第二章信号与系统

1、描述描述LTILTI连续系统的数学模型是常系数线性微连续系统的数学模型是常系数线性微分方程，一般形式为分方程，一般形式为11101110(n)(n)n(m )(m)mmy(t ) ay(t )a y(t ) a y(t )b x(t ) bx(t )b x(t ) b x(t )1.1.齐次通解齐次通解11100(n)(n)ny(t ) ay(t )a y(t ) a y(t )特征方程特征方程11100nnnaaa解得特征根解得特征根12 n按照按照P53P53页表页表2-12-1写出通解形式写出通解形式代入初始条件，确定待定系数，得到通解表代入初始条件，确定待定系数，得到通解表达式达式)(

2、t )(th)(tx)(ty)(t ( )s tdttdt)()( ( )( )ds th tdt /4( )(1) ( )ts tet /4/4/4( )1( )(1) ( )( )41( )4tttds th tetetdtet sCCutudttduRC )()()()()(tthdttdhRC )()()(4tthdttdh ( )sut ( )( )Cuth t (0 )0Cu 0)()(4 0 thdttdht 0 )(4/tKetht 000000)()()(4dttdtthdtdttdh 1)(| )(40000 dtthth4/1)0( h 0 41)(4/tetht4/1)

3、0( hK)(41)(4/tetht 1)0()0( 4 hh0)0( h)()()(tcxtbytya )()()(tctbhtha 0)()( 0 tbhthatabs/ )()(tKethtab Khh )0( 0)0(cdttbhdttha 0000)()(ach/)0( )()(teacthtab )()()()(012txtyatyatya )()()()(012tthathatha 0)()()( 0012 thathathat21,sststseKeKth2121)( 1)()()(000001002 dtthadtthadttha)(),(thth 2/1)0(0)0()0(

4、ahhh )()()()()(01012txbtxbtyatyatya )()()()()(01012tbtbthathatha )()()()(000102tthathatha )()()(0001thbthbth )(2)()(3)(4)(txtxtytyty 0)(3)(4)( 0000 thththt3-1,21 ss)()()(3210teKeKthtt )()(3)(4)(000tththth 1)0( , 0)0(00 hh5 . 0 , 5 . 021 KK)()(5 . 0)(30teethtt )()(5 . 0)(2)()(300teethththtt )()(1thtg

5、 nnnthnxtyntgnxtx)()(lim)()(1)(lim)(00)(*)()()()(thtxdthxty记记为为 )(*)()(thtxty dthxthtxty)()()(*)()()(tx)(ty( )(1) ( )ts tet ( )( )( )th ts tet 1)(1)(*1)(*)()()()( ttttCdedtetethtxtu )(*)()()()(ttxtdxtx dthxthtxty)()()(*)()( dthxthtxty)()()(*)()( x(t)t020.5-0.5 h(t)t00.512 x( )020.5-0.5 h( )00.512 h(

6、- ) 00.5-1-2 h(t- ) 00.5t-1t-2 00.5-0.5t-1t-2 x( ) h(t- )( )( ) ()y txh td 00.5-0.5 x( ) h(t- )00.5-0.5 x( ) h(t- )00.5-0.5 x( ) h(t- )( )( ) ()y txh td x(t)t020.5-0.5 h(t)t00.512 y(t)t011.50.52.5x(t)t022 h(t)t024 x( )h(1- )t022-31 x( ) h(t- ) 022)2()( 2)( tttx )4()(5 . 0)( tttth dttdttdttdttdthxtht

7、xty)4()(2()()(2()4()()()()()()(*)()()(5 . 0)()()()(20tttdtdttt )4()85 . 0()4()()4()(240 tttdtdttt )2()225 . 0()2()()()(2(22 ttttdtdttt )6()625 . 0()6()()4()(2(242 ttttdtdttt )6()625 . 0()2()225 . 0()4()85 . 0()(5 . 0)(2222 ttttttttttty )()(*)(txttx )()(*)(00ttxtttx )()(*)(00ttxtttx )()(*)(txttx 并联级联

8、)(*)()()()()(thtxtyjiji x(t)t020.5-0.5 h(t)t00.512 x (t)t00.5-0.5(2)(2) h(-1)(t)t00.512 y(t)t010.51.5-12.5)()(1tth )1()(2 tth ?)( th)1()2()1()1()1()1(*)()1(*)()1(*)()(*)()(*)()(*)()(21 tttttttttttttthtthtth 0)()1( kaykyzizi )0()1()2( 1)0()1( 02ziziziziziyaayykayyk )0()(zikziyaky 0)()1( kaykyzizi0 a

9、a kkziAaAky )()0(ziyAAayzi 0)0(kziziayky)0()( 0) 0() 1 () 1()(011 zizizinzinyayankyankya)1(,),2(),1(),0( nyyyyzizizizi )() 2() 1 (/ 1) 1( 1)1() 1 () 0 (/ 1)( 0110110nyayayaanyknyayayaanykzinzizinzizinzizinzi )(kyzi0) 0() 1 () 1()(011 zizizinzinyayankyankya00111 aaaannnn n ,21 nikiiknnkkziAAAAky12211

10、)( )1(,),2(),1(),0( nyyyyzizizizi)1()1()0(1122111221121 nyAAAyAAAyAAAzinnnnnzinnzin 0)(6)1(5)2( kykykyzizizi2)0( ziy3)1( ziy0652 3, 221 0 32)(212211 kAAAAkykkkkzi 13332)1(2)0(212121AAAAyAAyzizi0 323)( kkykkzi21, je|1 je |2 jeAA|1 jeAA |2)cos(|2|)()(2211 kAeeAAAkkjkjkkk0)(2)1(2)2( kykykyzizizi2)0( zi

11、y4)1( ziy0222 0 )(2211 kAAkykkzi 4/324/31211211 jjejej 4/24/122112121214) 1 (2) 0( jjziziejAejAAAyAAy0 )443cos()2(22)cos(|2)( kkkAkykkzi )()(6)1(5)2(kxkykyky 1)1( y2)2( y)()(kkx 0652 0 )(2211 kAAkykkzi 3, 221 0)1()1(6)0(5)1( xyyy1)1()1( , )0()0( yyyyzizi1)0()0(6)1(5)2( xyyy3/2)0()0( yyzikimkikikk 1,

12、 0)(8)1(12)2(6)3( kykykyky1)1( ziy2)2( ziy0)0( ziy0812623 )( 21三三重重 0)2()2()2()(23212321 kkAkAAkAkAAkykkkkkkzi 43,45, 0321 AAA0 )2)(4345()(2 kkkkykzih(k)1(3)(2)( kxkxky)1(3)(2)( kkkh )()() 1() 1()(011kxkyakyankyankyann 0 0)()()() 1() 1()(011kkhkkhakhankhankhann 1210121010nkn, n, n,h()h( )h()h(n)kh(n

13、 )a 分分别别令令，可可得得令令得得 nnnanhnhhhkhakhankhankha1)( , 0) 1() 2() 1 (0)() 1() 1()(011)()(6) 1(5)2(kxkykyky 0 0)()()(6)1(5)2( kkhkkhkhkh 1)2( , 0)1(0)(6)1(5)2(hhkhkhkh 3/12/11)2( , 0)1(32)(2121AAhhAAkhkk)1()23()1()331221()(11 kkkhkkkk )() 1() 1()()() 1() 1()(011011kxbkxbmkxbmkxbkyakyankyankyammnn 0 0)()()

14、() 1() 1()(00001010kkhkkhakhankhankhann )() 1() 1()()(0001010khbkhbmkhbmkhbkhmm )(3)2()(6) 1(5)2(kxkxkykyky 0 0)()()(6)1(5)2(0000kkhkkhkhkh )1()23()(110 kkhkk ) 1()236()() 1()23( 3) 1()23()(3)2()(11111100 kkkkkhkhkhkkkkkk ) 1(2) 2(7)(1 . 0) 1(7 . 0) 2( kxkxkykyky)()(kkx 2)0( ziy4)1( ziy0)(1 . 0)1(7

15、. 0)2( kykykyzizizi01 . 07 . 02 2 . 0, 5 . 021 0)2 . 0()5 . 0()(212211 kAAAAkykkkkzi 101242 . 05 . 0)1(2)0(212121AAAAyAAyzizi0 )2 . 0(10)5 . 0(12)( kkykkzi 0 0)()()(1 . 0)1(7 . 0)2(0000kkhkkhkhkh )1()2 . 0(350)5 . 0(320)(0 kkhkk )()2 . 0(2)5 . 0(5)1(2)2(7)(00kkhkhkhkk )()2 . 0(5 . 0)5 . 0(55 .12)(*)

16、()(kkhkxkykkzs 0 )2 . 0(5 .10)5 . 0(75 .12)()()( kkykykykkzszi nnknxkxkxkxkx)()() 1() 1 ()() 0 () 1() 1()( nzsnnkhnxkynknxkx)()()()()()( )()(khk )()()()(nkhnxnknx )(*)()(khkxkyzs )(kx nzsnkhnxkhkxky)()()(*)()(nx(k )*(k )x(n) (kn)x(k ) nzsnkhnxkhkxky)()()(*)()()(nxn0 1 2 31234)(nhn0 1 2123)( nh n01 2 1234 ,15,19,13, 7 , 2)(*)()( khkxky)()(nhnx n020 k)1()(nhnx n0 1341 k)2()(nhnx n0 1 216 62 k41519137286421296343211324321 4 ,15,19,13, 7 , 2)(*)()(