资源描述
234567891011121312,1()0,1nnx nn 2,0()1,0nny nnn12,13()(),1221,0nnnx ny nnnn 1412,13()(),1221,0nnnx ny nnnn 151612,1()0,1nnx nn 2,0()1,0nny nnn10,11()(),12(1)2,0nnx ny nnnn 1710,11()(),12(1)2,0nnx ny nnnn x(n)181912,1()0,1nnx nn 22,11(1)0,11nnx nn 20 x(n)22,11(1)0,11nnx nn 212212,1()0,1nnx nn 12,14()0,1nnx nn 232412,1()0,1nnx nn 12,1()0,1nnxnn25 设序列为设序列为x(n),则序列,则序列 (1.7)定义为对定义为对x(n)的累加,表示将的累加,表示将n 以前以前的所的所有有x(n)值求和。值求和。nkkxny)()(2627)()1(2)2()()1()()(2nxnxnxnxnxnxnx)2()1(2)()1()()()(2nxnxnxnxnxnxnx(按二项式定理展开按二项式定理展开)28(/),0,1,2,()0,x n m n ml lz nn其 它 2930312|()|nEx n32()()()()()my nx nz nx m z nm33341001()()()1nnnnmnmmmmaynxmzn maa aa 1001()()()1nnnnm nmmmmaynxm znm a a aa 35aaaaaanynnmmmnmn1)(144040aaaaaanynnmmmnmn 1)(144040410660()nnmkmnky naa47101066001nnnkkkkaaaaaa36370,00,1)(nnnmnmnmn0,1)(38 1,0()0,0nu nn1,()0,nmu nmnm(n)=u(n)-u(n-1)0()()()nkku nnkk39 1,01()0,NnNR n 其 它 NmNmnnR0)()()()()NRnu nu nN40()()nx na u n41 得到得到x(n)=Asin(n+)=/fs (线性关系线性关系)42 n用用表示表示()e(cosjsin)ecosejsinnnnx nnnnnjarg()j()()eeex nnnx nx n 43 为例讨论周期性为例讨论周期性()x n 44 kN2 ()5sin(3)4x nn45 任何任何k 都不能使都不能使N 为正整数,这为正整数,这时正弦序列不是周期序列。时正弦序列不是周期序列。3()2cos(7)4x nn3()2cos(7)4x nn 46()()()mx nx mnmmnmnnxmnmx,0),(=)()(47 4849 50):51 n(1)y(n)=2x(n)-3,n(2)y(n)=x(Mn),其中,其中M为正整数。为正整数。52 nm 为为任意常整数任意常整数 53 n(1)y(n)=2x(n)-3,n(2)y(n)=x(Mn),其中,其中M为正整数。为正整数。54 55()()(-)mx nx mn m()()()(-)my nT x nTx mn m()()(-)my nx m Tn m()()(-)()()my nx m h n mx nh n 56 5758h(n)=0,n0 ()()(-)()(-)nmmy nx m h n mx m h n m000()()(-)nmy nx m h n m59 1()()(-)()(-)()(-)mnmmny nx m h n mx m h n mx m h n m 60n(1)()=(+1)-();n(2)。61 62 63|()|nh n+|()|()()|()|()|M|()|mmmy nh m x nmh mx nmh m 64|()|nh n 1,()0()1,()0hnx nhn(0)()()|()|()|mmmyx m h nmhmh m 65 ()()my nx m1,0()()0,0mnny nu mn66 1|111,|1|()|,|1annnnnah naaa67 68 31()(1)(2)3022y ny ny n69:00()()(1.44)NMkrkra y nkb x nr0010()()()(1.45)krNMabaakry ny nkx nr:70 71720()0(1.46)Nkka y nk00Nkknkca120120(1.47)NNNNaaaa 73111221()(1.48)NnnnniiNNiy ncccc1211121111122311()(1.49)mnmnnnmmnnnnmmNN mNN my nc nc ncnccccc74 5)1(,0)0(0)2(6)1()(yynynyny 062122,3 nnccny3)2()(21121,1cc nnny3)2()(7500()()()()(1.50)MrrrNkkkb Dy nx nH D x na D20012201201212()111MrMrrMNNkNkkNNb Dbb Db Db DH Daa Da Da Da DAAADDD NkMrrrkknxDbnyDa00)()(7612121()()()()()()111()NNNiiAAAh nH DnnnnDDDh n22()()(1)()()1niiiiiiiiAh nnADDnAu nD 21()()()()()(1.51)Nniiiy nh nx nAu nx n1()()Nniiih nAu n77 h(n)-3h(n-1)+2h(n-2)=(n)2()3()2()()h nDh nD h nn2121()()()132121h nnnDDDD()(221)()nnh nu n2()()*()(221)()*()(23)()nnnh nh nu nu nu nnu n78 ()()nh na u nh(n)=ah(n-1)+(n)7980 ()()()()()()()(1.53)()()(1.54)aaaannanxtxtp txttnTxttnTxnTtnT 时时()()(1.52)np ttnT 1(j)(j)(j)2aaXXp81 j()esrtrrp tc222222jjj011()ed()ed111()edeTTssTTTsTrtrtrnrtcp tttnTtTTttTTTj1()esrtrp tT j12(j)Fe(jj)(1.55)srtsrrprTTWpWd WW+=-=-=-邋82 1(j)F()()(j)(j)21(j)(jj)1(jj)(1.57)aaaasrasrXx tp tXpXrTXrTn取样信号的频谱是连取样信号的频谱是连续时间信号频谱以取续时间信号频谱以取样频率为周期进行周样频率为周期进行周期延拓而成期延拓而成n频谱幅度是原信号频频谱幅度是原信号频谱幅度的谱幅度的1/T1/T倍倍83s。2sc 84n利用理想低通滤波器还原满足奈奎斯特取样定利用理想低通滤波器还原满足奈奎斯特取样定理的取样信号。理的取样信号。1212,|(j)0,|sasTH(j)F()(j)(j)(j)aaaaYy tXHX85n单位脉冲响应单位脉冲响应h(t)()()aax tx t22jj221()(j)ed(j)ed2sinsin(/)(1.59)(/)sssstth tHHtt Tt Tt()()*()()()d()()()d()()()d()()(1.60)aaaanaax tx th txh tx nTnT h tx nTnT h tx nT h tnT 86n内插函数内插函数 h(t-nT)sin()/()()/tnTTh tnTtnTT8788 89 90919293 9495 96求总和求总和 求总和求总和 97 9899 100101102
展开阅读全文