通信原理第2章-確定信號(hào)分析

1、2004-9-12004-9-1確定信號(hào)變確定信號(hào)的表確定信號(hào)通過(guò)線性系確定信號(hào)變確定信號(hào)的表確定信號(hào)通過(guò)線性系變信頻帶信號(hào)與帶通系2004-9-21變f(t)F(表達(dá)式)f (t)eFf(t)1變f(t)F(表達(dá)式)f (t)eFf(t) F()ejtf(t)dt t1t t 0t且(t)dt (t) 2004-9-3變換的運(yùn)F(kF(a1F1() a2F2 () 變換的運(yùn)F(kF(a1F1() a2F2 () F *()f(tkf(ta1 f1(t)f *(tf2(tF1af(at a F(e f(t t0eF(0f(t2004-9-4變換的運(yùn)1F(f(t)cos )F(2000jF(f(

2、t變換的運(yùn)1F(f(t)cos )F(2000jF(f(t)sin )F(2000F1() F2(F1() F2(2f(f1(t) f2(tf1(t) f2(tF(tdjnF(f(tntjF0 F(f2004-9-5常用信號(hào)變F(2()1a f(t1ut常用信號(hào)變F(2()1a f(t1uteat ut sgnt22 F( F )0nn0T t (tnT0 (n00 T2004-9-6常用信號(hào)變1ftrect t 0t2FFSa 常用信號(hào)變1ftrect t 0t2FFSa 02Ff sincf30f212004-9-71.2 F(f(t 1WtWrectW W22W00tW W21tri t

3、Sa2 1.2 F(f(t 1WtWrectW W22W00tW W21tri tSa2 20t02004-9-8實(shí)信號(hào)f(t變)f (t)eFf(t)costdt實(shí)信號(hào)f(t變)f (t)eFf(t)costdt j f(t A jBFA2 B2A B 偶函arctgB 奇函A 即：FF*.2004-9-92確定信號(hào)的表示能量信號(hào)：能量有限(限時(shí)或非限時(shí)信號(hào)2dt F()2 EfEF E 2 f F f 2確定信號(hào)的表示能量信號(hào)：能量有限(限時(shí)或非限時(shí)信號(hào)2dt F()2 EfEF E 2 f F f Hz22或單邊能量譜密度(針對(duì)實(shí)信號(hào) G() 2E(1fE G(G(2 f2004-9-0

4、02確定信號(hào)的表示R f *(t)f(tR2確定信號(hào)的表示R f *(t)f(tRR0E REf1*(t) f2(t R12E12 F1*F22004-9-2確定信號(hào)的表示號(hào) tt 2 其它fT(t)FT ( 2 22確定信號(hào)的表示號(hào) tt 2 其它fT(t)FT ( 2 2dt2TPFfTTTT2EF ) d f2tPTTTTTT2004-9-2確定信號(hào)的表示f 2FFP limP2 f HzTTlim或TTT T 單邊功率譜密度(針對(duì)實(shí)信號(hào)B(2確定信號(hào)的表示f 2FFP limP2 f HzTTlim或TTT T 單邊功率譜密度(針對(duì)實(shí)信號(hào)B() 2P(0 1Pf B(f002004-9

5、-2確定信號(hào)的表示1T R f *(t)f(tT T2確定信號(hào)的表示1T R f *(t)f(tT TRR0PRPlimT f *(t)f (tR12TT TR12P12 2004-9-2確定信號(hào)的表示F(f(t號(hào) tf tt 2確定信號(hào)的表示F(f(t號(hào) tf tt 2 其它Tft jn0,011T jnF2004-9-2確定信號(hào)的表示周期信號(hào)(續(xù)F2Fn(n02確定信號(hào)的表示周期信號(hào)(續(xù)F2Fn(n0P2 2( Fn0R2 e F周期函數(shù)(周期為n2004-9-2確定信號(hào)的表示(正頻率部分)-EfEf 12確定信號(hào)的表示(正頻率部分)-EfEf 12004-9-0f-f0EB 例.門(mén)函數(shù):

6、 B1 1 B Ef2E 2確定信號(hào)的表示占總能量(功率)的百分比帶寬BEfdfBPf442200或EPE2確定信號(hào)的表示占總能量(功率)的百分比帶寬BEfdfBPf442200或EPEf -f02004-9-3確定信號(hào)通過(guò)線性系統(tǒng) CL xy t3確定信號(hào)通過(guò)線性系統(tǒng) CL xy t Ct iiii iL(t)htL(t) ht htH Y Hej X2004-9-y(t3確定信號(hào)通過(guò)線性系統(tǒng)h(t) k(t y(t) kx(t 3確定信號(hào)通過(guò)線性系統(tǒng)h(t) k(t y(t) kx(t H() j|H()k00d(d( ) 2004-9-32004-9-諧波相移32004-9-諧波相移3確

7、定信號(hào)通過(guò)線性系統(tǒng)3dB帶寬H( f ) 保持在其最大值的2Hf 1fB03確定信號(hào)通過(guò)線性系統(tǒng)3dB帶寬H( f ) 保持在其最大值的2Hf 1fB02004-9-3確定信號(hào)通過(guò)線性系統(tǒng)理想帶通濾波器H理想低通濾波器H1WW0W H rect3確定信號(hào)通過(guò)線性系統(tǒng)理想帶通濾波器H理想低通濾波器H1WW0W H rect je2W Wht2004-9-14Hilbert變換f(t 1f ( df (t H f(t )t- 1f(t t1f( d 4Hilbert變換f(t 1f ( df (t H f(t )t- 1f(t t1f( d f(t Hf(t )t - 1 f(t(tf f2004

8、-9- 4Hilbert變換濾波器(理想寬帶相移網(wǎng)絡(luò)j j jsgn( ) 1 h4Hilbert變換濾波器(理想寬帶相移網(wǎng)絡(luò)j j jsgn( ) 1 htH ( ) 2f(t)cos0t例(t) cos t 02 sin022004-9-4Hilbert變換HHf(t)f(t)dt 4Hilbert變換HHf(t)f(t)dt 22(tf (t) (t)d (t) (t) f(t)f(t)2004-9-4Hilbert變換常用變t (tsin 0 cos4Hilbert變換常用變t (tsin 0 cos0m tsin fcos0 sin 0m tcos00m tsin m tcos00t

9、 - , .02004-9-5信號(hào)f(tz(t) f(t) j (tf(t) Rez5信號(hào)f(tz(t) f(t) j (tf(t) Rez(t) 1z(t)z*(t2f(tF(),z(t Z()Z() 2F( 0 1F z(t)0 Fz*t2F(), 2004-9-5信號(hào)f (t)能量的2z(t) 的能量為其實(shí)信信z tt 12 tt zz15信號(hào)f (t)能量的2z(t) 的能量為其實(shí)信信z tt 12 tt zz12f t求已知實(shí)函數(shù)信號(hào)的方法時(shí)域：f(t (t) z(t f(t j (t1F() z(t)F f(tf(t)jd0e z(t)cos0t jz(t)mtef(t) m(tm

10、 t .2004-9-06頻帶信號(hào)與帶通系統(tǒng)頻帶信號(hào)：信號(hào)的頻譜集中在某一頻率附近(帶通信號(hào)f(t) F(Ac c c 6頻帶信號(hào)與帶通系統(tǒng)頻帶信號(hào)：信號(hào)的頻譜集中在某一頻率附近(帶通信號(hào)f(t) F(Ac c c c 0Z(z(t) f(t) j (t)Z()c c 0FL(FL Zc jfL(t) cf(t)絡(luò)2004-0 6頻帶信號(hào)與帶通系統(tǒng)fLt fct jfst,6頻帶信號(hào)與帶通系統(tǒng)fLt fct jfst,(f(t) fc(t)cosct fs表示方法若令 fL t) atjtf (t) a(t)cosc t (t)表示方法絡(luò)f(t) Rez(t相f(t) Re fL(t)ejc

11、t表示方法f(t)2004-9-fL tf t6頻帶信號(hào)與帶通系統(tǒng)h(t) H(Ac 0Z(c c c 6頻帶信號(hào)與帶通系統(tǒng)h(t) H(Ac 0Z(c c c z(t)h(t) jZ()c c 0Hc uc 1H (LAh (t)z(t)eL20W2004-9-h (t)6頻帶信號(hào)與帶通系統(tǒng)f(tf(t) Re f (t)ejcLt6頻帶信號(hào)與帶通系統(tǒng)f(tf(t) Re f (t)ejcLtjc h(t) 2ReLfL (tr(t)tr (tcL2004-9-結(jié)論：在處理頻帶信號(hào)激勵(lì)帶通系統(tǒng)時(shí)，可以由等價(jià)的低通分析代替，即由f L(t ) 激hLt r tLejc t hLrL(th(tr(t6頻帶信號(hào)與帶通系統(tǒng)0 t 其ht cos0tx(t) mtcos例已知t求y(t ，00 x(t) mtcos0z(t)mtcos6頻帶信號(hào)與帶通系統(tǒng)0 t 其ht cos0tx(t) mtcos例已知t求y(t ，00 x(t) mtco