通信原理教程第二章信号

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1、1/22/21lim()TTTPs t dtT20()Es t dt 22/2/00000)(1)(TTtjndtetsTjnC2/2/00000)(1)(TTtjndtetsTjnC2/2/00000)(1)(TTtjndtetsTjnC2/2/00000)(1)(TTtjndtetsTjnC 2/2/00000)(1)(TTtjndtetsTjnC2/T2/Ttjn00000dte)t(sT1)jn(Cntjn00e)jn(C)t(s3 t)Tt(f)t(f)2/T(t2/02/t2/V)t(f2nsinTnV2jneeTVejnVT1dtVeT1)jn(C0002/jn2/jn2/2/2

2、/2/tjn0tjn0000045ttftftttf)1()(10)sin()(10222/2/00)14(2)sin()(1)(000ndtetdtetsTjnCntjTTtjn1f(t)tnntjentf221412)(6dtetsStj)()(deStstj)()(2/02/1)(tttg2/)2/sin()(1)(2/2/2/2/jjtjeejdteG7ttsin)t(Sa其他处011sin)(dtettSatj00)(1)(ttdtt1)(1)()(dttdtetftj8 1)(dtktSakttt)(lim)(ktSaktkf(f)10t(t)09u(t)=(t)dt)tt()t(

3、f)t(f00dttttftf)()()(00)t()t(0,1,0,0)(tttu当当t10图2.2.6 单位阶跃函数102)(2)(2lim2/)(2/)sin(2/)(2/)sin(2limcoslim)(0000002/2/0SaSadtteFtj)()()(00Ft000(b)频谱密度(a)波形11dttsE)(2dffSdttsE22)()(dffGE)(0)(2dffGE12dffSdttsETTTT22/2/2)()(2)(1lim)(fSTfPTTdffPdffSTPTTTT)()(1lim2/2/213dttstsR)()()(2/2/)()(1lim)(TTTdttsts

4、TR14,)()()(2112dttstsR2/2/2112,)()(1lim)(TTTdttstsTR)()(1221 RR)()()()()()()()(1221121221RdxxsxsdxxsxsdttstsR1516nikikXxxxxxpxxxF10)(11111718dxxdFxpXX)()(baXdxxpbXaP)()(xXXdyypxF)()(pX(x)01)(dxxpX19niiiXxxupxF1)()(niiiXxxpxp1)()(20222)(exp21)(axxpX21其他0)/(1)(bxaabxpXbax0pA(x)220)exp(2)(2xaxaxxpX23dx

5、xxpXEX)()(CCE)()()()(YEXEYXE)()()()(2121nnXEXEXEXXXE)()(XECXCE)()()(YEXEXYE CE(X)E(CX)24)()(22XXEXDX的数学期望标准偏差，XXX22)(XXXD2222222222)(XXXXXXXXXEXXEiiipXxXD2)()(dxxpXxXDX)()()(225dxxpaxaXEXkk)()()(dxxpxXmXkk)()(Xa dxxpXxXMXkk)()()()()(1XEXm22)()(XXDXM26)()()(iXXitmdxxxptXEi2)()()(iiitXEtXEtXD)()(),(21

6、21tXtXEttRX27常数Xm EX(t)常数22X)t(XE)t(XE)t(XD21tt)(R )t-(tR )t ,(tRX21X21X282/2/)(1limTTiTXdttXTm2/2/)()(1lim)(TTiiTXdttXtXTR2930XPtXER)()0(2)()(RR)0()(RR)()(2tXER2)()0(XRRTfSfPTT2)(lim)(TfSEfPEfPTTX2)(lim)()(dfTfSEdffPPTTXX)(lim)(2312/2/2/2/)(2/2/2/2/2/2/2/2/2)(1)()(1)(*)(1)(TTTTttjTTtjTTtjTTtjTTTtjT

7、TdtdtettRTdtetsdtetsTEdtetsdtetsTETfSE)()()(tstsEttRTTjTdeRTTfSE)(1)(2deRdeRTTfSEfPjTTjTTTX)()(1lim)(lim)(232deRfPjX)()(dfefPRjX)()(0,!)()(kkeTkPTk+a-ax(t)tt0t-33)t(x)t(xE)(R)5()3()1()4()2()0()()()(22PPPaPPPatxtxER222322!3)(!2)(!11)(eaeeaeaR3422)(eaR22)(eaR4)()(22202202222adeeadeeadeeadeRfPjjjj35002

8、2cos22sin42cos22cos)(2)()(21ffffAdffAdfffPdfefPRfffj2,212012ffffff36)(22)()(00ndfendfefPRjjX)0(2)0(0nRPn(f)n0/20fRn()n0/2037HHHffjfffndfenRHH22sin22)(00n0/2Pn(f)0f-fHfHRn()01/2fH-1/2fH382212exp21),(axtxpX39njnkkkkjjjjknnnnXaxaxBBBtttxxxp112/1212/212121exp)2(1),;,(11121221112nnnnbbbbbbB kjkkjjjkaxaxE

9、b40),(),(),(2exp21),;,(22112212121nnXXXkkknkknnXtxptxptxpaxtttxxxp41)()(xapxap)2/(11)(dxxpaadxxpdxxp2/1)()(2exp21)(2xxp42axdzazdzazxFxx22222)(exp212)(exp21)(dzzxx2exp21)(243dzexerfxz022)(dzedzexerfxerfcxzxz22221)(1)(0axaxerfcaxaxerfxF,2211,22121)(44频率近似为fc4500)t(a),t(tcos)t(a)t(XXXXtsin)t(Xtcos)t(X)

10、t(Xsc00)(cos)()(ttatXXXc)(sin)()(ttatXXXs4602exp)(222XXXXXXaaaap2021)(XXp47)()cos()(0tntAtr0,21exp)(222202xAxAxIxxpr482/12222/1222cos1sin2exp22cos22/exp)/(AerfAAApr dppprrr/)(2020exp)(1 12exp21)0/(222GGerfGApr2cosAG GtdteGerf022)(49瑞利分布r概率密度包络r(a)莱斯分布包络的概率密度均匀相位相 位概率密度(b)莱斯分布相位的概率密度50)()()(2211txatx

11、atx)()()(2211tyatyaty51线性系统输入输出x(t)y(t)X(f)Y(f)h(t)H(f)图2.10.1 线性系统示意图t(t)h(t)t00dhtxdthxthtxty)()()()()()()(dtthtth)(0,0)(对于物理可实现系统：对于物理可实现系统：52)()()(fHfXfYdfefYtytj)()(53ntjnejnCtx0)()(02/2/00000)(1)(TTtjndtetxTjnC0=2/T0T0 信号的周期 f0=0/2是信号的基频ntjnenHjnCty0)()()(0054图2.10.4 RC滤波器RCx(t)y(t)RCjCjRCjfH1

12、1)/1(/1)(RCttjtjeRCdfeRCjdfefHth/111)()(55dexRCdthxthtxtyRCt/)()(1)()()()()(0,00,)(ttetxataRCeeaRCeRCedeeRCtyRCtattaRCRCttRCta1/11)(/0)/1(/0/)(56)()(dttkxtydtjefkXfY)()(dtjefkXfHfXfY)()()()(jtjkeke)f(Hddft2|H(f)|k0ff0570)()()(dtxhty0)()()(dtXhtY00)()()()()(dtXEhdtXhEtYEEX(t-)=EX(t)=k，k=常数。0)()(dhktY

13、E0000dt)t(h|dte)t(h|)f(H)(Hftjf)0()(kHtYE58 001100111111)()()()()()()()()()(),(dudvvtXutXEvhuhdvvtXvhduutXuhEtYtYEttRYvuRvtXutXEX)()(11 0011)()()(,YXYRdudvvuRvhuhttR59dvevuRvhuhduddeRfPjXjYY00)()()()()()()()()()(*)()()()(200fPfHfPfHfHdeRdvevhdueuhfPXXjXvjujY60其它处,0,)(HtjffkefHdHffkfH,)(22HXYffnkfPfHfP,2)()()(022)2/2(sin4/)()(0202HffHHjjYYfffnkdfenkdfefPRHH61