完整版信号与系统的公式汇总分类

1连续傅里叶变换???tj??dt)e?f(F(jt)??1???tj??d)(jf(t)?eF?2??连续傅里叶变换对??t?j??dt(tF(je)?)f??傅里叶变换函数2连续拉普拉斯变换(单边)?st??dte(tF(s)?)f0?1??j?st?dss)t)?eF(f(?j2??j?拉普拉斯变换对（单边）??st?dtts)?)ef(F(0?函数象函数3离散Z变换(单边)??k?z(kF(z)?)f0k?11?k?0)z,k?f(k)?dzF(z?j2LZ变换对（单边）F函数象函数4离散傅里叶变换????kjj?ef(kF(e)?)???k1??jkj??dFf(k)?(e)e?2?2??k?z)f(k(z)?0k?函数象函数线性??)((aFjj)?bFaf(t)?bf(t)?2112?)tf()F(j线性)?bf(t)?aF(s)?bF(s)af(t1122f(t)线性)sF()bF(zbf(k)?aF(z)?af(k)?21120?k),kf(线性??jj)ebF(aF(e)?(k)?bf(k)?af21120),k?f(k时移?t?j?)(jFtf(t?)?e00????1t)()2(1时移st?)?e(sFf(t?t)00?)(t时移1?mf(k?m)?zF(z)（双边）1?)k(时移??jm?j)eFf(k?m)?e(?0),m?(k?mm?z频移?tj???))?)?F(ej(tf(00nn()?????)jj(t)t)((频移ts?)f(t)?s(se?F00??)(t频移s???j?kj（尺度变换）kf()?Fe(ez)00z11z?频移???)jk?j(?)(()eFfe?k00z?0m?(k?m),m?z?z?1尺度变换b??j1af(at?b)?eF(j)a||a1????)(?)t(?j尺度变换bss1a)()?eFf(at?ba||a?(t)尺度变换1szk)()?Faf(kaz?)(k1z?尺度变换)/nf(k??jn)eF(f(k)???)n(0?2zz?2?)(kk3)?1(z反转?(?t)?F(?j)f1??????j)()tt(反转)?s)?F(f(?t1n??t)t)(tt(反转!n?1f(?k)?F(z)（仅限双边）z?)(kk2反转?j?)(ef(?k)?F2zk?)(1)ak(k?时域卷积?t??e??(ft)*f(t)?F(j)F(j)22112?11?t???0,(t)tet)?(2??时域卷积(s)?f(t)*f(t)F(s)F21122s1???t?t??(et)(t)te?时域卷积1?ns12)F(z)F(zf(t)*f(t)?2112)(z?1zk?)(ka时域卷积??jj)FF(e(e)f(k)*f(k)?21122)(z?az1?k?)kka(2频域卷积1??)f(t)f(t)?F(jF)*(j2211?2?j??(?j)????????)cos(t)]?[(??()000时域?)f(0?sF(s)?ft()?2???)yf)(t)?sF(s?sy(0)?0(???s??))tcos((t2s??)(t)sin(t2时域差分?)?(ss2???21?)(?1F(z)?(fk?1)?zf1?2?)2f1)?(??zF(z)?zf(?2f(k?)))0?zf(f(k?1)?zF(z22)1zf)?f(k2)?zF(z?zf(0)?(a?zz?k?)ke(?e?zz?kj?(ke)频域卷积1???)j?j(??d)F(Fe(f(k)f(k)?e)2121?2?2)?a(zazk?)k(ka2时域微分)n(n??????)jF(j()j)F(j)f)(tf(t????????)tsin()])j[?(??(0001??sgn()?j微分时域差分??jj)e)F?1)?(1?e(f(k)?f(k(z?a)22za?azk2?)ak(k频域微分n??(dFjd)F(j)ntf(t)(?jt)f(t)?jn?d?dt2?|t|S域微分n)F(dsn?)(??Fstf(t)(?t)f(t)ndss??)t)cosh((tZ域微分??sdF(z)zkf(k)??dz?je?zzkka?(?a)?)(k频域微分?j)(edFj)?kf(k?d3)az?(2kkz)aa?(??)(k时域积分?)j(Ft????)f(??)?0F(0)(??dxf(x),?j??2?)2(??????tj?e00时域积分)?1()(0f)sF(t???fdx?(x)ss??2s??)t)sinh((t2部分求和2???2kz??(k)?f(i)?f(k)*1z???i?22a?za2zk(k?1)?)(k3时域累加???j)(eF??0j????)2(?kF(fk)?(e)??je1???k????k22a2a?z2(k?1)kz?)k(频域积分?)f(t????)t?F(j)dF,(??)?00?f()jt?(?????j?t???ecos(t)(t)22域S积分)(tf????dF?()tss?t???)cos(e(t)tZ域积分????s22?)F(f(k)?m??d?z1m?mk??z)?1(z2zkkba??)(k,)]0?zf(z?lim[zF(?(0)limF(z))f(1)fzz????1?M)M)[z?zf(F(zlimf(M?1)?,?z?32)1(z?2z1?k?1kb?a)(?k)b(z?a)(z?b)ba???)sinz??)k)(sin(k对称??)f(?jtF()?2?????)j(??t???)e)sin(t(t初值)(s(f(0)?limsFs),F为真分式???s?s(??t???)(t)etsin(初值??)?Mlimf(M)?zF(z)（右边信号）??zz??(za)(b?a?cos(zz??kcos(k)()帕斯瓦尔1??22????d)jF|(|?|)tf|(?Edt?2????终值在收敛域内ssF)?lim(s),?0?f(?s0终值（右边信号）)z)(?f()?limz?1F(1?z帕斯瓦尔?1??22j??d|)(|fk|?)e(F|?2?2???k信号与系统公式性质一览 表 关于同志近三年现实表现材料材料类招标技术评分表图表与交易pdf视力表打印pdf用图表说话 pdf ．常用连续傅里叶变换、拉普拉斯变换、Z变换对一览表222222????????)?j(1?cosz2z??cosz2?1z?)?s(?2?||t???0),e?(t22???)n(nn???????ttj2()2(j)()s?bb10)(()?t?bbt102sbs?bbb01?t?00?)?(?b)et(1?)(ss???22??????)sin??zzsin()??zzcoscos(??????)(k))?ksin(cos((k?k)22??1z??2zcos1cosz??2z??)acosz(z?sinazkk????)(k)aksin(a(cos(kk))2222??a2azcos?zz?2azcosa??)tsgn(2?j1???)tsin((t[)]t?3?1222?)s?s(k??(k)acosh(k)?)?acoshz(z22?acosh?z?2azk??)(k)aksinh(?sinhaz22?a?z2azcosh??t?0t??e,??)?(0,??t??0?e,t??2j?22???1???)t[1?(t)]sin(t)3?21222?)?(ska?(k),k?0kz??ln??a?z??ka?)k(!kaze????t|cos(t),|???2??)cos(??21sk)(lna111?)(tf????|0,|t?2?????222)(()?22??)(tt)tsin(?2222?)?(s?)k(!kza)!(2kcoshz??t?jneFn???n??2?????),F(??n2?nT??n?1))cos(()][sin(????tttt??22s222?)?(s1)(?k?k1z???lnz?1z???1?)(k12k?1z?1zln2z?1????)nT(?t?)(tT??????)????n(()????n??)(t)tcos(t22??s?b?b??t01([e??bb??t?01)()]?tebs?b01??n??2??T222?)(s???????(s???)s?)(???t,||1??2?(gt)???????2?????sinSa???????t??eb]bt)?[(b?110bs?b0122??b?b?b?t?021e[?????)(?)(2??bb?b??t?210?e????)?()(?2sb2?bs?b01??t||0,?2?22?????)?(s2??b?b?b?t?102e?????)??()(?)(t]?s?)((??)?)(ss?)Wtsin(W?t)WSa(W???||1,??2??jF()?W其中,?t????))sin(tAet?(??)?b(j?b?j10b?bs0122??2???bb?b?t?120[?e2??)(?2??bb?b??t?210te????2bs2?bs?b012??t???,0||?2??Ae??s(?)???b?b?b?(2201?2??)(??)?t??(et)](s???)?(s)?|t2|??|t,1?|???2?(ft)????????2Sa??42??t?t????(te)bb?b[e22121?t22????2bs?b?sb0123?2??b?bb??210e[22????t???)()]t?Asin(?t2bs2??bs?b0122???)?s())(?ss(?)(te)b?b?t(b]?2??jbb(?b)??|,0t|201其中?2j120??Ae2????)j?(??1???11,|t|??2????||2t?2??bb?b??t?210e?[?t????)ttAe?(sin()]?|?(t),t|???22?t)(f????,0|t|?2???????j?1????2Sa?je?????2????1t()??(1?),f?????2?1???|0,t|?2??|t|222?????)((?bb其中?j10?Ae2????)?(?bj)?j22bs2?)[(?s(?bs?b0122??)]?)?s???)?(8??1sin???24???)(???1．???)(???1sin???4??????)j??(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函数?st??dts)?et)f((??F(s)象函数和收敛域双边Z变换对??z(z)?)(kfF???k象函数函数k?F(z)??)t)(k(1，整个Z1，整个S平面nznn)(,|??)k)(?t(n，有限S平面sn)1z?(z1??)(k)(t}?0,|z,Re{ss1z?2z1??0}?s,Re{,|)t(t)k((k?1)22s)?1(znn?1z1)!(k??1nt?0?s},Re{,|?)k()(tnn)!1!(n?ks)?1(z(n?1)!z1??)1?k??()(??t0?,Re{s|,z}s1?z2z1?0s}?,Re{|,)?tt(??)?(k?1)1(?k?22s)1(z?n1n?z1(k?n?1)!t?0}?,Re{s,|)1?k??(?)??t(nnk!(n?1)!s)?1(z)!?1(nz1at?}aRe{?z,Re{s}?,|k??)e(t)a(ks?aaz?21z}as}?Re{?,Re{at?,|n?)tte(?)a(n?1)k(2)a(s?2)az?(n1n?1z(k?n?1)!t}Re{?aRe{,s}?n?at?|,)(ak?)(ten)a(s?nk!(n?1)!)az?()!1(n?z1?atz,|},Re{s}?Re{?ak??)?t(?e)1?ak?(?a?sa?zn11?nz)!1?n?(ktn}Re{,Re{s}??a?at?,|)?1(??ak?)t?e(?n)a(s?n)!?1!(nk)a(z?)!(n?12scoszz?0,Re{s}?????)cos((k)k))tcos((t22??s22zzcos???sinz0s}?,Re{????)k(sin(k))sin(tt)(222??scos?2zz?2?scosza?z}?a}?Re{,Re{s?kt?????)(cos(cos(atk)t(k)e)22????)(s22zacosz??sinza}}?Re{?a,Re{s?tk?????)sin()tet(asin(k)(k)222????)(scosz?2za2?1)z(aa2??||k}?aRe{Re{,a}?Re{s}?|?|t,|1a?a,||0,Re{a?}e22(z?a)(az?1)a?s?2|t|?)?(azzs2sgn(t),e||k}a??sRe{?a,Re{}}Re{|,1?a|sgn,a|22az(?)(1az?)as?0}Re{a?和收敛平a卷积积分一览表f(t)?f(t)*12f(t)f(t))*ff(t121?????df(t?f())1??f(t)f(t)*(t))tf(2112f(t)?)ft(??(t)t?(t)?(tf?(t)t)f(?)(t??)t)(t(t)tf(?df()??1??t??)(te?t?(1?e?)t(??(t?)t()1?)()tt2?t(2?t??e(t)11??t???t???(ee)e(t212???12t?????),()t?t?e21?t??t??)(tte?)(et?t??)(tet1?????1)(t?t?12e??1?t??2)(et???)((?2??12????1?t??(t)e?2?(t2?)???21?t?11?)t???t??)(et?22???12????)?cos(cos(?t??t??e1????)???t??)et(2??t????)cos(te?)(t122????)??((??t???)et(212??????arctan????????2122????)??t??12?te1?t2??ett?)t(?)(et2(卷积和一览表?f(t)*f(t)12?(i)f(fk?i)?1??i?f(t)f(t)21f(t)f(t)f(t)*112f(t)2f(t)*f(t)21?(k)(fk)(fk)(k)f?)(kk?)(if??i???)((k)k??kk()(k?1)k(?)k)(1?(kk)k?1)(2?k)k(?a)(k1?ka1?k??0a?k(),a(k1a?1k?)()ak2k?1k?1a?a21?aa?(k),21a?a21kk??k)aka((?k(kk?))(ak(k?1)k)?)ak(k?1)ka(a??)(k)?k(2a1?)?a(1k?acos(k?1k?a1??)()k1k?1??????1)?a?cos(cos[](k?222?cosaa??aa??()kkk(k1)?)(k?1)k(k?1)k(6k?)a(k??2112???sina1arctan???aacos???21关于、函数公式一览表)k??(t)(??)(f(t)(t)?f(0)t???)tt?)t(?t?f(t)tf()((?000?????)?)?(?)(tt?(tt)??????0)(t)?f(t)f?(t)f(0)(???)?)f(t)(tdtf(0?????[?tdt)f(t?(tt)?f()00??n1??)(tt(t)??fi?|)|f(ti1i??)(n(n)n???(?tf()1)ft()dt??1???)()(tat||at???????????)t?d()1dt)t(?(??????t???????)dtt()(?)(d0?t???????t?)?)(?)?tf()(ttft(ttf(00000??(k)))?f(kf()0(k11?)n)(n(????)?(t?at()????)(k?k)?(ak)?(k)(???)f?)t)(ftt(?dt?(t?00?))k(f((f)k?0n||aa????k?