超声无损检测中的二维快速Fourier变换及Wigner-Ville变换

FourierWigner2Ville,(,200092):Fourier(2DFFT)WignerWigner2Ville,:;;:TG115.28+5;G202:A:100026656(2001)0720313204TWO2DIMENSIONALFASTFOURIERTRANSFORMANDWIGNER2VILLETRANSFORMINULTRASONICNONDESTRUCTIVETESTINGTADe2an,LIUZhen2qing(InstituteofAcoustics,TongjiUniversity,Shanghai200092,China)Abstract:Adescriptionon2DfastFouriertransform(FFT)andWigner2Villetransform,aswellastheirapplicationinultra2sonicnondestructivetestingisgiven.Theadvantagesanddisadvantagesofthemethodsareillustratedandanalysed.Keywords:Ultrasonictesting;Fouriertransform;Signalprocessing(NDT),,,,,;,,,,,(,;),Fourier(2DFFT)Wign2er2Ville:2001203226:(19604010)1FourierNDTx,U(x,t)U(x,t)=A()ei(kx-t-)(1)A()=2fkk=/CpCp(1)(),,Fourier(1)FFT,H(k,f)=kU(x,t)e-i(kx+t)dxdt(2)31323720017NDTVol.23No.7July2001©1995-2004TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.FFT,FFTNDT,[1]FFT,NDT1a125mm3mm,a0,,(a0),;FFT1b1MHz,,,1b,,,,a0a1,FFT,1,,Alleyne[2,3]FFT,,(a)(b)1FFT,FFT2a3mma0,115mm,2bFFT2b,a0,a1s0,FFT(a)(b)21.5mmFFTFFTLamb[3,4]2,,Lamb,FFT,223a3mma1[1],3b22,3aFFT,a1,s0s1,;a1,1MHz,,s01MHz,s1,Lamb,413:FourierWigner2Ville©1995-2004TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.(a)(b)3a1FFT,FFTLamb,,FFT,,;,Fourier2,,2,,Wigner2Ville2Wigner2VilleNDTWigner1932(Wigner),,Wigner;(1993Jeon),WignerFourier1/4,Wigner,1948Ville,Nyquist,2Wigner2Ville(Wigner2Ville)s(t),2W(t,)[5]W(t,)=12me-j(t+-)(,)s3-12s+12ddd(3)s3s(t)2(,),2Wigner2Ville,1,(3)W(t,)=12s3t-12st+12e-jd(4)W(mt,kt)=2t2N-1n=0s[(m+n)t]s3[(m-n)t]e-ink/N(5)tNMalik[6],,(4a)4bWigner2Ville,,Wigner2VilleWigner2Ville,,Wigner2Ville;,NDT,,Wigner2Ville,,[7],GaussG(t,)Wigner2Ville,Wigner2Ville,,2,;513:FourierWigner2Ville©1995-2004TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.(a)(b)4Wigner2Ville3,,,FFTWignerWigner2VilleNDT,,FFT,,,FFT,Wigner2Ville,,,NDT,,Wigner2Ville,,NDT,,:[1].[J].,1999,21(9):409-413.[2]AlleyneDN,CawleyP.OptimizationofLambwaveinspec2tiontechniques[J].NDT&EInt,1992,25(1):11-22.[3]AlleyneDN,CawleyP.Atwo2dimensionalFouriertransformmethodforthemeasurementofpropagatingmultimodesignals[J].JAcoustSocAm,1991,89(3):1159-1168.[4],.[J].,2000,19(4):212-214.[5]CohenL.Time2frequencydistributions:areview[J].ProcofIEEE,1989,77(7):941-981.[6]MalikMA,SaniieJ.Performancecomparisonoftime2fre2quencydistributionsforultrasonicnondestructivetesting[A].IEEEUltrasSymp[C].SanAntonio,Texas,USA:1996.701-704.[7]ProsserWH,SealeMD,SmithBT.Time2frequencyanalysisofthedispersionofLambmodes[J].JAcoustSocAm,1999,105(5):2669-2676.[phone](021)65556775,483,361;[phone](021)65550277;[phone](021)65559079613:FourierWigner2Ville©1995-2004TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.