(完整版)信号与系统的公式汇总分类

信号与系统公式性质一览表1连续傅里叶变换dejFtfdtetfjFtjtj)(21)()()(2连续拉普拉斯变换(单边)jjststdsesFjtfdtetfsF)(21)()()(03离散Z变换(单边)LkkkkdzzzFjkfzkfzF0,)(21)()()(104离散傅里叶变换2)(21)()()(deeFkfekfeFkjjkkjj线性)()()()(2121jbFjaFtbftaf线性)()()()(2121sbFsaFtbftaf线性)()()()(2121zbFzaFkbfkaf线性)()()()(2121jjebFeaFkbfkaf时移)()(00jFettftj时移)()(00sFettfst时移)()(zFzmkfm（双边）时移)()(jmjeFemkf频移))(()(00jFtfetj频移)()(00ssFtfets频移)()(00zeFkfejkj（尺度变换）频移)()()(00jjkeFkfe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)()(1zFkf（仅限双边）反转)()(jeFkf时域卷积)()()(*)(2121jFjFtftf时域卷积)()()(*)(2121sFsFtftf时域卷积)()()(*)(2121zFzFtftf时域卷积)()()(*)(2121jjeFeFkfkf频域卷积)(*)(21)()(2121jFjFtftf时域微分)0()0()()()0()()(2ysysFstffssFtf时域差分)1()0()()2()0()()1()2()1()()2()1()()1(22121zffzzFzkfzfzzFkfffzzFzkffzFzkf频域卷积deFeFkfkfjj)()(21)()()(22121时域微分)()()()()()(jFjjFjtftfnn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(FdjFjttftfS域积分sdFttf)()(Z域积分dFzmkkfzmm1)()()(lim)0(zFfz,)]0()([lim)1(zfzzFfz对称)(2)(fjtF初值)(),(lim)0(sFssFfs为真分式初值)(lim)(zFzMfMz（右边信号）,)()([lim)1(1MzfzFzMfMz帕斯瓦尔djFdttfE22|)(|21|)(|终值0),(lim)(0sssFfs在收敛域内终值)()1(lim)(1zFzfz（右边信号）帕斯瓦尔222|)(|21|)(|deFkfjk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dtetfjFtj)()(拉普拉斯变换对（单边）0)()(dtetfsFstZ变换对（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)(t1)(k10),(mmkmz)()()(ttnnjj)()(ts11zz0),(mmkmzzz1)(t)(1j)(ts1)(k1zz)(2kk32)1(zzz)(tt21)(j)()(ttttn12!1nsns)(kk2)1(zz)()1(kakk22)(azz0,)()(ttetett2)(11jj)()(ttetett2)(11ss)(kakazz)(1kkak2)(azz)sin()cos(00tt)]()([)]()([0000j)()cos(tt22ss)(kekezz)(kkak2)(azazt1)sgn(j)()sin(tt22s)(kekjjezz)(2kakk322)(azzaaz||t22)()cosh(tt22ss)(2)(kaaakk22azz)(2)(kaaakk222azztje0)(20)()sinh(tt22s)(2)1(kkk3)1(zz)(2)1(kkk32)1(zz)()cos(ttet22)(jj)()cos(ttet22)(ss)(kbabakk))((bzazz)(11kbabakk))((2bzazz)()sin(ttet22)(j)()sin(ttet22)(s)()cos(kk1cos2)cos(2zzzz)()sin(kk1cos2sin2zzz0),(||tet222)()(10tbtb210ssbb)()cos(kk1cos2)cos(cos22zzzz)()sin(kk1cos2)sin(sin22zzzzntt)()(2)(2)(nnjj)()(100tebbbt)(01ssbsb)()cos(kkak22cos2)cos(aazzazz)()sin(kkak22cos2sinaazzaz)sgn(tj2)()]sin([13ttt)(1222ss)()cosh(kkak22cosh2)cosh(aazzazz)()sinh(kkak22cosh2sinhaazzaz)0(,0,0,tetett222j)()sin()]1[213ttt222)(1s0),(kkkakazzln)(!kkakzae2||,02||),cos()(ttttf22)2()2()2cos(2)()sin(21ttt222)(ss)(!)(lnkkakza1)!2(1kz1coshntjnneFTnFnn2,)(2)()]cos()[sin(21tttt2222)(ss)(11kk1lnzzz)(121kk11ln21zzznTnTtt)()(Tnn2)()()()cos(ttt22222)(ss)(])([1010tebbebbtt))((01ssbsb2||,02||,1)(tttg2sin22Satebtbb])[(110201)(sbsb)(]))(())(())(([221022102210tebbbebbbebbbttt))()((0122sssbsbsbtWtWtSaW)sin()(2||,02||,1)(WWjF)()sin(ttAet,其中)(10jbbAej2201)(sbsb)(])()2()([2210221022210tebbbtebbbebbbttt)()(20122ssbsbsb2||,02||,||21)(ttttf422Sa)(])(21)2([22210212tetbbbtebbebttt30122)(sbsbsb)()]sin([222210ttAebbbt其中)()(1220jjbbbAej))((220122ssbsbsb2||,02||),2(1)(ttttf212Saejj4)(sin4)(sin)(82||,02||2),||21(2||,1)(1112111tttttf)()]sin()([222210ttAeebbbtt其中)()()(2210jjbjbbAej)]))[((220122ssbsbsb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dtetfsFst)()(双边Z变换对kkzkfzF)()(函数象函数)(sF和收敛域函数象函数)(zF和收敛域)(t1，整个S平面)(k1，整个Z平面)()(tnns，有限S平面)(kn0||,)1(zzznn)(t0}Re{,1ss)(k1||,1zzz)(tt0}Re{,12ss)()1(kk1||,)1(22zzz)()!1(1tntn0}Re{,1ssn)()!1(!)!1(knknk1||,)1(zzznn)(t0}Re{,1ss)1(k1||,1zzz)(tt0}Re{,12ss)1()1(kk1||,)1(22zzz)()!1(1tntn0}Re{,1ssn)1()!1(!)!1(knknk1||,)1(zzznn)(teat}Re{}Re{,1asas)(kak||||,azazz)(tteat}Re{}Re{,)(12asas)()1(kann||||,)(22azazz)()!1(1tentatn}Re{}Re{,)(1asasn)()!1(!)!1(kanknkn||||,)(azazznn)(teat}Re{}Re{,1asas)1(kak||||,azazz)()!1(1tentatn}Re{}Re{,)(1asasn)1