Wavelets and Wavelet Transform Systems and Their Applications - A Digital Signal Processing Approach

657 Pages·2022·28.97 MB·english

by  Cajetan M. Akujuobi

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
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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
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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.
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