J.V. Candy, R.W. Ziolkowski, a) and D. Kent Lewis. Universityof California, Lawrence Livermore National Laboratory. P.O. Box 5504, L-156, Livermore,.
Transient
wave estimation:
A multichannel
deconvolution
application J.V. Candy,R.W. Ziolkowski, a)andD. KentLewis Universityof California, Lawrence Livermore NationalLaboratory. P.O.Box5504,L-156,Livermore, California94550
(Received6 April 1990;accepted forpublication 27luly 1990)
Theevolution of newconcepts in wavetheoryhaveledto proof-in-principle experiments aimed at validating thegeneration of a specified wavefront.Not onlyhavetheseconcepts initiated research in transientwavetheory,buttheyhavealsocausedrenewedeffortin multichannel signalprocessing. In thispaper,thedevelopment of a processor to deconvolve a transient acoustic wavefromsensor arraymeasurements isdiscussed. Thedesign of themultichannel deconvolver coupled withmodel-based signalprocessing techniques usingacoustic pressure fieldmeasurements isdiscussed. Here,it isshownthatanefficient solution to thisproblem can beobtained usinga vectorformof theLevinson-Wiggins-Robinson (LWR) algorithm. PACS numbers: 43.60.Gk
INTRODUCTION
Signalspropagating in bothspaceandtimearecharacterizedby wavetype phenomenology satisfyingthe scalar waveequation.Typicalsolutionsto thisequationare based onthetheoryof planewavespropagating in a givenmedium. Recently,interesthasbeenkindledin thepossibility of transmittingwaveenergyin spacein nonstandard manners.This interesthad led to the discoveryof pulseswith enhanced localizationandenergyflueneecharacteristics that are transient in nature. From the pioneeringresearchof Brit-
tingham • suggesting thepossibility of solutions to thewave
ily concernedwith enhancingthe signal-to-noiseratio (SNR) andprovidinga reasonable estimateof the transient wave.In orderto accomplish thisgoal,we selecta modelbasedapproach,that is,we developsimplemodels,not only of wave propagation,but alsoof the instrumentationand noise inherent in the acoustic medium and utilize them for
analysisanddesignfrom a signalprocessing perspective. In Sec.I, we discussthe necessary backgroundinformationon transientwaves.Next we discuss the model-based approach to characterizethe experimentin Sec.II andshowhowit is usedto developthe requiredsignalprocessing models.In Sec.III, we developthe multichanneldeconvolverandbriefly discuss the vectorLWR approach.We designandevaluatethe performance of the processor in See.IV andsumma-
equationthat describea focusedtransferof energy,much effort has beendevotedto obtainingtheseclassesof solutions.2-• In thiscontext,wedefinea localizedwave(LW) as rize the results in the final section. a pulsethatexhibitslocalizedtransmission of energy,that is, it canbeviewedasa transientbeamhavinga Gaussian-like centerand low-amplitudetails translatingthroughspace I. BACKGROUND: TRANSIENT WAVES anddeforminglocally.ThusratherthanthetraditionalsoluThepioneering workofBrittingham • firstsuggested the tionsto the waveequationconsisting of planewavesor their possibility of solutions of Maxwell's equations that describe superposition, new classes of solutionshaveevolvedbased energy in onthe LW andtheirsuperpositions. It hasbeendemonstrat- efficient,focusedtransfer of electromagnetic that theseoriginal"foed that the LW transmission of energyis possible in many space.It hasbeenrecentlydiscovered realphysicalsystems, andthat thesesolutionscanberecov- cuswave modes"representGaussianbeamsthat translate andareanother eredapproximately fromanarray(seeZiolkowski6). These throughspacewith onlylocaldeformations transientwaveshavea vastnumberof potentialapplications includingmicroscopes and telescopes with extremelylarge depthsof field,low-losspowertransmission, securecommunications,remotesensing,and directedenergyweaponsexplainingthe wide rangeof military and industrialinterest. Here, we areconcernedwith the processing of a specific classof thetransientsolutionsto thewaveequation--thesocalledmodifiedpowerspectrum(MPS) pulse.Our goalisto developsignalprocessing techniques to estimatethepulseat the sourcelocationin order to validateits generation.This problem is complicatedbecausethis pulseis a transientin bothtime andspaceleadingto a broadbandresponse in both thespatialandtemporalfrequencydomains.We are primary)Presentaddress: Dept.of Elec.and ComputerEng., Univ. of Arizona, Tuscon, AZ 85721.
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J. Acoust.Sec. Am.88 (5), November1990
fundamental set of modes from which classes of solutions of
the scalarwaveequationcanbe constructed.In thissection, we briefly discussthe MPS pulse---ourparticular transient waveof interest.In particular,assuminga solution
