Wavelets and Wavelet Transform Systems and Their Applications - A Digital Signal Processing Approach PDF
Preview Wavelets and Wavelet Transform Systems and Their Applications - A Digital Signal Processing Approach
Cajetan M. Akujuobi Wavelets and Wavelet Transform Systems and Their Applications A Digital Signal Processing Approach Wavelets and Wavelet Transform Systems and Their Applications Cajetan M. Akujuobi Wavelets and Wavelet Transform Systems and Their Applications A Digital Signal Processing Approach CajetanM.Akujuobi PrairieViewA&MUniversity PrairieView,TX,USA Solutionmanualcanbedownloadedathttps://link.springer.com/book/9783030875275 ISBN978-3-030-87527-5 ISBN978-3-030-87528-2 (eBook) https://doi.org/10.1007/978-3-030-87528-2 ©SpringerNatureSwitzerlandAG2022 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartofthe materialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. The publisher, the authors and the editors are safe to assume that the advice and information in this bookarebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor theeditorsgiveawarranty,expressedorimplied,withrespecttothematerialcontainedhereinorforany errorsoromissionsthatmayhavebeenmade.Thepublisherremainsneutralwithregardtojurisdictional claimsinpublishedmapsandinstitutionalaffiliations. ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Dedicated to my family: My Wife Caroline and my Children Obinna and Chijioke. I also dedicate this book to all my students, particularly all of my many master’s and doctoral students from all over the world. Preface Overview Thisbookisallaboutwavelets,wavelettransforms,andhowtheycanbeappliedto solve problems in different fields of study. The question asked often is, what are wavelets?Theanswer isthat wavelets arewaveforms oflimitedduration thathave average values of zero. In comparison to sinusoids, wavelets do have a beginning and an end, while sinusoids theoretically extend from minus to plus infinity. Sinusoidsaresmoothandpredictableandaregoodatdescribingconstantfrequency which otherwise can be called stationary signals. In the case of wavelets, they are irregular,oflimitedduration,andoftennon-symmetrical.Theyarebetteratdescrib- inganomalies,pulses,andothereventsthatstartandstopwithinthesignal. Thisbookonwaveletsandwavelettransformsystemsandtheirapplicationshas grown out of my teaching “Wavelets and Their Applications” graduate course and my research activities in the fields of digital signal processing and communication systemsformanydecades.Thenotesonwhichthisbookisbasedonhavebeenused foraone-semestergraduatecourseentitled“WaveletsandTheirApplications”thatI have taught for several decades at Prairie View A & M University. The book chapters have increased to 21 because of additional new materials considered and therefore can be used for a two-semester course as well. The materials have been updatedcontinuouslybecause ofactiveresearchintheapplicationofwaveletsand wavelettransformstoseveralareasofscienceandengineeringandlotsofresearch withmygraduatestudentsintheareasofwaveletapplications. WeliveintheInformationAgewhereinformationisanalyzed,synthetized,and storedatamuchfasterrateusingdifferenttechniquessuchasdifferentwaveletsand wavelet transforms. For many decades, wavelets and wavelet transforms have receivedmuchattentionintheliteratureofmanycommunitiesintheareasofscience and engineering. There are different types of wavelets. These wavelets are used as analyzing tools by pure mathematicians (in harmonic analysis, for the study of vii viii Preface Calderon-Zygmundoperators),bystatisticians(innonparametricestimation),andby electricalengineers(insignalanalysis). In physics, wavelets are used because of their applications to time-frequency or phase-space analysis and their renormalization concepts. In computer vision research, wavelets are used for "scale-space" methods. In stochastic processes, they are used in application of self-similar processes. Because of wavelets and wavelet transforms’ connections with multirate filtering, quadrature mirror filters, and sub-band coding, they have found home in the digital signal processing com- munity. The image processing community uses wavelets because of their applica- tions in pyramidal image representation and compression. In harmonic analysis, wavelets are used because of the special properties of wavelet bases, while the speechprocessingcommunityuseswavelets becauseoftheirefficientsignalrepre- sentation,eventextraction,andthemimickingofthehumanauditorysystem. Mostimportantly,waveletanalysistoolscanbeusedasanadaptableexchangeto Fourier transform analysis and representation. While there may be many books written over the past decades in the area of wavelets, it is hard to find a wavelet book that is not heavily into rigorous mathematical equations, and in most cases, little or no real applications. In addition, most of the books are not written as textbooks for classroom teaching and to make students understand what wavelets areandhowtoapplythemtosolvingsocietalproblems. Inthisbook,itisverysimplifiedtorealapplicationsinsolvingsocietalproblems. Itisnotburiedintorigorousmathematicalformulas.Thebookisverysuitableasa textbook for upper-level undergraduate study and graduate studies. The practicing engineersinindustrywillfindthebookveryuseful.Notonlycanthebookbeused for training of future digital signal processing engineers, it can also be used in research, developing efficient and faster computational algorithms for different multi-disciplinary applications. Engineering and scientific professionals can use thisbookintheirresearchandwork-relatedactivities. In actuality, wavelets provide a common link between mathematicians and engineers.Topicssuchasdecompositionandreconstructionalgorithms,subdivision algorithms, fast numerical computations, frames, time-frequency localizations, and continuous- and discrete-wavelet transforms are covered for their use of wavelets and wavelet transforms. In addition, topics such as fractals and fractal transforms, mixed signal systems, sub-band coding, image compression, real-time filtering, radar applications, transient analysis, medical imaging, segmentation, blockchain systems, information security, and vibration in aeroelastic systems are some of the areas covered in the book. Applications of many of these wavelets and wavelet transformanalysesaredevelopedacrossdisciplinesinthebook.Thisbook,entitled WaveletsandWaveletTransformAnalysisandApplications:ASignalProcessing Approach isaunique bookbecause ofitsin-depthtreatmentoftheapplications of wavelets and wavelet transforms in many areas across many disciplines. The book doesthisinaverysimplifiedandunderstandablemannerwithoutthemathematical rigor that scares many people away from the field. It uses lots of diagrams to illustrate points being discussed. In addition, the concepts introduced in the book arereinforcedwithreviewquestionsandproblems.MATLABcodesandalgorithms Preface ix are introduced in the book to give readers hands-on experience. As a disclaimer, becausesomeofthecodeswerewrittenindifferenttimesbasedondifferentversions ofMATLAB,it isanticipated thatthecodes may needrevisions beforethey canbe adapted to the recent versions of MATLAB. The readers are encouraged to do whateverrevisionstheydeemnecessaryfortheirwork. Asevidentfrom theoutline,thebookisdividedintoseven parts.It beginswith thefundamentalconceptsofwavelets, wavelet transform,andFouriertransformin Chapter 1. The areas of similarities and dissimilarities are also discussed. Part 1 discusses wavelets, wavelet transforms, generations of wavelets, and similarities between wavelets and fractals. Part 2 deals with wavelets and wavelet transform applications to mixed signal systems. Part 3 addresses wavelets and wavelet trans- formapplicationtocompression.Part4exploreswaveletsandwavelettransformsto medical applications. Part 5 covers wavelet and wavelet transform application to segmentation.Part6discusseswaveletandwavelettransformapplicationtocyber- security systems. Part 7 deals with wavelet and wavelet transform application to detection,identification,discrimination,andestimation. InChap.2,wedescribewhatwaveletsareandwhywedolookatwavelets.We describe 19 different types of wavelets with illustrations of how they can be represented.ThegenerationsofwaveletsarediscussedinChap.3.Thesegenerations ofwavelets arealso compared. Thedifferentdimensionsofwavelettransforms are discussed in Chap. 4. These include the one and two dimensions of wavelet trans- forms.ThesimilaritiesbetweenwaveletsandfractalsarediscussedinChap.5.The test point selection using wavelet transformation for digital-to-analog converters (DACs) is discussed in Chap. 6 while in Chap. 7, we discuss the wavelet-based dynamictestingofanalog-to-digitalconverters(ADCs).InChap.8,wediscussthe wavelet-basedstatictestingofADCs.Themixedsignalsystemstestingautomation usingdiscretewavelettransform–basedtechniquesarediscussedinChap.9. In Chap. 10, we discuss wavelet-based compression using nonorthogonal and orthogonally compensated W-Matrices. Wavelet-based application to image and data compression is discussed in Chap. 11 while the application of wavelets to video compression is discussed in Chap. 12. We explore wavelet application to electrocardiogram(ECG)medicalsignalinChap.13.Theapplicationofwaveletsto image segmentation is covered in Chap. 14 while the hybrid wavelet and fractal- basedsegmentationiscoveredinChap.15.Wecoverwavelet-basedapplicationto information security in Chap. 16 and the application of wavelets to biometrics in Chap.17.Theemergingapplicationofwaveletstoblockchaintechnologysystemsis covered in Chap. 18. We discuss wavelet-based signal detection, identification, discrimination, and estimation in Chap. 19. In Chap. 20, we cover wavelet-based identification, discrimination, detection, and parameter estimation of radar signals. Theapplicationofwaveletstovibrationdetectioninanaeroelasticsystemiscovered inChap.21. Theprerequisitefortakingthecourseisseniororgraduatelevelstandingaccom- panied by background in digital signal processing, communication systems, and mathematical sciences, with a basic knowledge of linear algebra and vector space. The book can be used in giving short and long seminars on wavelets and wavelet x Preface transform applications. In addition, it may serve as a reference for engineers and researchersincommunicationsystems,digitalsignalprocessing,andotherscientific disciplines. There is a solution manual prepared for this book which will be very helpfultoprofessorswhohaveadoptedthisbookfortheirclasses. Acknowledgments InthemanydecadesthatIhavetaught“WaveletsandTheirApplications”anddone research-using wavelets and wavelet transforms, I have taught many students and havesupervisedmanyundergraduate,master’s,anddoctoralstudents.Ithankeach and everyone of these students for their contributions. My specialthanks go to the followingformerstudentsandcurrentstudentsofmine:LanHu,CarySmith,Emad Awada,ShumonAlam,EhijeleUnuigbe,BrandeeRogers,JaymarsT.Davis,Basil A. Kandah, Nana K. Ampah, Jie Shen, Dexin Zhang, Ben Franklin, Olusegun Odejide, Michael C. Ndinechi, Collins Acheampong; Dan Sims, Jr., Midge Hill, JamesSpain,AshleyKelsey,KhalidFerdous,AugustineAjuzie,Omonowo(David) Momoh, Kelechi Eze, Pankaj Chhetri, Emmanuel Okereke, Faith Nwokoma, Shemar Hunter, Odinaka Ekwonnah, Qamiyon Marshall, Bernice Hoedzoade, and manyothers.IthankeverystudentwhohastakenmyELEG6333WaveletandTheir Applications Course at Prairie View A&M University. They have all made me a betterteacherandabetterresearcherdoingworkusingwavelets.Theencouragement andsupportofallmystudentshavemadeitpossibleformetowritethisbook.The numerousresearchworksmanyofthemdidwithmehavehelpedmeinwritingthis book,andIsincerelythankeachofthem. Ithankallofmysponsorsoverthesemanydecadesincluding,TexasInstruments, Sprint Corporation, LL3-Communications, Litton Advanced Space Systems, Nor- throp Grumman, National Science Foundation, Los Alamos National Laboratory, Argonne National Laboratory, U.S. Department of Education, U.S. Department of Defense, NASA, Lockheed Martin, and many others for supporting my work over these many years. My students and I benefited a lot from the support. This book would not have been possible without this support. I specially thank some of the members of the Mathematics and Computer Science Division (MCS) at Argonne National Laboratory. These are Man Kam Kwong, Sohail Zafar, Biqun Lin, and WilliamsReynolds.Specialthanks goestoManKamKwong for histotalsupport, collaboration, and guidance in the W-Matrices project. The Argonne Division of Educational Programs administered the program with funding provided by the U.- S.DepartmentofEnergy. xi
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