离散时间信与系统课件

1、1,0( )0,0nnn1,0( )0,0nu nn101( )00NnNRnnnN或0( )()( )( )(1)( )( )()kNu nnknu nu nRnu nu nN nAanx0( )00nanx nn0,jjeaaeAA 0000cossinnnj njnjnx nA eaeA aeA anjn1a2 rnjjnnrjeAeAenx2200r200和22, 0,或02T000cos()cos()AnAnN02Nk2( )nSx n( )() ()mx nx mnm kx nx knk1()0mnnmmn( )( ) ()0 x nmnx mnmmn( )( ) ()mx nx

2、mnm( ) ( )() ()my nT x nTx mnm( ) ( )h nTn( )( )()my nx m Tnm()()Tnmh nm( )() ()( )( )my nx m h nmx nh n对序列对序列xn和和hn进行卷积运算，首先将进行卷积运算，首先将xn分解分解成脉冲和的形式，然后将每个脉冲分别作用到成脉冲和的形式，然后将每个脉冲分别作用到hn上得到响应，最后将响应累加起来即得到卷积结上得到响应，最后将响应累加起来即得到卷积结果。因为该过程需要运用叠加定理，所以卷积运果。因为该过程需要运用叠加定理，所以卷积运算只能用于线性时不变系统。算只能用于线性时不变系统。203 x

3、nxnx nx n强调：只有线性时不变系统才可以应用单位脉冲响强调：只有线性时不变系统才可以应用单位脉冲响应卷积输入信号来表示结果。应卷积输入信号来表示结果。203 y nyny ny n*nxnhnhnxkknhkxnhnx*knm*nxnhmhmnxnhnxm)*)(*2121nhnxnhnxnhnhnxknm( )kSh k ( )( ) ()( )kmy nh k x nkmh k ()( )0()( )0( )0hnh nhnx nh n2( )(0)() ( )( )kkh kyxk h kSh kdnnnhothersMnMMMknMMnhMMk0111121212121nknu

4、nnknh0001 1nnnh 1nnnhnjenxnh() ( )jn kj nj kkky nh k eeh k ekkjjwekheH)(njjeeHny)()(jweH)()()(jwIjwRjwejHeHeH)()()(jweHjARGjwjweeHeH 1,2,3,4,5,( 11)h nh51() jwj kj kkkH eh k eke-10-8-6-4-20246810246810121416()jH e()( )jj nnX ex n e1( )()2jj nx nX eed)()()(jwIjwRjwejHeHeH)()()(jweHjARGjwjweeHeH)(jweH

5、()jwARG H e, deemxdeeXnxnjnnjnjj21)(21 demxmnjn)(21)()(sin21)(mnmnmndemnj mxmnmxnxn*nxnxee*nxnxoonxnxnxoe)(21*nxnxnxe)(21*nxnxnxojeXnx*nnjjenxeX)(*nnjjenxeX)( x n* x n jx nX e设， x n* x njeXnx* jx nXejeXnx*jeXnx*jxnXejeeXnxRe-10-8-6-4-20246810246810121416182022-10-8-6-4-20246810246810121416182022jeXn

6、xjeeXnxRejeXnxjeeXnxRe-2-1.5-1-0.500.511.52-4-3-2-101234-2-1.5-1-0.500.511.52-4-3-2-10123421Re*nxnxnxjejjeXeXeX*21-10-8-6-4-20246810246810121416182022-10-8-6-4-20246810246810121416182022频 率幅度jeXnxIm jojx nXe21Im*nxnxnxjjojjeXeXeX*21-2-1.5-1-0.500.511.52-4-3-2-101234-2-1.5-1-0.500.511.52-4-3-2-101234

7、21Im*nxnxnxjjojjeXeXeX*21jeXnxIm jojx nXe)(21*nxnxnxeRe*21jjjeXeXeX-10-8-6-4-202468100510152025-10-8-6-4-20246810246810121416182022-2-1.5-1-0.500.511.52-4-3-2-101234jeXnx1*Re2jjjX eXeX eRejX e-2-1.5-1-0.500.511.52-4-3-2-101234)(21*nxnxnxoIm*21jjjeXjeXeX-10-8-6-4-202468100510152025-10-8-6-4-202468102

8、46810121416182022Im*21jjjeXjeXeX-2-1.5-1-0.500.511.52-4-3-2-101234-2-1.5-1-0.500.511.52-4-3-2-101234ImjjX e/ 2/ 2或者-jeXnx*nxnx*jjeXeXReRejjeXeXjjX eX eIm Im jjX eX e jjX eX e jeXnxjeYnyjjebYeaXnbynax j nj nj nnnj nj nnnax nby n eax n eby n eax n eby n ejnjdeXennxdjeXnx-2-1.5-1-0.500.511.52-4-3-2-101

9、234-2-1.5-1-0.500.511.52-4-3-2-101234jeXnxjnjdeXennxdjeXnx)(00jnjeXnxe-2-1.5-1-0.500.511.52-4-3-2-101234-2-1.5-1-0.500.511.52-4-3-2-101234jeXnx)(00jnjeXnxe0jeXnx jeXnx-2-1.5-1-0.500.511.52-4-3-2-101234-2-1.5-1-0.500.511.52-4-3-2-101234jeXnxjeXnx jeXnxdedXjnnxj-10-8-6-4-20246810246810121416182022-10-

10、8-6-4-2024681020304050607080jeXnxdedXjnnxjjeXnxdeXnxEjn2221 deYeXnynxjjn*21能量密度谱能量密度谱能量有限信号能量有限信号jeXnxjeYny* jjeYeXnynx* jjkeYeXknykx* deeYeXknykxnjjjk*21 deeYeXnkykxnjjjk*21 deYeXkykxjjk*21jeXnxjeHnh*nhnxny jjjeHeXeY nknjnnjjeknhkxenyeY mkkjmjmkkmjknmeemhkxemhkx jjmkkjmjeYeHekxemh*nhnxnydnnnhdnjjeeH jjjeHeXeYdnjjjeeXeYjeXnxjeWnwnwnxnydeXeXeYjjj21dedeXeXdeeYnynjjjnjj212121 2121dedeXeXnjjj2121deeXdeeXnjjnjjnwnx 5nuanxn 555nuaan5511jjjeaeaeX4 32 143210nanananananuan443322110011jjjjjjjeaeaeaea