信号与系统第二版张小虹课后答案1-8章.pdf

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2()2 2(2( ec e 2i)t- (2 2i)2 3030 c 0 1 1 3030 )( e)(e2)(2)()h( - 2tt3- ttttt ipippii H 32 2/1 32 1/22 )32p)(32p(p 2610pp3 )314pp(p 2610pp3 (p) 2 2 2 )( cos3t)e2()h( - 2t tt 2 1 1 2 23pp 3p (p) 2 pp H 2)(p1(pA(p) ecec)(y - 2t 20 - t 10x t e2cec)(y - 2t 20 - t 10x t 3c 4c 2c2c 1c 20 10 2010 2010 c 0 t3ee4)(y - 2t- t x t (t) e2e()h( - 2t- t t (t)0.5ee 2-(1.5 (t)e-(1 2 1 -(t)e-2(1(t)ee2(*)()(*)()(y 2t-t -2t-t -2t-t - f tthtft (t)2.5ee 2(1.5 )(y)(y y(t) - 2t- t fx tt (t)ee ( (t)e-(e )e-(e(t)ee2(*)(e)(*)()(y - 2t- t- 3t- 2t- 3t- t- 2t- t- 3t f tthtft (t)4ee 5( )(y)(y y(t) - 2t- t fx tt 3 3 20 2)(p1p2)(p1 e 4)(y )(y x x4 42 20 4, 0 4/)2(1 4/ 0 )(*)()(y 2 2 f t t tt t tthtft A)( 1)i(0 V)( 1)0(- u)i(0R - c - (t)e )(i 1 0, (t)e )(i 0 )i(t)1(p 0 1/p)i(t)(1 t - x 1 - t 1x t cct f (t)e 10(t)e -10(1-(t)10(t)10*(t)e )(t)f*(t) )(y (t)e )( )(h 1 1 1 1/11 1 (p) (t)f1/p)i(t)(1 t -t -t - 11f t - 111 1 tht tt pp p p H f (t)e - (1(t)*(t)e (t)f*(t) )(y (t)e )(h 1 1 (p) (t) p)(1 1 i(t) (t)p)i(t)(1 (t),i(i(t) p 1 -Ri(t) t -t - 22f t - 22 s 2 ht t p H ii ss (t) 1(10e )(y (t)y)( (t)11e - (1 )(y )(y (t)y t - xf - t fff 21 tty tt ) 1(p) 1p2p(A(p) 22 t)ecc ()(y - t 1110x t ect)ecc ()(y t 11 - t 1110x t 3c 1c 2cc- 1c 11 10 1110 10 0 te )31 ()(y - t x tt (10e )(10e ) 1 - (1 - (1 t - t (10e )(10e ) (t)e -1(t)e (t)(t) p) t - is (t) 1(t) 1 (t) (t) 1 1 1 K 1 K 12pp 1p (p) 2 2 1 2 ppp H (t)e)h( - t t (t)e-(e(t)e*)(e)(*)()(y - 2t- t- 2t- t f tthtft (t)e(t)e )3(2 )(y)(y y(t) - 2t- t fx ttt (t)e)( - 2t tf 1Q )(2)(44 )(4)(y )(2)(y )()(y 0 222 000 2 0p 2 0p 2 0p teeteQQQ teQt teQt teQt ttt t t t 0 te)(y - 2t p t (t)e )3(2)(yy(t)(y - t ph ttt )()(f f(t) 21 tft )(2)(f )(1)(f 2 1 tt tt 1 1 e t) (p) 212 1 1/2 (p) 12 (p) )(u)(u u(p) 21 f p p pp f p f pp ppppp p p2 2 1 2/1 2/1 2 2 1 12 1 212 1 H(p) (t)2ee 2 1 )( )( 2t- t 2 1 - tth (t)e(e(t)1 *)(e2)(e 2 1 )()(*)()(y 2t- 2 t - 2t- 2 t - 1x tttthtft (t)e-e-(12(t)*)(e2)(e 2 1 )( 2)(*)()(y 2t- 2 t - 2t- 2 t - 2f tttthtft (t)e-e-2()(y)(y)y( 2t- 2 t - fx ttte- e- e(eee 2 2 t - (e e 2(t)*)(t)(* 0sinsin 1 coscoscos)( 0 2 0 22 0 ntnt n ntdtntdtntdttf fnt 2/00 02/ )( T TA tf AdtA T dttf T a T T0 2/0 0 2 )( 2 0 sin2 cos 2 cos)( 2 0 2/ 0 2/0TT T n n tn T A dttn T A tdtntf T a ,6 , 4 , 20 ,.5 , 3 , 1/2 1cos cos2 sin 2 sin)( 2 0 2/ 0 2/0 n nnA n n A n tn T A dttn T A tdtntf T b TT T n 0 0 2/2/TAT 2/2 0 2 2 1 1 ) 12sin( ) 12( 2 2 .5sin 5 2 3sin 3 2 sin 2 2 sin 2 )( n n n tn n AA t A t A t AA tnb A tf 4/34/0 4/4/ )( TT TTA tf AdtA T dttf T a T T T4/ 4/0 0 2 )( 2 2/sin 2sin2 cos 2 cos)( 2 4/ 4/ 4/ 4/0 n n A n tn T A dttn T A tdtntf T a T T T T T n 0 cos2 sin 2 sin)( 2 4/ 4/ 4/ 4/0 T T T T T n n tn T A dttn T A tdtntf T b 1 1 ) 12cos( ) 12( 2) 1( 2 .5cos 5 2 3cos 3 2 cos 2 2 cos 2 )( n n n n tn n AA t A t A t AA tna A tf 4/ /T T 2 2 AA A2 2 tn tn n 4/4/ n n tn t T T cos2n T T A ) 1 1 2 coscos t t) 1 1 t TT TtA tf 2/0 2/0sin )( ) 1(cos )1 (2)1 ( ) 1( )cossin( )1 ( )( )cossin( sin)( 1 222 22 2/ 0 22 2/ 00 n n A nT eA jne nT A jn ttjne T A dtte T A dtetf T F jn jn T tjn T tjntjn T n j A t jT A dteee jT A dtte T A F T tjtjtj T tj T 42 )( 2 sin 2/ 0 2/ 0 2/ 0 1 j A t jT A dteee jT A dtte T A F T tjtjtj T tj T 4 )( 2 )( 2 sin 2/ 0 2/ 0 2/ 0 1 1 4 ,.5, 30 ,.4, 2 )1 ( 2 n A jn n n n A Fn jTjT 0 3, ,.4, 2,.4, 2 t t jTjT A AT T 2 2 2/ 0 dtede t e e ) ) jt e e ,.5 . 2/0 4 02/ 4 )( Tt T A A Tt T A A tf ,.2, 00 ,.3, 1 4 )cos1 (2 )cos1 (cos)cos1 (cos 441 ) 4 () 4 ( 1 22 22 2222 2/ 2/ 2/ 0 0 2/ 2/ 0 0 2/ n n n A n nA n nA jn nA n nA jn nA dtAedtte T A dte t T A T dtet T A Adtet T A A T F T T tjn T tjntjn T T tjntjn T n )2() 1()(2)2() 1()1()( 2)(ttttttttf j t 1 )()( 2 1 )()( 2 )(2 1 )( 1 )( 1 )(2)( 2 2 2 jj jj jj ee j j e j e j e j e jj jF )1()1()1()1() 1() 1) 1() 1 d jdFj ttf d jdF tjtfjFtf )2/( 2 )2(, )( )(, 22 1 )2( )(2 )( )()2(jF d jdF jtft )2/( )2/( 2 )2()2(, 22 1 )2(jF d jdFj tftjFtf )()()( )( ,)( )( jFjFjFjj dt tdf tjFj dt tdf j jjj jjj ejFj ejjFejFjejF ejFjejFtftejFtftf )1 ()1 (,)1()1 ( j e e , ( ) F F( (F F( 1 (1 (ft ft ft ft )()()()()()(*)( 2 jFjjFjjFtftf 22 11 1 1 1 )()1 ( j j jj tet t )()( 1 1 )( 1 1 )( 2 2 tetf j jF j jF t 1 4 ,.5, 30 ,.4, 2 )1 ( 2 n A jn n n n A Fn 1 1 1 1 F F( ( ) ) )( ( j j )()F F()F F( () )( 2 )( 2 )2( )41 ( 2)(2)( 2 AjAj n n A nFtfF nn n ,.2, 00 ,.3, 1 4 22 n n n A Fn ,.2, 00 ,.3, 1)( 8 ) 12( ) 12( 4 2)(2)( 2 22 n nn n A n n A nFtfF n nn n HzfsTsTsrad ss m mm 100 , 10050 2 /100 HzfsTsTsrad ss m mm 200 , 200100 2 /200 HzfsTsTsrad ss m mm 100 , 10050 2 /100 HzfsTsTsrad ss m mm 120 , 12060 2 /120 m m 100 TsTs m T T m 5050 sTs s T 100100 T T T T T T s 2 )(2)()()(3)()(4)()( 2 jFjFjjYjYjjYj )(2)()(3)(4)( 2 jFjjYjj 1 2/1 3 2/1 3)(4)( 2)( )( )( )( 2 jjjj j jF jY jH )( 2 1 )( 3 teeth tt )1 ()( )(1( )/1( )(/1( )( )( )( 2 21 12 12 12 jRR jRRj jRjR jRjR jI jU jH s o K RR RR H 2222 21 22 2 22 1 2 )1 ()( ) 1)( )( 1, 1,1, 1 122112 2 2 RRRRRRR 0)(, 1)(H )()( )()( 2 21 tetftetf tt 2Res 2-s 1- 2 - dtdt)()( - 1Res s1 1 1 - dtdt)()( 0 - )2( 0 )2(2 2 0 )1( 0 )1 ( 1 s e eetesF s e eetesF ts tsstt ts tsstt 2Res1- 2-s 1 - s1 1 )()()( 21 sFsFsF -Res )-( s 1 dtdt)1() 1()( 1 1 - 1 1 ss st stst ee s e eettsF 1Res3- , 3s 1/2 1s 1/2 3)1)(s(s 2s )(sF (- t)-(t)( 3 2 1 tt eetf 2Res , 3s 2/5 2s 3/5 3)2)(s(s 1s )(sF (t) 5 2 5 3 )( 32tt eetf ( ( s s 1 1 1 - 1 - s s s -Res 2-1 1 dt-dtdt)()( -Res )1 ( cossindtsin)( -Res )-(1 dtdt)()( 2 2 1 1 -0 2 1 1 00 22 2 2 0 22 2 0 00 ss stst ststst f sst st d sT T stst a ee ss e s e eeetfsF s e tts s e e tsF s e eetfsF )e-(1 2s 1 e 2s e 2s 1 F(s)1)-(t-(t)( 2(s-s - - 2 2t etf )e-1 ( ss 1 s e-1 s e-1 js e-1 js e-1 2 1 s e-1 F(s) 2)-(t-(t)1(sin)( 2s- 2222 2s-2s-)j2(s-)j2(s-2s- j ttf 2 0 2 2 0 0 2 2 s F(s)(t)cos)( s t dt d tf 1 Res Res 1 1 2 s s 1 22 0 s 1 F(s) 1 sin)( ss tdttf t ) 2 2s F( 2 1 )2( 2 tfe t 2s-22 (2s)eF2)2( 2 1 )2() 1 2 1 ()2(tfttft ) 3 1s (F 3 1 )3( tfte t s aa b tafbatf a b - )e a s F( 1 )()( 0 )(*)()( n a nTttftf a a s a )e 2 - - 2 T - - 2 T - 2 T - e1 1 e-1 e-1 e-1 1 )e-(1 1 F(s) )e-(1 1 )2/()()( T s sT s sT s s a s ss s Ttttf 0 )2(*)()( n c nttftf s c tttf - e-1) 1()()( ss s -2- - e1 1 e-1 1 )e-(1F(s) 1 106 3)s(s )()()0( 2 0 limlimlim ss ssFtff sst 0 106 3)s(s )()()( 2 00 limlimlim ss ssFtff sst )(10)(5)()( 3 10 2 5 1 65 55s 1 65 1s 32 22 2 tetettf ssssss tt 2 4/1 2 4/12/1 )4( 2 2 jsjssss )(sin)()2cos1 ( 2 1 )(2cos 4 2 )( 2 1 )( 2 ttttttttf 0 0 m m ( 1 106106 3) 6 6 6 6 6 s(ss(s 2 2 0 0 lim m s s s s 2222 4/14/14/4/ j ) 1( 1 jsjsjs j jss )(cos 2 1 )(2/cos 2 1 )(ttttttf )1 ( )1 ( 11 )1 ( )1 ( )1 ( 1 22 s ss s s e eses e es ) 12()2( ) 12()2(*)() 1()(*)2(*)()( 0 00 n nn ntnt ntnttttntttf 1 1 )(, 3 3 2 2 1 1 )()()()( s sF sss sYsHsFsY ff )()21 ()( 3 2 2 11 3 6 2 2 2 1 )( 1 )()()( 3 6 2 2 2 3 ) 1( 3 2 ) 1(2 1 )( )( )( 32 teetg ssssss sY s sFttf sss s s s sF sY sH tt f f ) ) t ( s s 1 1 )( ) s ( 3 3 2 3 s )0()()()2( )0()()()()2( 0)()(2)0()( )()()(2)0()( 212 121 1222 2111 ysYsYs ysFsYsYs sYsYyssY sFsYsYyssY )()( 12 52s 12 2)F(s)(s )( )()( 12 4s 12 F(s) )0()0(2)(sF(s) 12 1 )( 1x1f221 2x2f 22 12 2 2 sYsY ss sY sYsY ss yy s sY 3s 1/2 1 3/2 12 52s )( 3s 1/6- 1 1/2- s 2/3 34ss 1 12 2)F(s)(s )( 3s 1/2- 1 3/2 12 4s )( 3s 1/6 1 1/2- s 1/3 34ss 1 12 F(s) )( s 1 F(s)(t)f(t) 2 1x 22 1f 22x 22 2f ss sY sss sY ss sY sss sY )() 2 1 - 2 3 ()(y, )() 6 1 2 1 3 1 ()(y )() 2 1 2 3 ()(y, )() 6 1 - 2 1 3 2 ()(y 3 2x 3 2 3 1x 3 1 teetteet teetteet tttt f tttt f )(U 42 2 )(U s 2 s ss s s )()(ttus 313142 2 )()(U 21 2 js K js K ss s sHs , ), ), ) 2 2 3 ()( 2 1 1 2 2 e e()( ee t t t e 6/ 2 6/ 1 3 2 , 3 2 jj eKeK )(t 3sin-t 3cos3 3 2 )() 6 t 3cos( 3 4 )(teteth tt )()(ttus 313142 2 )()(U 21 2 js K js K ss sHs 2/ 2 2/ 1 3 1 , 3 1 jj eKeK )(t 3sin 3 2 )() 2 t 3cos( 3 2 )(tetetg tt 16 6 1 1 1 11 1 1 1 1 1 1 sRsC R sC R sC R Z 13 3 1 1 1 22 2 2 2 2 2 2 sRsC R sC R sC R Z )(U 4/1 1 24 1 2 1 )(U 312 6 )(U)(U sss 21 2 s s s s s s ZZ Z s )( 6 1 )(t 6 2 )( 6 1 )( 6 1 )(t 2 1 )(*)()( )( 24 1 )(t 2 1 )( 4/4/ 4/ tetettthtg teth tt t )(U)(U)(U s 21 2 s 21 2 s RR R s ZZ Z s )( RR R )(*)()( )(t RR R )( 21 2 21 2 ttthtg th )()()(1 )(Y 21 sHsFsHs )2-(t)()( )1 ( )()(1 F(s) Y(s) )( 2 21 tth s e sHsHsH s )()(tttf)()()(Y, 1 )( f 2 sHsFs s sF 3 2 )1 ( s e s )2-(t2 2 1 )(t 2 1 )( 2 2 tttyf )( )( 1 1 )( )( )()( 2( )( ) ) ) ) )(s)X)(Y 3Y(s)2F(s)(s)X(s)sX 2Y(s)3F(s)(s)sX 2 12 1 sFs )( 32 )(1 23 )()(3)(2 1 )( 2 )( 31 )( 22 sY ss sF ss sFsYsF s sY s sF ss sY 23 32 F(s) Y(s) )( 2 2 ss ss sH )(3)(2)(t)(2)(3)(tftfftytyty2)(t2)(t(3)(3) 653224321 ,HHHHLHHHL 1, 175211 HHHHP 6532432 1HHHHHHH 6532432 7521 1 )( HHHHHHH HHHH P sH i ii )34(1 2 34 2 ) 3)(1( 2 )( 21 21 2 ss ss ss s ss s sH )12167(1 2 12167 12 )65)(2( 12 )( 321 321 23 2 2 2 sss sss sss ss sss ss sH 4(14( 2 2 1 1 2 2 1 2 2 4( 4( ss2 2 321 1 23 22 814718147)4)(2)(1( )( sss s sss s sss s sH 3 2/1 1 2/1 3 1 1 2 ) 3)(1( 2 )( ssss s ss s sH 1 1 1 717 1 1 7 7 1 s s 2 2 )(, 1, 1)(, 2 2 )( s s sHAH s s AsH aaa )2)(1( 1 )(, 1, 2/1)0(, )2)(1( 1 )( ss s sHAH ss s AsH bbb j j j j a js aa e Be Be eH j j sHjH a )( )(, 2 2 )()( , )2)(1( 1 )()( jj j sHjH js bb 4, 1 )( 2)( 21 21 Be BBeAe Ae eH j jj j j b b , 23)( 2 1 sssA 0 02 03 2 1 0 02 03 2 1 0 03 01 3 1 2 03 21 3 1 03 21 02 02 02 02 dd cc dd cc 23 3 3 3 3 3 1 1 1 1 , 2 0 2 2 0303 2 2 2 basssA bass s sH 2 2 )(, 1 )( 0 0 0 1 0 0 0 1 0 0 01 1 0 1 1 0a b1 02 02 02 02 b a b d b a b d aa cb a b a c dd cc )8()2()()( 1 kkkfa 404 044 )()( 2 kk kk kfb )6()2(2)2()()( 3 kkkkfc )() 1()()( 4 kkfd k 8 2 , 4 1 0 0 40 0 0 k k k k 2)2)2)2(22()2)2)2)2 4 5 8 522 , 5 8 0 0 , 4 , 4 1 0201 , 4 , 2 0201 8 2 , 4 2 0201 k ii ikfifikfifkfkfkf 0 212121 )()()()()(*)()( )0( 1 1 11 00 )( k kk k k k i i k k i iki ki k kik i kkik k k kfkfkf 02 2/11 2 22 02 2/11 1 22 )(*)()( )( 0 1)( 21 fk)kfkkfk 2 f f f f ) i 1 1 i i 2 2 2 0 (ik k ik ,.0 , 5 . 1 , 5 . 1 , 5 . 0 , 5 . 0 ,0, 0 , 0 , 1 , 0.)()( 0 12 k kfkf 3210 1 2 3 5 . 15 . 15 . 05 . 0 0 0 0 1 5 . 45 . 45 . 15 . 10003 33110002 5 . 15 . 15 . 05 . 00001 00000000 5 . 15 . 15 . 05 . 00001 33110002 5 . 45 . 45 . 15 . 10003 5 . 45 . 7 6 4 0 4 8 3 5 . 05 . 00123 ,.0 , 5 . 4 , 5 . 7 , 6 , 4 , 0 , 4, 8, 3, 5 . 0, 5 . 0, 0 , 1, 2, 3, 0.)( 0k kf 4 5 1111 1 0 3210 1 2 3 3210123 3210123 3210123 3210123 3210123 3 5 6 6 5 0 5- 6- 6- 5- 3- 0k ,.0 , 3 , 5 ,6, 6 , 5 , 0 , 5.,6, 6, 5, 3, 0.)( 0k kf 12 2 2323 3 3 3 3 3 10 0 0 0 1 1 12 2 2 1 1 1 45 . 7 65 . 7 ,.0 , 5 . 4 , 5 .,.0 , 5 . 4 1 0 10 )()()()()( 2 kdfkcEfkbykaEykyE baEE dcE kf ky EH 2 )( )( )( )(3)()(5)(4)( 2131 kfEkfEkyEkyEky 54 3 541 3 )( )( )( 23 2 31 21 EE EE EE EE kf ky EH )1)(1(1) 1(22)(, 22 1 )( 22 2 jEjEEEEEA EE E EH 4 3 2, 1 21 j ejr 4 3 sin 4 3 cos)2()( 21 k c k cky k x 2, 02 2 2 2) 1 (, 0)0( 2121 cccycy xx 22 2 )2(44)(, 44 2 )(EEEEA EE E EH k x kccky)2()( 1110 2, 12)2() 1 (, 1)0( 1110111010 ccccycy xx )1)( 11 )(),( 1 )( 2 0 2 1 2 31 2 31 EEH E EE E EE EHkf E EE ky )() 1()( 2 1 )() 11 ( 2 1 1 )( 0 2 0 kkkh E E E E E E EH k )2() 1(1 2 1 )()( 2 2 0 2 0 kkhEEH k kk )2() 1(1 2 1 )() 1(1 2 1 )( 2 kkkh kk ) 1()()() 1( 2 1 2 1 ) 1()() 1(1*)()(*)()(kkkkkkkkhkkg kk )()() 1( 2 1 2 1 kkk k )21 ( 6 . 0 10 5 . 0 10 )5 . 0)(6 . 0( 2211 3 . 01 . 0 2211 3 . 01 . 01 2211 )( 1 221 21 E E E E E EE E EE E EE EE EH ) 1()6 . 0(5 . 020)()6 . 0(5 . 010)( 11 kkkh kkkk ) 1()6 . 0(145 . 025 11 k kk ) 1()6 . 0(14)5 . 0(25*)8()()(*)()( 11 kkkkhkfky kk f 9 1 1 1 9 1 1 1 )( 6 . 01 6 . 01 14)( 6 . 01 6 . 01 14)( 5 . 01 5 . 01 25)( 5 . 01 5 . 01 25 kk k kk k kk k kk k kkkk )9()6 . 0(175. 8) 1()6 . 0(175. 8)9()5 . 0(5050) 1()5 . 0(5050 88 kkkk kkkk ()6 . 0 )6 . 0 1 1k k 5 . 0)(6 . 00( 22 2 )(6 .( )(6)(6 .( )6 . 0( 1 1k k ) 1) 1 1 1 2 1 )()()(2)( E EHkfkykEy k x cky)2()( 0)0(cyx 0k ) 1()2()( 1 2 )( 1 kkh EE E EH k 1 1 1 1 )( 2 1 )2( 1 ) 1()2(*)()(*)()( kk k k kk f k e e kkekhkfky )()()()(kykykyky ffx )3)(2(65651 1 )()()()(6)(5)( 2 2 2 21 1 121 EE EE EE EE EE E EHkfEkfkyEkyEky )()3()2()( 21 kccky kk x ( ( ( (h h( ( ( f(*)(*)( ()2() 1 1 ()2( k )()2(3)3(4)( 2 3 3 4 )(kkh E E E E EH kk )( 21 )2(1 3 31 ) 3(1 4)()2(3) 3(4*)()(*)()( 11 kkkkhkfky kk kk f )()2(2) 3(3k kk )()2(2)3(3)()3()2()()()( 21 kkcckykyky kkkk fx 1689274)2( 123)0( 21 21 ccy ccy 7 7 2 1 c c )()3(4)2(5)(kky kk )2(2) 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