Digital Audio Processing Fundamentals PDF
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Springer Topics in Signal Processing Aurelio Uncini Digital Audio Processing Fundamentals Springer Topics in Signal Processing Volume 21 SeriesEditors JacobBenesty,INRS-EMT,UniversityofQuebec,Montreal,QC,Canada WalterKellermann,Erlangen-Nürnberg,Friedrich-Alexander-Universität, Erlangen,Germany The aim of the Springer Topics in Signal Processing series is to publish very high quality theoretical works, new developments, and advances in the field of signal processingresearch.Importantapplicationsofsignalprocessingarecoveredaswell. Withinthescopeoftheseriesaretextbooks,monographs,andeditedbooks. Topicsincludebutarenotlimitedto: *Audio&AcousticSignalProcessing *BiomedicalSignal&ImageProcessing *Design&ImplementationofSignalProcessing *GraphTheory&SignalProcessing *IndustrialSignalProcessing *MachineLearningforSignalProcessing *MultimediaSignalProcessing *QuantumSignalProcessing *RemoteSensing&SignalProcessing *SensorArray&MultichannelSignalProcessing *SignalProcessingforBigData *SignalProcessingforCommunication&Networking *SignalProcessingforCyberSecurity *SignalProcessingforEducation *SignalProcessingforSmartSystems *SignalProcessingImplementation *SignalProcessingTheory&Methods *Spokenlanguageprocessing **Indexing:ThebooksofthisseriesareindexedinScopusandzbMATH** Aurelio Uncini Digital Audio Processing Fundamentals AurelioUncini DIET SapienzaUniversityofRome Rome,Italy ISSN 1866-2609 ISSN 1866-2617 (electronic) SpringerTopicsinSignalProcessing ISBN 978-3-031-14227-7 ISBN 978-3-031-14228-4 (eBook) https://doi.org/10.1007/978-3-031-14228-4 ©TheEditor(s)(ifapplicable)andTheAuthor(s),underexclusivelicensetoSpringerNature SwitzerlandAG2022 Thisworkissubjecttocopyright.AllrightsaresolelyandexclusivelylicensedbythePublisher,whether thewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,reuse ofillustrations,recitation,broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,and transmissionorinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilar ordissimilarmethodologynowknownorhereafterdeveloped. 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ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Preface The recent evolution in the field of information and communication technologies (ICT) has made possible many innovative ways in the use of voice, music, audio- visual, multimedia and, in general, multimodal information. In the case of music, forexample,theimpactoftoday’stechnologiesiscomparabletowhatthepresshas had on literary work: in the world of the arts, music is, in fact, among those that mostintimatelycomparesitselfwiththemeansthatscienceandthetechniquemake available. Inthiscontext,deeplylinkedtotheworldofmultimediaandmultimodalcommu- nication,inthevolume“DigitalAudioProcessingFundamentals,”weintendtofocus onsomeaspectsthatcharacterizethebinomialsaudio-technologyandengineering music.Themethodsofdigitalmanipulationofsounds,thestudyofartificialspaces andaudioeffectsformusicaluse,themethodsandtechniquesfordigitalsynthesis ofthemusicalsignal,signalcompression,soundspatialization,virtualaudioarejust someconcretetechnicalexamples. Inmore recenttimes,thecollaboration between scientistsfromICT,communi- cation sciences, modeling and acoustic physics has led to the emergence of new disciplines such as the science of auditory communication, whose salient aspects range from the computational analysis of the auditory scene, the study of multi- modalhuman–computerinterface,augmentedrealitysystems,audioforvirtualenvi- ronmentsandsoon.Themedium,infact,doesnotsimplycoincidewiththetech- nicaltransmission–receptionapparatus,butconsistsofacomplexsystemwhich,in additiontothetechnologicalapparatus,impliestherelationshipbetweenthisappa- ratusandtheperceptualandcognitiveprocessesofman;inthiscontext,thesound information,vocal,non-vocal,musical,etc.,takesonaroleofprimaryimportance. Theinterestindigitalaudiosignalprocessinganditsspin-offsinvariousmanu- facturingsectors,aswellasthecross-cuttingskillsneeded,areverybroad.Thebasic disciplinestoaddressnotsuperficiallysuchtopicsinarehardlycoveredinthecore coursesofasingledegreeprogram. This text, born from twenty-five years of teaching experience of the author in thecourseofDigitalAudioSignalProcessing,heldattheUniversityofRome“La Sapienza”—Italy,forstudentsofdegreecoursesinEngineering,isatransversaland v vi Preface interdisciplinarywork,mainlydedicatedtothevariousspecializationsofcomputer science, communications but also others such as electronics, mechanics and other courseswherethereareofteninterestsindigitalaudiosignalprocessing. Theworkprovidesanoverviewanddidacticallyconsistentoftheproblemsrelated to the processing of the audio signal in its various aspects, from the numerical modeling of vibrating systems to the circuits and algorithms for manipulation and generationofsoundsignals. The topics covered, while requiring strong interdisciplinary skills, acoustics, mechanical, electrical and computer science, are developed in a self-contained fashion,usingamathematicsthatshouldbeknownfrompreviouscoursesinthefirst two years of science faculties. The two volumes, while complementary in subject matter,areautonomousandself-containedworks ThefirstvolumeDigitalAudioProcessingFundamentalsisorganizedconceptu- allyintothreeparts. The first introductory part consists of two chapters, where the fundamental concepts of vibration mechanics, and the various modes of possible generation of soundwavesarereported.Linearandnonlinearvibrationmodelsincontinuousand discretesystemsareintroduced.Thecircuitanalogiesofmobilityandimpedanceare introduced, and the concepts of sound waves in air and the electro-acoustic trans- ducersarebrieflyrecalled.Alsointhefirstpart,discrete-timecircuitmodelsandbasic methodologiesforone-andmulti-dimensionalnumericalfilteringareintroduced. The central part deals specifically with audio signal processing methodologies. Filtersforaudio,multiratesystemsandwavelettransformsareintroduced,so-called specialtransferfunctionsforaudioapplicationsarediscussed,andcircuitmodeling methodsforphysicalmodelingofcomplexacousticphenomenawithbothlumped anddistributedparametersarediscussed. Inthethirdpart,theso-calledaudioeffectsareintroduced,suchasreverberators, dynamic range control of the audio signal, effects based on time–frequency trans- formations.Inthelasttwochapters,abstractsoundsynthesismethodsandphysical modelingareintroducedanddiscussed. Rome,Italy AurelioUncini July2022 Acknowledgments Many friends and colleagues have contributed to the creation of this book by providing useful suggestions, rereading drafts or endorsing my ruminations on the subject. I would like to thank my colleagues Stefania Colonnese, Danilo Comminiello, Massimo Panella, Raffaele Parisi, Simone Scardapane and Michele ScarpinitioftheDepartmentofInformationEngineering,ElectronicsandTelecom- municationsoftheUniversitàdegliStudidiRoma—“LaSapienza,”Italy;Giovanni Costantini of the Università degli Studi di Roma—“Tor Vergata,” Italy; Stefania Cecchi,oftheUniversitàPolitecnicadelleMarche,Ancona,Italy. I would also like to thank all the students who provided me with very useful verificationsforthecorrectexpositionofthetopicsinthetext. vii Contents 1 VibratingSystems .............................................. 1 1.1 Introduction .............................................. 1 1.2 VibratingSystemsinOneDimension ......................... 1 1.2.1 SimpleHarmonicMotion ........................... 2 1.2.2 DampedHarmonicOscillator ........................ 5 1.2.3 PhasorRelatedtoQuantitiesx,vanda ............... 9 1.3 ForcedOscillations ........................................ 10 1.3.1 Transfer Function, Frequency, and Impulse Responses ........................................ 11 1.3.2 TransientandSteady-StateResponse ................. 15 1.3.3 SinusoidalResponse,MobilityandImpedance ......... 16 1.3.4 CalculationofCompleteResponse ................... 18 1.3.5 GenericHelmholtzOscillatingSystems ............... 18 1.4 ElectricalCircuitAnalogies ................................. 21 1.4.1 KirchhoffLaws .................................... 22 1.4.2 AnalogyofMobility ............................... 23 1.4.3 AnalogyofImpedance .............................. 26 1.5 NonlinearOscillatingSystems .............................. 27 1.5.1 GeneralNotationandStateSpaceRepresentation ....... 27 1.5.2 2nd-OrderNonlinearOscillatingSystems ............. 31 1.5.3 UndampedPendulum ............................... 32 1.5.4 VanDerPolandRayleighOscillators ................. 35 1.5.5 DuffingNonlinearOscillator ........................ 38 1.5.6 MusicalInstrumentasaSelf-sustainedOscillator ....... 42 1.5.7 MultimodalNonlinearOscillator ..................... 47 1.6 ContinuousVibratingSystems .............................. 47 1.6.1 IdealStringWaveEquation .......................... 48 1.6.2 SolutionoftheStringWaveEquation ................. 50 1.6.3 StringsVibrationandMusicalScales ................. 60 1.6.4 LossyandDispersiveString ......................... 65 1.6.5 TheVibrationofMembranes ........................ 71 ix
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