第二章信號(hào)與系統(tǒng)

1、描述描述LTILTI連續(xù)系統(tǒng)的數(shù)學(xué)模型是常系數(shù)線性微連續(xù)系統(tǒng)的數(shù)學(xué)模型是常系數(shù)線性微分方程，一般形式為分方程，一般形式為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.齊次通解齊次通解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頁(yè)表頁(yè)表2-12-1寫出通解形式寫出通解形式代入初始條件，確定待定系數(shù)，得到通解表代入初始條件，確定待定系數(shù)，得到通解表達(dá)式達(dá)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記記為為 )(*)()(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 并聯(lián)級(jí)聯(lián)

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 分分別別令令，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)(*)()(