信号与系统的公式汇总分类.docx
1连续傅里叶变换F(j)=f(t)ejtdtJ-X1r00=-1F(j"d2JT2连续拉普拉斯变换(单边)F(S)=RfMdff(t)=iCF(s)e,ds3离散Z变换(单边)尸(Z)=SyWZT幻=上(Z)ZIdZ,k04离散傅里叶变换F(ej)=ff(k)d泌Jt=Vf(k)=4,Fei)eikd2万J"线性助Q)+彷aF(j)+bF(j)线性HjQ)+M(f)CM(S)+hF2(S)线性af(左)+帆伏)西(')+hF2(Z)线性助(A)+妨(A)<->°6(")+玛(e")时移fQ±0)ce±加。F(jaf)时移f(-e±M(s)时移/(j1.±w)ZiwF(Z)(双边)时移f(k±ni)enFkei)频移e±'吗"f)cF"3千例)频移e±W(f)÷÷产(S干SO)频移<产(3j%z)(尺度交排)频移e±M"f(A)c"(M"%>)尺度变换.bJat+b)-eF(j-)Ia1.a尺度变换bf(ct+b)<-eaF()Ia1.a尺度变换a*(Jt)F(-)a尺度变换Ao杵片、尸(巴反转J)cF(-jai)反转/(-)<F()反转f(一幻CF(ZT)仅限双边)反转f(-k)F(e-j0')时域卷积力a)*6(,)c6(a)七"&)时域卷积力(r)*Z2(f)一历(S)B(S)时域卷积AS*-")C耳(Z)玛(Z)时域卷积力优)*(幻÷÷H(")B(e1.)频域卷积力(r)Zz(r)÷->I好(,。)*B(jO)2时域微分/")csF(s)-(0.)(0C.v2F(.v)-.n<0.)-/(0,)时域差分/(*-1)4->2-,F(z)+(-1)f(k-2)z-2F(z)+z-7(-D+/(-2)/(+1.)zF(z)-(0)Kk+2)Z2F(Z)-z2(0)-WI)频域卷积/1(k)f2(k)W1.r尸(e/w>e3-6)d时域微分(w(CjF(j)(j)nF(Jai)时域差分f(k)-f(k-I)C(I-e")F(e")领域微分W)(-W/Se娱/粤”d/dnS域微分f(-)nf(t)-FNZ域微分.d尸(Z)kf(k)-zdz频域微分"小.小(/")Wvi)CJatf时域积分f(x)dx,/(x>)=0F(iM)+F(O)<J(<w)Jfj时域积分f'MQ尸(s'/",。-)fix)(ixC+JrSS部分求和k&)*£(&)=(07-r=-co时域累加XFr*'6Z(A)+川)Yt-2k)=-c-6k=Tf频域积分f()f4(0»+<->IF(j)d,F(-0>)=0(一)JyS域积分畔F()dZ域积分/(O)=IimF(Z),/(1)=Iim1.zF(Z)-Zf(O)Z->00Z->00对称尸5)6冽'S)初值/(0+)=IimsF(s),r(5)为其分式3->00初值/(M)=IimZMF(Z)(右边信号)./(M+1)=1.imzjwF(Z)-女M)Zx*z帕斯瓦尔E=ICIfsF力=口F(jI2d终值f(8)=IimsF(s),$=O在收敛域内.v0终值/(¢0)=Iim(Z-I)F(Z)(右边信号)z1帕斯瓦尔伏)F=勺Fdek-信号与系统公式性质一览表常用连续傅里叶变换、拉普拉斯变换、Z变换对一览表连续傅里叶变换对F(M=jWdi拉普拉斯变换对(单边)产(S)=Ifte-s,dtZ变换对(单边)尸(Z)=E/(k)z-*Jt=O函数傅里叶变换F(J函数/3象函数F(S)函数f(k),kO象函数函数/(),0象函数(t)1.I2m5(o)勤1汉A)1(k-ni),m0ZrWj(j)n小)S1(k-ni),m0工.-I£(/)+()£«)1.S£伏)二k2(k)z2+2(Z-I)3t(r)jb<3)-!t(t)tn(t_!_/旦"s同k(k)(Z-D2(+I)工2(z-)2ea,()tea,'),a>Oa+J(a+j)2ea,(t)te-a!)s+(s+0)2ak(k)ZZ-akak1.(k)Z(z-a)2CoS(%)sin(tyj)加6(切+例)+6(。一例)jn(+例)-(-例)COS&,)Ss2+2eok(k)z-eakake(k)C1.Z(z-a)2-jsgn)Sin()£«)S?+"ejf1.k(k)ZZ-"k2ak(k)2*>-z+-z(Z-)3Id22COSh柄)£(/)$s2-2J7-叽2az2-a2爱上世£2aZ2Z2-A2e±j«v2(T(0)Sinh侬)£(。0“即止与2(-I/出挥工2(Z-D3etaCOS)6()js+a(j+a)2+2eoacos()()s+a(s+a)2+2ak-bk-(k)a-bZ(z-z-份士吧的a-b二z-a)z-b)e-,sin()z(r)e*wsinKa)COS(k)c(k)Z(Z-CoSmSin婢)式k)ZSin"(j+a)2+2(5+)2+2z2-2zcos?+1z2-2cos+1ee(t),a>02a2+2(Mr+许阳力M+如1.rcoa(k+ff)(k)二2COS"-Z8C0-O)Z2-2zcos7+1.Sin依+仍2(A)z2sin<?+zsin(-/7)Z2-2cosjff+1.NZZZB1.Za1.-1:O+VU-TIZ+SWC1.£ZZ0+CSyD§I-§CJC1.NrrN-ZV»>_.11.-I,D:C0I7¾EII(bIQ:UI0St8ZCekR1IW1.t1.+i>tXfVfi453+-U1>V0-T?C¾22C1.,+0二0I2VmUWiG1.7*0I3rKZgKVI乏+M、诫-W'I"«vDUDS"Ii+一r¾+eeS-SC1.Sn二Ir+fc+3+SWZf+3¾3I3会&-&-E0Z-SITeI.I<AJVV+aa?IIS1B-fiz直-。Z虑3Za+,1OcJ-S小IZC1.S0WI&迟3?焉M二11/CZ-§hZfAI1.zJjPVH立IC1.XAe0.二,一,I1.尽VZ2-*s寸-XZ邪O工%5*,II27uIZQJ1.ZK1.ZAo苣I尸】,8MA品u<nZ1.eI1.*MI1.二kCNIZI*¼Ir.1UAI*3I1.S-*1SI1.i+r斐(0f1.ms+wf.-(1.¾+f50SICXZZ1,2-2。.|”彳t1r1(I)产值司I,X(T7>fs-8“17、IiSr7=z§1,*II7J-Ifa>(0kIfyI1.S双边拉普拉斯变换与双边Z变换对一览表双边拉普拉斯变换对F(S)=1./""I双边Z变换对F(Z)=f(k)zk北=YO函数象函数F(S)和收敛域函数象函数尸(Z)和收敛域加)1,整个S平面3(幻1,整个Z平面W)s",有限S平面nJ(Zt),z>0(z-De(f)i,Re5>0S£(女)-1.rjZ1.>1z-1th4r,Re5>0S-(+1.>()"A1A1.t)5-1)!",Res>O优+一1)!小k巾5-1)!TJZI>(Z-DwY(T)-,Re<OS-(-k-1)-1.rJZ1.<1z-1Te(T)-y,Re1.y<0-(k+)(-k-Y)2(Z-1)2tni£(一。(n-1.)!"es<O一生在!(H-I)!z”,z<1(z-1.)e-a,t-,Res>Re-s+aak(k),z>Z-ate-a,t)二,Res>Rej(s+aY(n+)an(k)2、2,z>.(z-)1.1.e'a,t(n-1.)!,Rei>Re-a(s+a)n+T)"e(Q!(w-1)!-Jz>(z-a)f,-e-a,(-t),Re5<Re-s+a-ak(-k-)-Az<az-ak-1-KeFz(T)(一1)!-1.-,Res<Re-a(s+)(&+-1)!a(-k-1)!(w-1.)!(z-0)fMCoS(仇)£(,)-T,Re5>0s1.+价COs(伙)£伏)Z?-ZCOS/?z2-2zcos+1sin()(t)-,Re5