常用的傅里叶变换和常用的积分

Af(t)F()F(f)1ni=1aifi(t)ni=1aiFi()i=1aiFi(f)2F(t)2f(-)f(-f)3f(at)1|a|Fa1|a|Ffaf(-t)F(-)F(-f)4f(t-t0)F()e-jt0F(f)exp(-j2ft0)f(at-t0)1|a|Fae-jt0a1|a|Ffae-j2ft0a5f(t)ej0tF(-0)F(f-f0)f(t)cos(0t)12[F(+0)+F(-0)]12[F(f+f0)+F(f-f0)]f(t)sin(0t)j2[F(+0)-F(-0)]j2[F(f+f0)-F(f-f0)]6df(t)dtjF()j(2f)F(f)dnf(t)dtn(j)nF()(j2f)nF(f)7-jtf(t)dF()ddF(f)df(-jt)nf(t)dnF()dndnF(f)dfn8t-f()d1jF()+F(0)()1j2fF(f)+F(0)2(f)9f1(t)*f2(t)F1()F2()F1(f)F2(f)10f1(t)f2(t)12[F1()*F2()]F1(f)*F2(f)11n=-f(t)(t-nTs)1Tsn=-F-2nTs1Tsn=-Ff-nTs12n=-ft-2nssn=-F()(-ns)fsn=-F(nfs)(f-nfs)13R12()R21()F*1()F2()F1()F*2()F*1(f)F2(f)F1(f)F*2(f)14R()|F()|2F(f)2405Bf(t)F()=|F()|ej()1Ae-atu(t)(a0)Aa+j2Ae-a|t|(a0)2aAa2+23A|t|20|t|2ASa2=2Asin2f(t)F()=|F()|ej()4Ae-t2Ae-225Acost|t|20|t|22Acos21-26A21+cos2t|t|20|t|2A2Sa21-22CX1,X2pX1,X2(x1,x2),Y1,Y2X1,X2:Y1=f1(X1,X2)Y2=f2(X1,X2)(C.1):X1=1(Y1,Y2)X2=2(Y1,Y2)(C.2):X1=11(Y1,Y2)X1=21(Y1,Y2)X2=12(Y1,Y2)X2=22(Y1,Y2)(C.3)(x1,x2)(y1,y2)C.1,C.2C.1C.2C.1C.2(C.1)(C.2)(C.3),P[A(y1,y2)dS]=P[B(x1,x2)dS1B(x1,x2)dS2B(x1,x2)dS3],P[A(y1,y2)dS]=P[B(x1,x2)dS1]+P[B(x1,x2)dS2]+P[B(x1,x2)dS3]+(C.4)(C.4)pY1Y2(y1,y2)dS=pX1X2(x11,x21)dS1+pX1X2(x12,x22)dS2+pX1X2(x13,x23)dS3+(C.5)pY1Y2(y1,y2)=pX1X2(x11,x21)dS1dS+pX1X2(x12,x22)dS2dS+pX1X2(x13,x23)dS3dS+(C.6)015,(x1,x2)dSK(y1,y2)dS,JJ=dSKdS=x1y1x2y1x1y2x2y2=(x1,x2)(y1,y2)(C.7)(x1,x2)(y1,y2)=1(y1,y2)(x1,x2)(C.8)(C.6)(C.7)pY1Y2(y1,y2)=pX1X2(x11,x21)(x11,x21)(y1,y2)+pX1X2(x12,x22)(x12,x22)(y1,y2)+pX1X2(x13,x23)(x13,x23)(y1,y2)+(C.9)(Y1,Y2)(X1,X2)(),pY1Y2(y1,y2)=pX1X2(x1,x2)(x1,x2)(y1,y2)=pX2X1[(x1(y1,y2),x2(y1,y2)]|J|(C.10),(Y1,Y2,,Yn)(X1,X2,,Xn)(),pY1Y2Yn(y1,y2,,yn)=pX1X2Xn(x1,x2,,xn)|J|(C.11)J=(x1,x2,,xn)(y1,y2,,yn)=x1y1xny1x1ynxnyn115D:X1,X2,,XnpX1,X2Xn(x1,x2,,xn),YX1,X2,,Xn,Y=(X1,X2,,Xn),YE(Y)=-ypY(y)dy=-(x1,x2,,xn)pX1,X2Xn(x1,x2,,xn)dx1dx2dxn(D.1)(D.1),E(Y)pY(y),X1,X2,,XnpX1,X2Xn(x1,x2,,xn),(D.1)(D.1):(1)c()c,E(c)=c(D.2)(2)c0,D(c)=E[c-E(c)]2=E[c-c]2=0(D.3)(3)E[cX]=cE(X)(D.4):X;c(4)D[cX]=E[cX-E(cX)]2=c2D(X)(D.5)(5)E(X1+X2++Xn)=E(X1)+E(X2)++E(Xn)(D.6)(6)X1,X2,,Xn,Eni=1Xi=ni=1E(Xi)(D.7)(7)Dni=1Xi=ni=1DXi(D.8)215Em(t)cos(2fct)m(t)sin(2fct)m(t)sin(2fct)-m(t)cos(2fct)cos(2fct)sin(2fct)sin(2fct)-cos(2fct)sintt1-costtrect(t)-1lnt-12t+12(t)1t11+t2t1+t21t-(t)315FQ1.QQ()=12exp-z22dz(F.1)Q(-)=1-Q()0(F.2)2.(erf)erf()=20exp(-z2)dz(F.3)(erfc)erfc()=2exp(-z2)dz(F.4)erfc()=1-erf()(F.5)3.Q12erfc()=Q(2)(F.6)erf()=1-2Q(2)(F.7)4.(1)recttT=tT=1-T2tT20t(F.8)(2)sincsinc(x)=sin(x)x(F.9)(3)SaSa(t)=sintt(F.10)(4)nJn(x)=12-exp(jxsin-jn)d(F.11)(5)I0(x)=12-exp(xcos)d(F.12)415G(1)exp(j)=cos+jsin(2)cos=12[exp(j)+exp(-j)](3)sin=12j[exp(j)-exp(-j)](4)sin2+cos2=1(5)cos2-sin2=cos(2)(6)cos2=12[1+cos(2)](7)sin2=12[1-cos(2)](8)2sincos=sin(2)(9)sin()=sincoscossin(10)cos()=coscossinsin(11)sinsin=12[cos(-)-cos(+)](12)coscos=12[cos(-)+cos(+)](13)sincos=12[sin(-)+sin(+)]515