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陈慧芳 谢磊版 通信原理答案.pdf

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2008-3-21 A B C D 4 1/2 1/4 1-1 [ ] 1/8 1/8 HX ()log E 1 p X ( ) 1 8 log2log4log8log8 111 248 3 113 8 228 31 (bits) 4 0 1 X 0 1 0.5 0.5 1 Y 0 1 1-3 [ ] 1/2 1 X pXp X (0)(1)0.5 (0)(1)0.5 (0)(1)0.5 (0)(1)0.5 (0)(1)0.5 (0)(1)0.5 (0)(1)0.5 (0)(1)0.5 pYXpY X (0|0)(1|0)0.5 (0|0)(1|0)0.5 (0|0)(1|0)0.5 (0|0)(1|0)0.5 (0|0)(1|0)0.5 (0|0)(1|0)0.5 (0|0)(1|0)0.5 (0|0)(1|0)0.5 (0|0)(1|0)0.5 (0|0)(1|0)0.5 (0|0)(1|0)0.5 (0|0)(1|0)0.5 (0|0)(1|0)0.5 (0|0)(1|0)0.5 (0|0)(1|0)0.5 (0|0)(1|0)0.5 (0|0)(1|0)0.5 0 0 1 Y Y pY X (0|1) 0 (0|1) 0 (0|1) 0 (0|1) 0 (0|1) 0 (0|1) 0 (0|1) 0 (0|1) 0 (0|1) 0 (0|1) 0 (0|1) 0 (0|1) 0 (0|1) 0 (0|1) 0 (0|1) 0 pY X pY X (1|1) 1 pXYpX (0,0)(0,1)0.25 Y pX Y (1,0) 0 pX Y (1,1)0.5 p Y (0)0.25 p Y (1)0.75 1
2 125 s 125 ss IXY (;)log E pX Y ) (, pXp Y ()( ) 2 0.25log0.25log0.5log 0.250.250.5 22 0.50.250.50.750.50.75 2 0.250.250.25log310.5log 3 1.50.75log3 (bits) 2 2 I XYHXHX Y (;)()(| ) 1(1)(|1) pYHX Y 1 3 h 10.75 1.50.75log3 (bits) 2 =0.3113(bit) hxxxx x ()log(1)log(1 ) 1-5 [ ] = 1/(12510 ) = 6 810 3 Baud = 810log 4 3 = 1610 3 bits/s bits/s 2
2-3 50Hz ( )x t n 0 1, 4 4 n 0, xnT ()1, 0 s x (0.005) (1) (2) (1) xtxkTWtkT ()()sinc2( k )s sT s 1 W 2 s 0.01( ) 4 k (0.005)sinc(0.5)sinc(0.5 x ) k k 1 sinc(0.5)sinc(4.5) (2) sin(0.5)sin(4.5 ) 0.54.5 0.566 0.566 0.566 tkT k sinc(),0,1, s sinc(),0,1, sinc(),0,1, sinc(),0,1, sinc(),0,1, sinc(),0,1, sinc(),0,1, sinc(),0,1, sinc(),0,1, sinc(),0,1, sinc(),0,1, sinc(),0,1, 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 s 8 8 8 8 100 2 ExtdxxkT 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 ExtdxxkT ExtdxxkT ExtdxxkT ExtdxxkT ExtdxxkT()( ExtdxxkT()( ExtdxxkT()( ExtdxxkT ExtdxxkT ExtdxxkT ExtdxxkT ExtdxxkT ExtdxxkT ExtdxxkT ExtdxxkT ExtdxxkT ()( ()( ()( ()( ()( ()( ()( ()( ()( ()( ()( ()( ()( ()( ()( ()( ()( ()( ()( ()( ()( ()( ()( ()( ()( ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) 2-11 xttf t ()sinc()cos2 ()sinc()cos2 ()sinc()cos2 1 1 1 1 100 100100 k 0 ( )y t x ttftxttf t ()sinc()cos2()sinc()sin 2 0 ˆ lx t ()sinc( ) t httfthttf t ()sinc()sin2()sinc()cos2 2 0 ˆ 2 lhtt e ()sinc( ) 2 j 2 1 httf t ()sinc()sin 2 2 0 0 0
ytyt e ()Re( ) l jf t 2 0 y txth t ()()( ) ll l 1 YfXfH f ) ()()( l ll 2 X f ( l ) H f ( l ) 1 2 1 2 1 0 f f fj (1)/0 fj (1)/1 1 0 f f 1 2 0 Y f ( l ) fj (1)/2 0 f fj (1)/ 2 1 f 2 ()( 1 y tYfedf ) 2 1 l 2 l jft 2 1 2 0 1 1 j j j j 2 2 2 2 2 2 t sin11 sin11 sin11 sin11 sin11 sin11 sin11 sin11 sin11 sin11 sin11 ttt ttt ttt ttt ttt ttt ttt 22 22 22 22 22 22 22 22 22 22 j j j j j j j t t t t t 4 4 4 4 4 4 4 4 4 4 4 4 42 2 4 42 2 4 4 4 2 2 2 2 2 2 2 2 2 22 2 j j j j j j j sin(1cos)sin(cos1) sin(1cos)sin(cos1) sin(1cos)sin(cos1) sin(1cos)sin(cos1) sin(1cos)sin(cos1) sin(1cos)sin(cos1) sin(1cos)sin(cos1) sin(1cos)sin(cos1) sin(1cos)sin(cos1) sin(1cos)sin(cos1) sin(1cos)sin(cos1) sin(1cos)sin(cos1) sin(1cos)sin(cos1) sin(1cos)sin(cos1) sin(1cos)sin(cos1) sin(1cos)sin(cos1) sin(1cos)sin(cos1) sin(1cos)sin(cos1) sin(1cos)sin(cos1) sin(1cos)sin(cos1) sin(1cos)sin(cos1) sin(1cos)sin(cos1) sin(1cos)sin(cos1) sin(1cos)sin(cos1) sin(1cos)sin(cos1) sin(1cos)sin(cos1) sin(1cos)sin(cos1) sin(1cos)sin(cos1) sin(1cos)sin(cos1) sin(1cos)sin(cos1) sin(1cos)sin(cos1) sin(1cos)sin(cos1) sin(1cos)sin(cos1) sin(1cos)sin(cos1) ttt ttt ttt ttt ttt 444 444 444 444 444 444 444 444 444 444 444 444 444 444 444 444 444 444 ttjt (1 f edffedf edffedf edffedf edffedf edffedf edffedf edffedf edffedf edffedf edffedf edffedf edffedf edffedf edffedf edffedf edffedf ) jft 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 j j j j 2 2 2 2 2 2 0 00 00 000 00 (1 1 (1 1 (1 (1 (1 1 2 2 jft 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 ) ) ) ) ) 1sin(cos 1 1 1 1 1 1 1 1sin(cos 1 1sin(cos t sin(cos sin(cos sin(cos sin(cos sin(cos sin(cos sin(cos sin(cos sin(cos sin(cos sin(cos sin(cos sin(cos sin(cos sin(cos sin(cos sin(cos sin(cos t t t t t t t 2 2 2 2 2 2 2 2 2 2 222 2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) t 1 y tttf t ()(1cos)sinsin(2 ()(1cos)sinsin(2 ()(1cos)sinsin(2 ()(1cos)sinsin(2 ()(1cos)sinsin(2 ()(1cos)sinsin(2 ()(1cos)sinsin(2 ()(1cos)sinsin(2 ()(1cos)sinsin(2 ()(1cos)sinsin(2 ()(1cos)sinsin(2 1 1 1 1 1 1 1 t 2 2 4 4 ) ) ) ) ) ) ) ) ) ) ) 1 1 1 1 1 1 1 4 4 t 1 2 2 t 0 2-19 ( )t t ()2cos(2 t ) P P (0)(/2)1/ 2 [()]E t R (0,1) EtPtP t [()](0)2cos(2)()2cos(2 ) cos(2)sin(2 ) t t 2 2 2
cf B R (0,1)[2cos2cos(2)] E P P (0)4()4coscos 2 5 22 2 P2-25 0 / 2N |H(f)| B -fc B fc f 0 P2-25 2-25 1 2 PfH f ()( N ) N 0 2 2 N 0 2 2 2 2 2 2 0 f f f f f f f f f f c c c f f fc f f f c c B BB 2 2 2 2 2 2 B B 2 R ()( ()( ()( ()( ()( ()( ()( ()( ()( ()( ) ) ) ) ) ) ) ) ) ) Pfedf NNPfedf Pfedf Pfedf Pfedf Pfedf N NN j j j j 2 f f f f NBB 00NBB NBB 0 00 f f f sinc()cos(2 sinc()cos(2 sinc()cos(2 sinc()cos(2 sinc()cos(2 sinc()cos(2 sinc()cos(2 sinc()cos(2 sinc()cos(2 sinc()cos(2 ) c ) ) ) ) ) ) ) ) ) 0 0 1 2 2 f n N ()exp 2 0N B 2 n 2 2 2-30 ( )t [ ] Yttt T ()()( ) R ( ) P2-30 3
EYtYtEttTtt [()()][(()())(()())] 12112 T 2 EttEtT t [()()][()()] 121 EttTEtTt T [( )()][()()] 121 RRTR T 2()()( ) PfRRTR Y T ()[2()()()] Pfe ()(2 PffT 2()(1cos2 jfTjfT 2 e ) 2 2 2 ) 2-35 ( )X t ( )Y t YtXtftXtf t ()()cos(2)()sin(2 0 ˆ ) 0f [0,2 ] P2-35 ( )Y t PX( f ) A -B ˆ YtXtX t ()()cos()sincos2 ()()cos()sincos2 ()()cos()sincos2 ()()cos()sincos2 ()()cos()sincos2 ()()cos()sincos2 ()()cos()sincos2 ()()cos()sincos2 ()()cos()sincos2 ()()cos()sincos2 ()()cos()sincos2 ()()cos()sincos2 ()()cos()sincos2 ()()cos()sincos2 ()()cos()sincos2 ()()cos()sincos2 ()()cos()sincos2 ()()cos()sincos2 ()()cos()sincos2 ()()cos()sincos2 ()()cos()sincos2 ()()cos()sincos2 ()()cos()sincos2 ()()cos()sincos2 ()()cos()sincos2 ()()cos()sincos2 ()()cos()sincos2 ()()cos()sincos2 ()()cos()sincos2 ()()cos()sincos2 ()()cos()sincos2 ()()cos()sincos2 ()()cos()sincos2 ()()cos()sincos2 ()()cos()sincos2 XtXtf t X ()sin()cossin 2 X ()sin()cossin 2 tXtf t tXtf t XX ()sin()cossin 2 XX ()sin()cossin 2 tXtf t tXtf t ()sin()cossin 2 ()sin()cossin 2 ()sin()cossin 2 ()sin()cossin 2 ()sin()cossin 2 ()sin()cossin 2 ()sin()cossin 2 ()sin()cossin 2 ()sin()cossin 2 ()sin()cossin 2 ()sin()cossin 2 ()sin()cossin 2 ()sin()cossin 2 ()sin()cossin 2 ()sin()cossin 2 ()sin()cossin 2 ()sin()cossin 2 ()sin()cossin 2 ()sin()cossin 2 ()sin()cossin 2 ()sin()cossin 2 ()sin()cossin 2 ()sin()cossin 2 ()sin()cossin 2 ()sin()cossin 2 ()sin()cossin 2 ()sin()cossin 2 ()sin()cossin 2 ()sin()cossin 2 ()sin()cossin 2 ()sin()cossin 2 ()sin()cossin 2 ()sin()cossin 2 ()sin()cossin 2 ()sin()cossin 2 ˆ ˆ B f ff 0 P2-35 f t 0 0 ZtXtX t ()()cos()sin ()()cos()sin ()()cos()sin ()()cos()sin ()()cos()sin ()()cos()sin ()()cos()sin ()()cos()sin ()()cos()sin ()()cos()sin ()()cos()sin ()()cos()sin ()()cos()sin ()()cos()sin ()()cos()sin ()()cos()sin ()()cos()sin ()()cos()sin ()()cos()sin ()()cos()sin ()()cos()sin ()()cos()sin ()()cos()sin ()()cos()sin ()()cos()sin ()()cos()sin ()()cos()sin ˆ ˆˆ ˆˆˆ ˆˆˆ ˆˆˆ ZtXtXtXtX t ()()cos()sin()sin()cos ()()cos()sin()sin()cos ()()cos()sin()sin()cos ()()cos()sin()sin()cos ()()cos()sin()sin()cos ()()cos()sin()sin()cos ()()cos()sin()sin()cos ()()cos()sin()sin()cos ()()cos()sin()sin()cos ()()cos()sin()sin()cos ˆ ˆ ˆ ˆ YtZtftZtf t ()()cos2()sin 2 ˆ 0 YREYtY t ()()( ) R Z fR ()cos2()sin 2 0 ˆ Z RR ()()cos()sin ZX 2 R X 0 f 2 0 EXtX t ()()cossin()()cossin ˆ XR ( ) 4 0 ( )X t ( )X t ˆ EXtX t
PfP f ) Z ()( X PfF R ()( ) Y Y PffPf ()( Z f 0 ) 2 Z 0 jfP f sgn()( ) Z fff ()( f 0 ) j 2 0 Pf Z ( 0 ) 1sgn( f 2 f Pf () Z PffBff () Z 0 f 0 00 f f ) 0 ) 0 Pf Z ( f 2 1sgn( f f ) 0 fff B 0 0 ff 0 f 0 PX( f ) A f0 f0+B [-1, 1] -B0 B f PY( f ) A -f0-B -f0 2-37 X(t)=A+Bt )=)=AA)=)= ++BtBt++ XR t t (, (, (, XX (, (, (, ) ) ) ) ) ) 2 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 Xm t ( ) A B AA BB ( )X tABt ( )( )XX tABt tABt ( )( )( )tABt tABt tABt tABt tABt tABt EXtEAEBt EXtEAEBt EXtEAEBt EXtEAEBt EXtEAEBt EXtEAEBt ( ) 0 0 0 XR ttEABtABt (,)()( 1 2 ) 1 2 EAEBt t 2 2 1 2 1 (1 3 t t 1 2 ) 5
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