信号与系统的公式汇总分类.pdf

信号与系信号与系统统公式性公式性质质一一览览表表1 连续连续傅里叶傅里叶变换变换dejFtfdtetfjFtjtj)(21)()()(2 连续连续拉普拉斯拉普拉斯变换变换(单边单边)jjststdsesFjtfdtetfsF)(21)()()(03 离散离散 Z 变换变换(单边单边)LkkkkdzzzFjkfzkfzF0,)(21)()()(104 离散傅里叶离散傅里叶变换变换2)(21)()()(deeFkfekfeFkjjkkjj线性)()()()(2121jbFjaFtbftaf线性)()()()(2121sbFsaFtbftaf线性)()()()(2121zbFzaFkbfkaf线性)()()()(2121jjebFeaFkbfkaf时移)()(00jFettftj时移)()(00sFettfst时移（双（双边边）)()(zFzmkfm时移)()(jmjeFemkf频移)()(00jFtfetj频移)()(00ssFtfets频移（尺度（尺度变换变换）)()(00zeFkfejkj频移)()()(00jjkeFkfe尺度变换)(|1)(ajFeabatfabj尺度变换)(|1)(asFeabatfsab尺度变换)()(azFkfak尺度变换)(0)/()()(jnneFnkfkf反转)()(jFtf反转)()(sFtf反转（仅仅限双限双边边）)()(1zFkf反转)()(jeFkf时域卷积)()()(*)(2121jFjFtftf时域卷积)()()(*)(2121sFsFtftf时域卷积)()()(*)(2121zFzFtftf时域卷积)()()(*)(2121jjeFeFkfkf频域卷积)(*)(21)()(2121jFjFtftf频域卷积deFeFkfkfjj)()(21)()()(22121时域微分)()()()()()(jFjjFjtftfnn时域微分)0()0()()()0()()(2 ysysFstffssFtf时域差分)1()0()()2()0()()1()2()1()()2()1()()1(22121zffzzFzkfzfzzFkfffzzFzkffzFzkf时域差分)()1()1()(jjeFekfkf频域微分nnndjFddjdFjtfjtttf)()()()()(S 域微分nnndssFdsFtftttf)()()()()(Z 域微分dzzdFzkkf)()(频域微分dedFjkkfj)()(时域积分)()0()(0)(,)(FjjFfdxxft时域积分sfssFdxxft)0()()()1(部分求和1)()(*)(zzifkkfki时域累加kjjjkkeFeeFkf)2()(1)()(0频域积分0)(,)()()()0(FdjFjttftfS 域积分sdFttf)()(Z 域积分dFzmkkfzmm1)()(,)(lim)0(zFfz)0()(lim)1(zfzzFfz对称)(2)(fjtF初值为为真分式真分式)(),(lim)0(sFssFfs初值（右（右边边信号）信号）,)(lim)(zFzMfMz)()(lim)1(1MzfzFzMfMz帕斯瓦尔djFdttfE22|)(|21|)(|终值在收在收敛敛域内域内0),(lim)(0sssFfs终值（右（右边边信号）信号）)()1(lim)(1zFzfz帕斯瓦尔222|)(|21|)(|deFkfjk常用常用连续连续傅里叶傅里叶变换变换、拉普拉斯、拉普拉斯变换变换、Z 变换对变换对一一览览表表连续连续傅里叶傅里叶变换对变换对dtetfjFtj)()(拉普拉斯拉普拉斯变换对变换对（单边单边）0)()(dtetfsFstZ 变换对变换对（单边单边）0)()(kkzkfzF函数)(tf傅里叶变换)(jF函数)(tf象函数)(sF函数0),(kkf象函数函数0),(kkf象函数1)(t)(21)(t1)(k10),(mmkmz)()()(ttnnjj)()(ts11zz0),(mmkmzzz1)(t)(1j)(ts1)(k1zz)(2kk32)1(zzz)(tt21)(j)()(ttttn12!1nsns)(kk2)1(zz)()1(kakk22)(azz0,)()(ttetett2)(11jj)()(ttetett2)(11ss)(kakazz)(1kkak2)(azz)sin()cos(00tt)()()()(0000j)()cos(tt22ss)(kekezz)(kkak2)(azazt1)sgn(j)()sin(tt22s)(kekjjezz)(2kakk322)(azzaaz|t22)()cosh(tt22ss)(2)(kaaakk22azz)(2)(kaaakk222azztje0)(20)()sinh(tt22s)(2)1(kkk3)1(zz)(2)1(kkk32)1(zz)()cos(ttet22)(jj)()cos(ttet22)(ss)(kbabakk)(bzazz)(11kbabakk)(2bzazz)()sin(ttet22)(j)()sin(ttet22)(s)()cos(kk1cos2)cos(2zzzz)()sin(kk1cos2sin2zzz0),(|tet222)()(10tbtb210ssbb)()cos(kk1cos2)cos(cos22zzzz)()sin(kk1cos2)sin(sin22zzzzntt)()(2)(2)(nnjj)()(100tebbbt)(01ssbsb)()cos(kkak22cos2)cos(aazzazz)()sin(kkak22cos2sinaazzaz)sgn(tj2)()sin(13ttt)(1222ss)()cosh(kkak22cosh2)cosh(aazzazz)()sinh(kkak22cosh2sinhaazzaz)0(,0,0,tetett222 j)()sin()1 213ttt222)(1s0),(kkkak azzln)(!kkakzae2|,02|),cos()(ttttf22)2()2()2cos(2)()sin(21ttt222)(ss)(!)(lnkkakza1)!2(1kz1coshntjnneFTnFnn2,)(2)()cos()sin(21tttt2222)(ss)(11kk1lnzzz)(121kk11ln21zzznTnTtt)()(Tnn2)()()()cos(ttt22222)(ss)()(1010tebbebbtt)(01ssbsb2|,02|,1)(tttg2sin22Satebtbb)(110201)(sbsb)()()()(221022102210tebbbebbbebbbttt)()(0122sssbsbsbtWtWtSaW)sin()(2|,02|,1)(WWjF,其中)()sin(ttAet)(10jbbAej2201)(sbsb)()()2()(2210221022210tebbbtebbbebbbttt)()(20122ssbsbsb2|,02|,|21)(ttttf422Sa)()(21)2(22210212tetbbbtebbebttt30122)(sbsbsb)()sin(222210ttAebbbt其中)()(1220jjbbbAej)(220122ssbsbsb2|,02|),2(1)(ttttf212Saejj4)(sin4)(sin)(82|,02|2),|21(2|,1)(1112111tttttf)()sin()(222210ttAeebbbtt其中)()()(2210jjbjbbAej)(220122ssbsbsb双双边边拉普拉斯拉普拉斯变换变换与双与双边边 Z 变换对变换对一一览览表表双双边边拉普拉斯拉普拉斯变换对变换对dtetfsFst)()(双双边边 Z 变换对变换对kkzkfzF)()(函数象函数和收敛域)(sF函数象函数和收敛域)(zF)(t1，整个 S 平面)(k1，整个 Z 平面)()(tn，有限 S 平面ns)(kn0|,)1(zzznn)(t0Re,1ss)(k1|,1zzz)(tt0Re,12ss)()1(kk1|,)1(22zzz)()!1(1tntn0Re,1ssn)()!1(!)!1(knknk1|,)1(zzznn)(t0Re,1ss)1(k1|,1zzz)(tt0Re,12ss)1()1(kk1|,)1(22zzz)()!1(1tntn0Re,1ssn)1()!1(!)!1(knknk1|,)1(zzznn)(teatReRe,1asas)(kak|,azazz)(tteatReRe,)(12asas)()1(kann|,)(22azazz)()!1(1tentatnReRe,)(1asasn)()!1(!)!1(kanknkn|,)(azazznn)(teatReRe,1asas)1(kak|,azazz)()!1(1tentatnReRe,)(1asasn)1()!1(!)!1(kanknkn|,)(azazznn)()cos(tt0Re,22sss)()cos(kk1cos2cos22zzzz)()sin(tt0Re,22ss)()sin(kk1cos2sin2zzz)()cos(ttetReRe,)(22asss)()cos(kkak1cos2cos22zazzaz)()sin(ttetReRe,)(22ass)()sin(kkak1cos2sin2zazza0Re,|aetReReRe,222asaasa1|,|aak|1|,)1)()1(2azaazazza0Re),sgn(|atetReReRe,222asaass1|sgn,|aak|1|,)1)()(2azaazazzza卷卷积积积积分一分一览览表表dtfftftf)()()(*)(121)(1tf)(2tf)(*)(21tftf)(1tf)(2tf)(*)(21tftf)(tf)(t)(tf)(tf)(t)(tf)(tf)(tdft)()(t)(t)(tt)(tet)(t)()1(1tet)(t)(tt)(212tt)(1tet)(2tet2112),()(121teett)(tet)(tet)(ttet)(1ttet)(2tet1221221212)()(1)(1)(21teettt)(tt)(tet)(1122tett)()cos(1ttet)(2tet1222122212arctan)()()cos()()cos(21teettt)(ttet)(tet)(212tett卷卷积积和一和一览览表表iikfiftftf)()()(*)(121)(1tf)(2tf)(*)(21tftf)(1tf)(2tf)(*)(21tftf)(kf)(k)(kf)(kf)(kkiif)()(k)(k)()1(kk)(kk)(k)()1(21kkk)(kak)(k0),(111akaak)(1kak)(2kak21211211),(aakaaaakk)(kak)(kak)()1(kakk)(kk)(kak)()1()1()(12kaaakakk)(kk)(kk)()1()1(61kkkk)()cos(1kkak)(kak2112122211211cossinarctan)(cos)cos()1(cosaaakaaaaakakk关于关于、函数公式一函数公式一览览表表)(t)(k)()0()()(tfttf)()()()(000tttftttf)()()()(tttt)()0()()0()()(tftfttf)0()()(fdtttf)()()(00tfdttttf)(|)(|1)(1iniitttftf)0()1()()()()(nnnfdtttf)(|1)(taatttddtt)()(1)()()(0)(tddttt)()()()()()(00000tttftttftttf)(1|1)()()(taaatnnn)()()()(kkkakkfkkfkfkkf)0()()()()0()()()()()(00tfdttttf