Table Of ContentApplied and Numerical Harmonic Analysis
Serge Dos Santos
Mostafa Maslouhi
Kasso A. Okoudjou
Editors
Recent Advances
in Mathematics
and Technology
Proceedings of the First International
Conference on Technology,
Engineering, and Mathematics,
Kenitra, Morocco, March 26-27, 2018
Applied and Numerical Harmonic Analysis
SeriesEditor
JohnJ.Benedetto
UniversityofMaryland
CollegePark,MD,USA
AdvisoryEditors
AkramAldroubi GittaKutyniok
VanderbiltUniversity TechnicalUniversityofBerlin
Nashville,TN,USA Berlin,Germany
DouglasCochran MauroMaggioni
ArizonaStateUniversity JohnsHopkinsUniversity
Phoenix,AZ,USA Baltimore,MD,USA
HansG.Feichtinger ZuoweiShen
UniversityofVienna NationalUniversityofSingapore
Vienna,Austria Singapore,Singapore
ChristopherHeil ThomasStrohmer
GeorgiaInstituteofTechnology UniversityofCalifornia
Atlanta,GA,USA Davis,CA,USA
StéphaneJaffard YangWang
UniversityofParisXII HongKongUniversityof
Paris,France Science&Technology
Kowloon,HongKong
JelenaKovacˇevic´
CarnegieMellonUniversity
Pittsburgh,PA,USA
Moreinformationaboutthisseriesathttp://www.springer.com/series/4968
Serge Dos Santos • Mostafa Maslouhi
Kasso A. Okoudjou
Editors
Recent Advances in
Mathematics and Technology
Proceedings of the First International
Conference on Technology, Engineering,
and Mathematics, Kenitra, Morocco,
March 26-27, 2018
Editors
SergeDosSantos MostafaMaslouhi
InstitutNationaldesSciencesAppliquées Informatics,LogisticsandMathematics
CentreValdeLoire UniversitéIbn-Tofail
Blois,France Kenitra,Morocco
KassoA.Okoudjou
NorbertWienerCenter
DepartmentofMathematics
UniversityofMaryland
CollegePark,MD,USA
ISSN2296-5009 ISSN2296-5017 (electronic)
AppliedandNumericalHarmonicAnalysis
ISBN978-3-030-35201-1 ISBN978-3-030-35202-8 (eBook)
https://doi.org/10.1007/978-3-030-35202-8
MathematicsSubjectClassification:42B10,37Mxx,82-06
©SpringerNatureSwitzerlandAG2020
Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof
thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,
broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation
storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology
nowknownorhereafterdeveloped.
Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication
doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant
protectivelawsandregulationsandthereforefreeforgeneraluse.
Thepublisher,theauthors,andtheeditorsaresafetoassumethattheadviceandinformationinthisbook
arebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor
theeditorsgiveawarranty,expressedorimplied,withrespecttothematerialcontainedhereinorforany
errorsoromissionsthatmayhavebeenmade.Thepublisherremainsneutralwithregardtojurisdictional
claimsinpublishedmapsandinstitutionalaffiliations.
This book is published under the imprint Birkhäuser, www.birkhauser-science.com by the registered
companySpringerNatureSwitzerlandAG.
Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland
Thisbookisdedicatedtotheauthors’
children:
Youssef,Mariam,andMouadMaslouhi;
Shadeh,Shola,andFemiOkoudjou;
Lauryne,Maëlys,Lazare,andAlcideDos
Santos.
ANHA Series Preface
The Applied and Numerical Harmonic Analysis (ANHA) book series aims to
providetheengineering,mathematical,andscientificcommunitieswithsignificant
developments in harmonic analysis, ranging from abstract harmonic analysis to
basic applications. The title of the series reflects the importance of applications
and numerical implementation, but richness and relevance of applications and
implementation depend fundamentally on the structure and depth of theoretical
underpinnings. Thus, from our point of view, the interleaving of theory and
applicationsandtheircreativesymbioticevolutionisaxiomatic.
Harmonicanalysisisawellspringofideasandapplicabilitythathasflourished,
developed, and deepened over time within many disciplines and by means of
creative cross-fertilization with diverse areas. The intricate and fundamental
relationshipbetweenharmonicanalysisandfieldssuchassignalprocessing,partial
differentialequations(PDEs),andimageprocessingisreflectedinourstate-of-the-
artANHAseries.
Our vision of modern harmonic analysis includes mathematical areas such as
wavelettheory,Banachalgebras,classicalFourieranalysis,time-frequencyanalysis,
andfractalgeometry,aswellasthediversetopicsthatimpingeonthem.
Forexample,wavelettheorycanbeconsideredanappropriatetooltodealwith
some basic problems in digital signal processing, speech and image processing,
geophysics, pattern recognition, biomedical engineering, and turbulence. These
areas implement the latest technology from sampling methods on surfaces to fast
algorithms and computer vision methods. The underlying mathematics of wavelet
theorydependsnotonlyonclassicalFourieranalysis,butalsoonideasfromabstract
harmonicanalysis,includingvonNeumannalgebrasandtheaffinegroup.Thisleads
toastudyoftheHeisenberggroupanditsrelationshiptoGaborsystems,andofthe
metaplectic group for a meaningful interaction of signal decomposition methods.
Theunifyinginfluenceofwavelettheoryintheaforementionedtopicsillustratesthe
justification for providing a means for centralizing and disseminating information
fromthebroader,butstillfocused,areaofharmonicanalysis.Thiswillbeakeyrole
of ANHA. We intend to publish with the scope and interaction that such a host of
issuesdemands.
vii
viii ANHASeriesPreface
Alongwithourcommitmenttopublishmathematicallysignificantworksatthe
frontiersofharmonicanalysis,wehaveacomparablystrongcommitmenttopublish
majoradvancesinthefollowingapplicabletopicsinwhichharmonicanalysisplays
asubstantialrole:
Antennatheory Predictiontheory
Biomedicalsignalprocessing Radarapplications
Digitalsignalprocessing Samplingtheory
Fastalgorithms Spectralestimation
Gabortheoryandapplications Speechprocessing
Imageprocessing Time-frequencyand
Numericalpartialdifferentialequations time-scaleanalysis
Wavelettheory
TheabovepointofviewfortheANHAbookseriesisinspiredbythehistoryof
Fourieranalysisitself,whosetentaclesreachintosomanyfields.
In the last two centuries Fourier analysis has had a major impact on the
development of mathematics, on the understanding of many engineering and
scientificphenomena,andonthesolutionofsomeofthemostimportantproblems
in mathematics and the sciences. Historically, Fourier series were developed in
the analysis of some of the classical PDEs of mathematical physics; these series
were used to solve such equations. In order to understand Fourier series and the
kindsofsolutionstheycouldrepresent,someofthemostbasicnotionsofanalysis
were defined, e.g., the concept of “function.” Since the coefficients of Fourier
seriesareintegrals,itisnosurprisethatRiemannintegralswereconceivedtodeal
with uniqueness properties of trigonometric series. Cantor’s set theory was also
developedbecauseofsuchuniquenessquestions.
A basic problem in Fourier analysis is to show how complicated phenomena,
suchassoundwaves,canbedescribedintermsofelementaryharmonics.Thereare
twoaspectsofthisproblem:first,tofind,orevendefineproperly,theharmonicsor
spectrumofagivenphenomenon,e.g.,thespectroscopyprobleminoptics;second,
todeterminewhichphenomenacanbeconstructedfromgivenclassesofharmonics,
asdone,forexample,bythemechanicalsynthesizersintidalanalysis.
Fourieranalysisisalsothenaturalsettingformanyotherproblemsinengineer-
ing, mathematics, and the sciences. For example, Wiener’s Tauberian theorem in
Fourieranalysisnotonlycharacterizesthebehavioroftheprimenumbers,butalso
provides the proper notion of spectrum for phenomena such as white light; this
latter process leads tothe Fourier analysis associated withcorrelation functions in
filtering and prediction problems, and these problems, in turn, deal naturally with
Hardyspacesinthetheoryofcomplexvariables.
Nowadays, some of the theory of PDEs has given way to the study of Fourier
integral operators. Problems in antenna theory are studied in terms of unimodular
trigonometric polynomials. Applications of Fourier analysis abound in signal
processing, whether with the fast Fourier transform (FFT), or filter design, or the
ANHASeriesPreface ix
adaptivemodelinginherentintime-frequency-scalemethodssuchaswavelettheory.
The coherent states of mathematical physics are translated and modulated Fourier
transforms, and these are used, in conjunction with the uncertainty principle, for
dealing with signal reconstruction in communications theory. We are back to the
raisond’êtreoftheANHAseries!
UniversityofMaryland JohnJ.Benedetto
CollegePark SeriesEditor
Preface
One of the impacts of the trifecta Technology, Engineering, and Mathematics
(TEM)onourdailylifeistheenormousamountofdatawegenerate.Forexample,
Technology and Engineering are increasingly becoming the main source of “big
data”production.Toanalyze,organize,process,andactuponthesedata,researchers
inbothacademiaandindustryaredevisingnewparadigms.Theseincludepowerful
machinelearningalgorithms,especiallydeeplearningmodelssuchasconvolutional
neural networks (CNNs), which have recently achieved outstanding predictive
performance in a wide range of multimedia applications, including visual object
classification, scene understanding, speech recognition, and activity prediction.
Many of these new applications are generally based on advances in mathematics,
and particularly, mathematical modeling, optimization, numerical analysis and
simulations,mathematicalsignalprocessing,andcomputersciences.
From the modern engineering point of view, the forthcoming digital trans-
formation also triggers opportunities in new and growing fields including big
dataanalytics,artificialintelligence,automation,andimaging.Advancesindigital
technologiesforindustrieslikeaugmentedreality,virtualreality,andmixedreality
willalsoseevaluablechangesanddevelopmentsineducationandtrainingdelivery
usingmodernmathematics.
Toofferaforumforresearchersworkinginthesefieldstodiscusstheadvances
and the challenges created by these new paradigms, the first edition of the
Technology, Engineering and Mathematics Conference (TEM18) was organized,
March26and27,2018,inKenitra,Morocco(seehttp://ensa.uit.ac.ma/tem2018/for
moredetails).Itbroughttogetheragroupofrenownedresearchersandprofessionals
both from academia and industries who presented their work on topics that were
thematicallydividedasfollows:
(cid:129) BigDataAnalyticsandApplications
(cid:129) Biomathematics
(cid:129) ComputerEngineeringandApplications
(cid:129) EconomicsandFinancialEngineering
(cid:129) HarmonicAnalysis
xi
