Springer Science+BusinessMedia, LLC, 233 Spring Street, New York, NY 10013, USA), except for briefexcerpts in connection with reviews or scholarly analysis. Use in connection withany form of information storage and retrieval, electronic adaptation, computersoftware, or by similar or dissimilar methodology now known or hereafterdeveloped is forbidden.The use in this publication of trade names, trademarks, service marks, and similarterms, even if they are not identified as such, is not to be taken as an expressionof opinion as to whether or not they are subject to proprietary rights.Printed on acid-free paper

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springer.com

Editor Biographies

David HavelockNational Research CouncilInstitute for Microstructural SciencesAcoustics and Signal Processing Group1200 Montreal RoadOttawa ON K1A 0R6Canada

Sonoko KuwanoOsaka UniversityGraduate School of Human SciencesDepartment of Environmental Psychology1-2 Yamadaok SuitaOsakaJapan

Michael VorlanderRWTH Aachen UniversityInstitute of Technical AcousticsAachenGermany

Editorial Board

Last Name Given Name(s) Affiliation/Address

Beauchamp James W. University of Illinois Urbana-Champaign,School of Music, Dept. of ECE,Urbana, IL, USA

Christie Douglas R. Earth Physics, Research School of EarthSciences, The Australian National University,Canberra, AUSTRALIA

Deffenbaugh Max ExxonMobil Research and EngineeringCompany, Annandale, NJ USA

Elliott Stephen J. Southampton University, Institute of Sound andVibration Research, Southampton, ENGLAND

Fastl Hugo Technische Universitaet MuenchenAG Technische Akustik, MMKMuenchen, GERMANY

Gierlich Hans Wilhelm HEAD acoustics GmbHTelecom Division, Herzogenrath, GERMANY

Guyader Jean-Louis Labratory for Vibration AcousticsVilleurbanne, FRANCE

Jacobsen Finn Technical University of Denmark,Lyngby, DENMARK

Karjalainen Matti Helsinki University of Technology, FINLAND

Kollmeier Birger Universitat Oldenburg, Oldenburg, GERMANY

O’Shaughnessy Douglas D. INRS-EMT (Telecommunications), Montreal,QC, CANADA

Riquimaroux Hiroshi Doshisha University, Department of KnowledgeEngineering & Computer Sciences, Sensory &Cognitive Neuroscience Research Laboratory,Kyotanabe, Kyoto, JAPAN

Sullivan Edmund J. EJS Consultants Portsmouth, RI, USA

viii Editorial Board

Last Name Given Name(s) Affiliation/Address

Suzuki Hideo 1-2-3-S2502, Utase, Mihama-ward, Chiba-city,JAPAN 261-0013

Taroudakis Michael University of Crete Department of Mathematics,and FORTH, Institute of Applied andComputational Mathematics, Heraklion,GREECE

Ueha Sadayuki Tokyo Institute of Technology, Director,Precision and Intelligence Lab, Yokohama,JAPAN

Verrillo Ronald T. (deceased)Institute for Sensory Research, Syracuse, NY,USA

Yamada Ichiro Aviation Environment Research Center, AirportEnvironment Improvement Foundation, Tokyo,JAPAN

Yamasaki Yoshio Waseda University, Graduate School of GlobalInformation and Telecommunication Studies,Saitama, JAPAN

Tohyama Mikio Waseda University, JAPAN

Preface

Acoustics has a special relationship with signal processing. Manyconcepts in signal processing arise naturally from our generalexperience with sound and vibration and, more than in manyother fields, acoustics is concerned with the acquisition, analysis,and synthesis of signals. Consequently, there is a rich resourceof signal processing expertise within the acoustics community.

There are many excellent reference books devoted to signalprocessing but the objective of the Handbook of Signal Processingin Acoustics is to bring together the signal processing expertisespecific to acoustics and to capture the interdisciplinary natureof signal processing within acoustics. It is also hoped that thehandbook will promote networking and the interchange of ideasbetween technical areas in acoustics.

The handbook comprises 104 Chapters organized into 17 Parts.Each Part addresses a technical area of acoustics, reflectingthe general demarcations of specialization within the acousticscommunity. An expert with broad knowledge of signal processingwithin their respective technical area was invited to act as aSection Leader for each Part of the handbook. These SectionLeaders contributed substantially to the handbook project byhelping to define the contents and scope of each chapter, findingan appropriate contributing expert author, and managing thereview and revision of material. Collectively with the Editors,they form the Editorial Board for the handbook.

Planned sections on Architectural Acoustics, NonlinearAcoustics, and Ultrasound are unfortunately omitted fromthe handbook; nevertheless, the handbook otherwise providesthorough coverage of the field of acoustics and we can hope thatpossible future editions might include these areas.

The handbook is written from the perspective of acoustics, byacousticians with signal processing expertise. Emphasis is placed

x Preface

in the description of acoustic problems and the signal processingrelated to their solutions. The reader is assumed to have basicknowledge of signal processing. Signal processing techniques aredescribed but the reader is referred elsewhere for derivations anddetails.

The authors were not required to adhere to strict standardsof style or notation, and were asked to prepare short, concise,self-sufficient chapters. This results in variations in style andnotation throughout the handbook that reflects the diversity ofperspectives within the acoustics community.

David Havelock

Acknowledgments

David Havelock gratefully acknowledges support from theInstitute for Microstructural Sciences, of the National ResearchCouncil of Canada, for making time and resources availableduring the preparation of this handbook. He also thanks John C.Burgess (University of Hawaii, retired) for the encouragement tobegin this project and expresses his gratitude to the co-Editors,Sonoko Kuwano and Michael Vorlander, who were a pleasureto work with throughout this project. The efforts of all of theSection Leaders are greatly appreciated and we thank each ofthem sincerely for their patience, perseverance, and faith thatwere required to see this project to completion. We thank eachof the authors for their contributions.

Contents

Editor Biographies v

Editorial Board vii

Preface ix

Acknowledgments xi

Contributors xvii

PART I ACOUSTIC SIGNALS AND SYSTEMS 11 Signals and Systems 3

2 Acoustic Data Acquisition 17

3 Spectral Analysis and Correlation 33

4 The FF T and Tone Identification 53

5 Measuring Transfer-Functions and Impulse Responses 65

6 Digital Sequences 87

7 Filters 107

8 Adaptive Processing 125

9 Beamforming and Wavenumber Processing 131

xiv Contents

PART II AUDITORY SYSTEM AND HEARING 14510 Anatomy, Physiology and Function of the Auditory System 147

11 Physiological Measures of Auditory Function 159

12 Auditory Processing Models 175

13 Speech Intelligibility 197

14 Signal Processing in Hearing Aids 205

PART III PSYCHOACOUSTICS 21315 Methods for Psychoacoustics in Relation

to Long-Term Sounds 215

16 Masking and Critical Bands 229

17 Aspects of Modeling Pitch Perception 241

18 Calculation of Loudness for Normaland Hearing-Impaired Listeners 251

19 Psychoacoustical Roughness 263

PART IV MUSICAL ACOUSTICS 27520 Automatic Music Transcription 277

21 Music Structure Analysis from Acoustic Signals 305

22 Computer Music Synthesis and Composition 333

23 Singing Voice Analysis, Synthesis, and Modeling 359

24 Instrument Modeling and Synthesis 375

25 Digital Waveguide Architecturesfor Virtual Musical Instruments 399

26 Modeling of Musical Instruments 419

Contents xv

PART V SPEECH 44727 Display and Analysis of Speech 449

28 Estimation of Speech Intelligibility and Quality 483

29 Gaussian Models in Automatic Speech Recognition 521

30 Speech Synthesis 557

31 Speech Coders 587

PART VI AUDIO ENGINEERING 62132 Transducer Models 623

33 Loudspeaker Design and Performance Evaluation 649

34 PA Systems for Indoor and Outdoor 669

35 Beamforming for Speech and Audio Signals 691

36 Digital Audio Recording Formats and Editing Principles 703

37 Audiovisual Interaction 731

38 Multichannel Sound Reproduction 747

39 Virtual Acoustics 761

40 Audio Restoration 773

41 Audio Effects Generation 785

42 Perceptually Based Audio Coding 797

PART VII TELECOMMUNICATIONS 81943 Speech Communication and Telephone Networks 821

44 Methods of Determining the Communicational Qualityof Speech Transmission Systems 831

xvi Contents

45 Efficient Speech Coding and TransmissionOver Noisy Channels 853

46 Echo Cancellation 883

47 Noise Reduction and Interference Cancellation 897

48 Terminals and Their Influence on Communication Quality 909

49 Networks and Their Influence on Communication Quality 915

50 Interaction of Terminals, Networksand Network Configurations 921

List of Important Abberviations 927

Contributors

Tomonari AkamatsuNational Research Institute of Fisheries Engineering, FisheriesResearch Agency of Japan, Kamisu, Ibaraki, Japan

Benoit AlcoverroCEA/DASE, BP 12, 91680 Bruyeres Le Châtel, France

Lydia AyersComputer Science Department, Hong Kong University of Scienceand Technology, Clear Water Bay, Kowloon, Hong Kong, China,e-mail: layers@cs.ust.hk

Juha Reinhold BackmanNokia, Espoo, Finland

Rolf BaderInstitute of Musicology, University of Hamburg, Hamburg,Germany

James W. BeauchampSchool and Music and Department of Electrical and ComputerEngineering, University of Illinois at Urbana-Champaign, 2136Music Building, 1114 West Nevada Street, Urbana, IL 61801,USA, e-mail: jwbeauch@uiuc.edu

Kim BenjaminNaval Undersea Warfare Center, Newport, RI, USA

A.J. BerkhoutDelft University of Technology, Delft, The Netherlands

Jeff BilmesDepartment of Electrical Engineering, University of Washington,Seattle, WA, USA

Ole-Herman BjorNorsonic AS, Lierskogen, Norway, e-mail: ohbjor@norsonic.com

xviii Contributors

Stanley J. Bolanowski (deceased)Institute for Sensory Research, Syracuse University, Syracuse,NY 13244, USA

Baris BozkurtIzmir Institute of Technology (IYTE), Izmir, Turkey

Nicolas BrachetProvisional Technical Secretariat, CTBTO, Vienna InternationalCentre, Vienna, Austria

Thomas BrandUniversity of Oldenburg, Oldenburg, Germany

David J. BrownGeoscience Australia, Canberra, Australia, (Provisional TechnicalSecretariat, CTBTO, Vienna International Centre, Vienna,Austria), e-mail: David.Brown@CTBTO.org

John C. BurgessDepartment of Mechanical Engineering, University of Hawaii,2540 Dole Street, Honolulu, HI 968221, USA, e-mail:jcb@hawaii.edu

Paola CampusProvisional Technical Secretariat, CTBTO, Vienna InternationalCentre, Vienna, Austria

Yves CansiCEA/DASE/LDG, BP12, 91680 Bruyeres-le-Châtel, France

Josef ChalupperSiemens Audiological Engineering Group, Gebbertstrasse 125,Erlangen 91058, Germany, e-mail: Josef.Chalupper@siemens.com

N. Ross ChapmanUniversity of Victoria, Victoria BC, Canada

Jakob Christensen-DalsgaardInstitute of Biology, University of Southern Denmark, Campusvej55, DK-5230 Odense M, Denmark, e-mail: jcd@biology.sdu.dk

Peter DanielBruel & Kjær, GmbH, Bremen, Germany

Roger B. DannenbergCarnegie Mellon University, Pittsburgh, PA, USA

Torsten DauTechnical University of Denmark, Lyngby, Denmark, e-mail:tda@elektro.dtu.dk

Contributors xix

Hans-Elias de BreeMicroflown Technologies, The Netherlands, USA

Max DeffenbaughExxonMobil Research and Engineering Company, Annandale,NJ, USA

Thierry DutoitFaculte Polytechnique de Mons, Mons, Belgium

Stephen J. ElliottInstitute of Sound and Vibration Research, Southampton, UK

Paulo A.A. EsquefNokia Institute of Technology, Rod. Torquato Tapajos, 7200,Tarumã 69048-660 Manaus-AM, Brazil, e-mail: paulo@esquef@indt.org.br

Richard R. FayParmly Hearing Institute, Loyola University Chicago, 6525 N.Sheridan Rd., Chicago, IL 60626, USA, e-mail: rfay@luc.edu

Michael FehlerMassachusetts Institute of Technology, Cambridge, USA

Sandy FidellFidell Associates, Inc., Woodland Hills, CA, USA

Petr FirbasProvisional Technical Secretariat, CTBTO, Vienna InternationalCentre, Vienna, Austria (International Atomic Energy Agency,Vienna International Centre, Vienna, Austria)

Erling FrederiksenBruel & Kjær, Sound and Vibration Measurement A/S, Skods-borgvej 307, 2850 Nærum, Denmark

Milton A. GarcesInfrasound Laboratory, University of Hawaii, Manoa, HI, USA,e-mail: milton@isla.hawaii.edu

H.W. GierlichHEAD acoustics GmbH, Herzogenrath, Germany

Norbert GoertzInstitute for Digital Communications, School of Engineering andElectronics, University of Edinburgh, King’s Buildings, MayfieldRoad, Edinburgh EH9 3JL, UK

Masataka GotoNational Institute of Advanced Industrial Science andTechnology (AIST), Tokoyo, Japan

xx Contributors

Philippe GournayUniversite de Sherbrooke, Sherbrooke, QC, Canada

Jørgen HaldBruel & Kjær, Sound & Vibration Measurements A/S, Nærum,Denmark

Joe HammondUniversity of Southampton, Southampton, UK

Colin H. HansenSchool of Mechanical Engineering, University of Adelaide,Adelaide, SA 5005, Australia, e-mail: chanson@mecheng.adelaide.edu.au

Uwe HansenDepartment of Physics, Indiana State University, Terre Haute,IN, USA

Sabih I. HayekDepartment of Engineering Science and Mechanics, UniversityPark, PA 16802, USA

Ulrich HeuteInstitute for Circuit and System Theory, Faculty of Engineering,Christian-Albrecht, University, Kaiserstr. 2, D-24143 Kiel,Germany

Thomas HoffmannProvisional Technical Secretariat, CTBTO, Vienna InternationalCentre, Vienna, Austria

Volker HohmannUniversity of Oldenburg, Oldenburg, Germany

Masaaki HondaWaseda University, Tokyo, Japan

Andrew B. HornerDepartment of Computer Science, Hong Kong University ofScience and Technology, Clear Water Bay, Kowloon, Hong Kong,China, e-mail: horner@cs.ust.hk

Adrianus J.M. HoutsmaAircrew Protection Division, U.S. Army Aeromedical ResearchLaboratory, Fort Rucker, AL 36362-0577, USA, e-mail:adrian.houtsma@amedd.army.mil

Finn JacobsenTechnical University of Denmark, Lyngby, Denmark, e-mail:fja@elektro.dtu.dk

Contributors xxi

Finn B. JensenNATO Undersea Research Centre, La Spezia, Italy, e-mail:jensen@nurc.nato.int

Walter KellermannMultimedia Communications and Signal Processing, UniversityErlanger-Nuremberg, Erlanger, Germany, e-mail: wk@lnt.de

Youngmoo E. KimElectrical & Computer Engineering, Drexel University, Phila-delphia, PA, USA, e-mail: ykim@drexel.edu

Anssi KlapuriInstitute of Signal Processing, Tampere University of Tech-nology, Korkeakoulunkatu 1, 33720 Tampere, Finland, e-mail:Anssi.Klapuri@tut.fi

Birger KollmeierUniversity of Oldenburg, Oldenburg, Germany

Jan Felix KrebberInstitute of Communication Acoustics, Ruhr-University Bochum,Bochum, Germany, e-mail: jan.krebber@rub.de

Christine E. KrohnExxonMobil Upstream Research Company, Houston, TX, USA

Sonoko KuwanoOsaka University, Osaka, Japan

Gerald C. LauchleState College, PA, USA

Walter LauriksKatholieke Universiteit Leuven, Heverlee, Belgium; Labora-torium voor Akoestick on Thermische Fysica, K.U. Leuven,Leuven, Belgium

Alexis Le PichonCEA/DASE/LDG, BP12, 91680 Bruyeres-le-Châtel, France

Philippe LeclaireUniversite de Bourgogne, Nevers, France; Laboratorium voorAkoestick on Thermische Fysica, K.U. Leuven, Leuven, Belgium

Roch LefebvreUniversite de Sherbrooke, Sherbrooke, QC, Canada

Cuiping LiDepartment of Earth and Atmospheric Science, Purdue Univer-sity, West Lafayette IN 47907, USA

xxii Contributors

Tapio LokkiDepartment of Media Technology, Helsinki University ofTechnology, Helsinki, Finland, e-mail: Tapio.Lokki@tkk.fi

Aki Vihtori MakivirtaGenelec Oy, Iisalmi, Finland

Brian H. MarandaDefence Research and Development Canada – Atlantic, Dart-mouth, NS, Canada

James MathewsPCB Piezoelectronics Inc., San Clemente, CA, USA

Manfred MauermannUniversity of Oldenburg, Oldenburg, Germany

Walter MetznerDepartment of Physiological Science, University of California,California, USA

Yasushi MikiComputer Science, Faculty of Engineering, TakushokuUniversity, Tokyo, Japan

Ben MilnerSchool of Computing Sciences, University of East Anglia,Norwich, Norfolk, UK

Riikka MottonenDepartment of Biomedical Engineering and ComputationalScience, Helsinki University of Technology, Helsinki, Finland

Swen MullerNational Institute of Metrology, Xerem, Brazil

Seiichiro NambaOsaka University, Osaka, Japan

Ramesh NeelamaniExxonMobil Upstream Research Company, Houston, TX, USA

David E. NorrisBBN Technologies, 1300 N. 17th St., Arlington, VA 22209, USA

Robert L. NowackDepartment of Earth and Atmospheric Science, PurdueUniversity, West Lafayette, IN 47907, USA

Yasuhiro OikawaWaseda University, Tokyo, Japan

Contributors xxiii

Kazuo OkanoyaLaboratory for Biolinguistics, Brain Science Institute,Riken, 2-1 Hirosawa, Saitama 351-0198, Japan, e-mail:okanoya@brain.riken.jp

John V. OlsonGeophysical Institute, University of Alaska, Fairbanks, USA

Thorkild Find PedersenBruel & Kjær, Sound & Vibration Measurements A/S, Nærum,Denmark

Ville PulkkiDepartment of Signal Processing and Acoustics, HelsinkiUniversity of Technology, Helsinki, Finland, e-mail:ville.pulkki@tkk.fi

Robert B. RandallUniversity of New South Wales, Sydney, Australia

Helmut RiedelUniversity of Oldenburg, Oldenburg, Germany

Francis RumseyInstitute of Sound Recording, University of Surrey, Guildford,UK

Masahiko SakaiOno Sokki Co., Ltd., 1-16-1 Hakusan, Midori-ku, Yokohama, 226-8507 Japan, e-mail: msakai@onosokki.co.jp

Rebecca SaltzerExxonMobil Upstream Research Company, Houston, TX, USA

Mikko SamsDepartment of Biomedical Engineering and ComputationalScience, Helsinki University of Technology, Helsinki, Finland

Lauri SaviojaDepartment of Media Technology, Helsinki University ofTechnology, Helsinki, Finland, e-mail: Lauri.Savioja@tkk.fi

Julius O. SmithCenter for Computer Research in Music and Acoustics(CCRMA), Stanford University, Stanford, CA 94305, USA,website: http://ccrma.stanford.edu/∼jos/

Stefka StefanovaProvisional Technical Secretariat, CTBTO, Vienna InternationalCentre, Vienna, Austria

Edmund J. SullivanEJS Consultants, Portsmouth, RI, USA

xxiv Contributors

David C. SwansonThe Applied Research Laboratory, The Pennsylvania StateUniversity, Philadelphia, PA, USA

Curt A.L. SzuberlaGeophysical Institute, University of Alaska, Fairbanks, USA

Hideki TachibanaInstitute of Industrial Science, University of Tokyo, Tokyo, Japan

Yasushi TakanoDepartment of Mechanical Engineering Research Laboratory,Hitachi, Ltd., Ibaraki, Japan

Ernst TerhardtTechnical University of Munich, Munich. Germany, e-mail:teirhardt@ei.tum.de

Christine ThomasDepartment of Earth and Ocean Sciences, University ofLiverpool, Liverpool, UK

Ippei TorigoeDepartment of Mechanical Engineering and Materials, ScienceFaculty of Engineering Kumamoto University, Kumamoto, Japan

Stefan UppenkampUniversity of Oldenburg, Oldenburg, Germany

Ronald T. Verrillo (deceased)Institute for Sensory Research, Syracuse University, Syracuse,NY 13244, USA

Tuomas VirtanenInstitute of Signal Processing, Tampere University of Technology,Korkeakoulunkatu 1, 33720 Tampere, Finland, e-mail: Tuomas.Virtanen@tut.fi

Stephen VoranInstitute for Telecommunication Sciences, Boulder, CO, USA

Erhard WernerTannenweg 16, D 29693 Hademstorf, Germany

Rodney W. WhitakerLos Alamos National Laboratory, PO Box 1663, Los Alamos, NM87544, USA

Paul WhiteUniversity of Southampton, Southampton, UK

Ru-Shan WuUniversity of California, Santa Cruz, CA, USA

Contributors xxv

Xianyn WuExxonMobil Upstream Research Company, Houston, TX, USA

Ning XiangSchool of Architecture and Department of Electrical, Computer,and Systems Engineering, Rensselaer Polytechnic Institute, Troy,NY 12180, USA, e-mail: xiangn@rpi.edu

Ichiro YamadaAviation Environment Research Center, Airport EnvironmentImprovement Foundation, Tokyo, Japan

Kohei YamamotoKobayasi Institute of Physical Research, Tokyo, Japan

Yoshio YamasakiWaseda University, Tokyo, Japan

Nobutoshi YoshidaOno Sokki Co. Ltd., 1-16-1 Hakusan, Midori-ku, 226-8507Yokohama, Japan, e-mail: yoshi@onosokki.co.jp

Udo ZolzerHelmut Schmidt University, Hamburg, Germany

PART IACOUSTIC SIGNALS

AND SYSTEMSFinn Jacobsen

Technical University of Denmark, Lyngby, Denmark

1 Signals and SystemsJoe Hammond and Paul White . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3Temporal Signal Classification • System Definition and Classification

2 Acoustic Data AcquisitionDavid C. Swanson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17Electronic Noise • Analog-to-Digital Conversion • Anti-aliasing Filters • BasicDigital Signal Calibration • Multichannel System Calibration • Data Validationand Diagnostic Techniques Summary

3 Spectral Analysis and CorrelationRobert B. Randall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33Introduction • The Fourier Transform and Variants • Practical FFT Analysis •Spectral Analysis Using Filters • Correlation Functions • Time–Frequency Analysis

4 The FFT and Tone IdentificationJohn C. Burgess . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53Introduction • The FFT (and DFT) • Leakage • Windows • Estimation ofAmplitude, Frequency, and Phase • Applications

5 Measuring Transfer-Functions and Impulse ResponsesSwen Muller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65Introduction • Measurement Methods • Excitation Signals

2 F. Jacobsen

6 Digital SequencesNing Xiang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87Introduction • Golay Codes • Binary Maximum-Length Sequences • Fast MLSTransform (FMT) • Gold and Kasami Sequences • Legendre Sequences •Application Remarks

7 FiltersOle-Herman Bjor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107Introduction • Frequency Weightings • Octave- and Fractional-Octave-BandpassFilters • Phase Linear Filters • In-Phase/Quadrature Filters • Perceptual Masking Filters

8 Adaptive ProcessingThorkild Find Pedersen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125Introduction • The LMS Algorithm • Adaptive Applications

9 Beamforming and Wavenumber ProcessingJørgen Hald . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131Planar Nearfield Acoustical Holography • Beamforming

1Signals and SystemsJoe Hammond and Paul White

University of Southampton, Southampton, UK

Signal processing is the science of applying transformationsto measurements, to facilitate their use by an observer or acomputer, and digital signal processing (DSP) is the enablingtechnology for applications across all disciplines and sectors.

The study of sound and vibration is highly dependent on theuse of special-purpose signal analysers or software packages. Theaccessibility and convenience of DSP analysis modules and proce-dures can sometimes create a deceptive air of simplicity in oftencomplicated phenomena. It is important that practitioners, whileavailing themselves of the full range of DSP capabilities, shouldhave a clear understanding of the fundamentals of the scienceof signal processing and so be fully aware of the assumptions,implications and limitations inherent in their analysis methods.

Signal processing and analysis involves the three phases of dataacquisition, processing and interpretation (of the results of theprocessing) and, of course, all three are linked in any application.The last phase is naturally very much related to the subject underinvestigation, but the first two may be discussed independentlyof specific applications. A vast body of theory and methodologyhas been built up as a consequence of the problems raised by theneed for data analysis; this is often referred to as “signal analysis”or “time-series analysis” depending on the context [1]. The choiceof methodology is often reliant on some prior knowledge of thephenomenon being analysed. This usually relates to classifyingthe characteristics of the data and/or the way in which the datamay be modelled owing to knowledge of (or assumptions about)the way in which the data may have been generated. This section

4 J. Hammond, P. White

considers signal and system characteristics that underpin signalprocessing.

In acoustics the signal in question is generally the output of apressure transducer. Such a signal is a time history that dependson the spatial location of the transducer. We denote this by p(t,r)where t denotes the time dependence and r is the vector represen-tation for its spatial location (with Cartesian co-ordinates x, y, z).Multiple signals may be available from an array of sensors asrequired, e.g., in beamforming. For the present it is convenientto drop the spatial dependence and consider signals as evolvingwith time.

1 • Temporal Signal ClassificationThe physical phenomenon under investigation is often trans-lated by a transducer into an electrical equivalent, and a singlesignal evolving in continuous time is denoted as x�t�. In manycases, data are discrete owing to some inherent or imposedsampling procedure. In this case the data might be characterisedby a sequence of numbers. When derived from the continuoustime process x�t� we write x�n�� or xn (n = 0�1�2� � � �), wherewe have implied that the sampling interval � is constant (i.e.uniform sampling). The time histories that can occur are oftenvery complex, and it is helpful to consider signals that exhibitparticular characteristics. This allows us to relate appropriateanalysis methods to those specific types of signal.

Figure 1 illustrates a broad categorisation of signal types.A basic distinction is the designation of a signal as “random”

or “deterministic” where by “random” we mean one that is not

FIGURE 1 Classification of signals.

1 • Signals and Systems 5

exactly predictable. Very often, processes are mixed and thedemarcations shown in Figure 1 are not easily applied and conse-quently the analysis procedure to be used may not be apparent.We have included chaotic processes under both “deterministic”and “random” categories since such signals are generated froma deterministic non-linear phenomenon but nevertheless havean output with an unpredictable, random-like behaviour. Theclassification of data as being deterministic or random might bedebatable in many cases and the choice must be made on thebasis of the knowledge of the physical situation. Often signalsmay be modelled as being a mixture of both, e.g. a deterministicsignal “embedded” in unwanted random disturbances (noise).

Many of the classes defined above, such as the stationary andperiodic signals, are mathematical constructs to which no real-world signal can belong. However, these classes do provide onewith a set of models which, in many cases, provide good approx-imations to measured processes and they suggest a suitableanalysis framework.

A brief note for each of the categories is given below –continuous time is used throughout. An analysis method appro-priate for each is also noted.

1.1 Periodic A signal is periodic with period Tp if x�t� = x�t+Tp�.Such a signal can be represented in the frequency domain as a

Fourier series:

x �t� = a0 +�∑

k=1

ak cos �2�kf0t�+bk sin �2�kf0t� =�∑

k=�cke2�ikf0t� (1)

The feature of this is that the frequencies in representation arethe fundamental, f0 = 1/Tp, and multiples (harmonics) (plus a d.c.term), and the coefficients, ak and bk (or ck), give the amplitudeand phase of the components.

Figure 2a shows the time-series of a small section of voicedspeech, the vowel /e/. The approximately periodic character ofthis signal is evident and suggests that it could be gainfullyanalysed by computing its Fourier series representation. ThisFourier series is shown in Figure 2b, which has been computedbased on the first period of the signal shown in Figure 2a. Oneshould appreciate that the assumption of periodicity does nothold exactly for this example, as is commonly the case.

6 J. Hammond, P. White

FIGURE 2 Example of voiced speech: (a) time-series, (b) Fouriercoefficients.

1 • Signals and Systems 7

1.2 Transient A transient signal is one which is essentially localised, i.e. a signalthat has a finite duration. Such a signal has a Fourier integralrepresentation:

x �t� =�∫

−�X �f �e2�iftdf� (2)

This differs from the periodic case in that the frequency rangebecomes a continuum and amplitudes “in a band” are X�f�df soX�f� is now an amplitude density.

Figure 3a shows an example of the time-series of an unvoicedspeech segment, in this case the sound /th/. The lack of a periodicstructure in this signal is apparent. It can be considered as atransient signal and analysed by employing the Fourier transformdefined in (2), which is shown in Figure 3b.

1.3 AlmostPeriodic

This could be regarded as a process where Tp in (1) varies withtime. There is no natural generalisation of (1) for this.

An alternative way of constructing a simple almost periodicprocess is, e.g.,

x �t� = sin �2�t�+ sin(2�

√2t)

� (3)

This process whilst being the sum of two periodic signals is itselfnot periodic because the ratio of the two frequency componentsis not a rational number. In this case using the Fourier integral(2) is appropriate.

Figure 4a shows the time-series of a segment of a sustainedpiano note. These notes contain discrete frequencies that areapproximately harmonically related. The inharmonicities presentin piano string vibrations mean that such signals should beregarded as almost periodic and so the use of the Fouriertransform (2) represents a suitable tool for analysis; the resultsof such an analysis are shown in Figure 4b.

1.4 ChaoticProcess

The range of phenomena that lead to chaotic dynamics iswide, but a feature is that the describing equation is decep-tively simple in its deterministic form, but generates intricatesignals. An example is a second-order non-linear system drivenby a sinusoidal excitation. The methodology of analysis usestopological feature analysis, by which one attempts to reveal theunderlying simple generation mechanism.

8 J. Hammond, P. White

FIGURE 3 Example of unvoiced speech: (a) time-series, (b) magnitude ofthe Fourier transform.