通信原理教程2-信号

1、1dt) t (sE022/T2/T2Tdt) t (sT1limP22/2/00000)(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(C00

2、02/jn2/jn2/2/2/2/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)0

3、9u (t) = (t) dt)tt () t (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)()(1lim2/2/213dt

4、tstsR)()()(2/2/)()(1lim)(TTTdttstsTR14,)()()(2112dttstsR2/2/2112,)()(1lim)(TTTdttstsTR)()(1221 RR)()()()()()()()(1221121221RdxxsxsdxxsxsdttstsR1516nikikXxxxxxpxxxF10)(11111718dxxdFxpXX)()(baXdxxpbXaP)()(xXXdyypxF)()(pX(x) 01)(dxxpX19niiiXxxupxF1)()(niiiXxxpxp1)()(20222)(exp21)(axxpX21其他0)/(1)(bxaabx

5、pXbax0pA(x)220)exp(2)(2xaxaxxpX23dxxxpXEX)()(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)()()(iXXitmdx

6、xxptXEi2)()()(iiitXEtXEtXD)()(),(2121tXtXEttRX27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

7、/2) (1) ()(1) (*)(1)(TTTTttjTTtjTTtjTTtjTTTtjTTdtdtettRTdtetsdtetsTEdtetsdtetsTETfSE)()()(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 )(eaee

8、aeaR3422)(eaR22)(eaR4)()(22202202222adeeadeeadeeadeRfPjjjj350022cos22sin42cos22cos)(2)()(21ffffAdffAdfffPdfefPRfffj2,212012ffffff36)(22)()(00ndfendfefPRjjX)0(2)0(0nRPn(f)n0/20fRn()n0/2037HHHffjfffndfenRHH22sin22)(00n0/2Pn(f)0f-fHfHRn()01/2fH-1/2fH382212exp21),(axtxpX39njnkkkkjjjjknnnnXaxaxBBBtttxxxp

9、112/1212/212121exp)2(1),;,(11121221112nnnnbbbbbbB kjkkjjjkaxaxEb40),(),(),(2exp21),;,(22112212121nnXXXkkknkknnXtxptxptxpaxtttxxxp41)()(xapxap)2/(11)(dxxpaadxxpdxxp2/1)()(2exp21)(2xxp42axdzazdzazxFxx22222)(exp212)(exp21)(dzzxx2exp21)(243dzexerfxz022)(dzedzexerfxerfcxzxz22221)(1)(0axaxerfcaxaxerfxF,22

10、11,22121)(44频率近似为fc4500)t (a),t (tcos)t (a)t (XXXXtsin)t (Xtcos)t (X)t (Xsc00)(cos)()(ttatXXXc)(sin)()(ttatXXXs4602exp)(222XXXXXXaaaap2021)(XXp47)()cos()(0tntAtr0,21exp)(222202xAxAxIxxpr482/12222/1222cos1sin2exp22cos22/exp)/(AerfAAApr dppprrr/)(2020exp)(1 12exp21)0/(222GGerfGApr2cosAG GtdteGerf022)(

11、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)()()(2211txatxatx)()()(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

12、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)RCjCjRCjfH11)/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)()(dhktYE0000dt)t (h|dte )t (h| )f(H)(Hftjf)0()(kHtYE58 001100111111)()()()()()()()()()(),(dudvvtXutXEvhuhdvvtXvhduutXuhEtYtYEttRYvuRvtXutXEX)()(11 0011)()()(,YXYRdudvvuRv