傅里葉變換性質(zhì)及常用變換

1、正反變換X(f)=：x(t)e2-ft-QUdtX()=：x(t)e-jtdt;x1(t)兀1(f)乂二XI()-X2()X(t)x(-f)2二X(-)x(t-T)X(f)e-j2-fTX()eTx(at)1X(f)|a|a1X()|a|ax(at-T)1f-j27；fTX()ea|a|a13fT3TX()ea|a|ax(t)y(t)X(f)Y(f)1I。)Y()12二tnx(t)jndnX(f)2二dfn()ndnj7nX()d二1二j2Tt1二(t-nT)=jeT、(f-n=:Tn=：=Tn=：-n)T-beo,X-n0)(0二n二2二、一）T傅立葉變換的性質(zhì)Rxy()X*(f)Y(f)=

2、ExyfX*Y()1x(t尸iX(f)珞dfx(t)=X()ejtd.2二-二x*(t)X*(-f)x(t)ej2-：f0tX(f-fo)x(t)sin2二fotjI.X(f-f0)-X(f-f0)l2x(t)cos2二fot1I.X(f-fo)X(ffo)l2x(t)y(t)X(f)Y(f)X*(-)X(一2二fo)j二IX(:)、)o)-X(.o)1二IX(.-,o)-X(-,；o)1X()Y()卷積x(t)*y(t)=x()y(t-)d=y()x(t-)d-CO相關(guān)Rxy()=：ix*(t)y(t)dt=j：y(t)x*(t)dt=y()x(-)Rx(T)=/*(t)x(t+T)dt=l

3、x。+7)x*(t)dt=x。)*x*(-T)dtnXt.x()d-beTx、(t-nT)n二二Rx()(j2二f)nX(f)(j)nX()X(f)12X(o),j2二f-bev、（fn二二二n)=Te-jn2TfTn二二二2X(f)|=Ex(f)X(),X(0),：()j-be2二“、(l-n0)n=fbo-box(t)*y(-t)=二x(t)y()d=：；x()y(-t)dRy()=1：匕y*(t)x(t)dt=RyX(-)常見傅立葉變換(t)rect(t)，.、1cos(2二fot)2u(t)e-：tu(t)(：0)-be、(t-nT)n二二二.：xy*(t)dtDCJ1sinc(f)k

4、(ffo)、(f-fo)111-(f)2j2-f1工“2二f1二n1%、(f-n)TnT16(f)3(t-t0)-j2jlft0e-j2nf0tesinc(t)rect(f)A(t)sinc2(f)sinc2(t)sin(2nf0t)j&f+f。)-6(f-f。)2sgn(t)1jnf1t16(t)+j22ntsgn(f)6(t)jf)n(t)teu(t)(o(0)1e1。0)26(n)(0)22.,-、2(。+j2nf)2久十（2冗f）TT2ecf2e_t2e_o2而e41=X(f)Y*(f)df=XX9)Y*(0)d0(帕斯瓦爾關(guān)系二2二-二一8o.父一 O-1一 X2(Jx(t)12