Chapter 2 Discrete-time signals and systems 2.1 Discrete-time signals sequences 2.2 Discrete-time system 2.3 Frequency-domain representation of discrete-time signal and system
1 2.3 Frequency-domain representation of discrete-time signal and system Chapter 2 Discrete-time signals and systems 2.1 Discrete-time signals:sequences 2.2 Discrete-time system
2.1 Discrete-time signals: sequences 2.1.1 Definition 2.1.2 Classification of sequence 2.1.3 Basic sequences 2.1.4 Period of sequence 2. 1.5 Symmetry of sequence 2.1.6 Energy of sequence 2. 1. 7 The basic operations of sequences
2 2.1 Discrete-time signals:sequences 2.1.1 Definition 2.1.2 Classification of sequence 2.1.3 Basic sequences 2.1.4 Period of sequence 2.1.5 Symmetry of sequence 2.1.6 Energy of sequence 2.1.7 The basic operations of sequences
2.1.1 Definition <n<+ Enumerative representation EXAMPLE xn]={1,2,1.2,0,-1,-2,-2.5},-1≤n≤5 xn]=0.9c0s(0.2m+7/2.0≤n<10 Function representation
3 2.1.1 Definition x = x[n] − n + EXAMPLE x[n] ={1,2,1.2,0,−1,−2,−2.5},−1 n 5 Enumerative representation x[n] = 0.9 cos(0.2 n + / 2),0 n 10 n Function representation
0.5 0 -0.5 6 0 10 Graphical representation
4 - 2 0 2 4 6 - 3 - 2 - 1012 0 5 10 - 1 -0.50 0.5 Graphical representation
Generate and plot the sequence in MATLAB n=-1:5 X=[1,2,1,20,-1,-2,2.5] stem(n, x, n=0:9 y=0.9.^n.*cos(0.2*pi*n+pi2) stem(n,y,)
5 n=-1:5 x=[1,2,1.2,0,-1,-2,-2.5] stem(n,x, '.') n=0:9 y=0.9.^n.*cos(0.2*pi*n+pi/2) stem(n,y,'.') Generate and plot the sequence in MATLAB
x[]=x() EXAMPLE Sampling the analog waveform 32 a Figure 2.2 256 samples
6 Figure 2.2 EXAMPLE Sampling the analog waveform x[n] x (t)| x (nT) = a t=nT = a
Display the wav speech signal in ULTRAEDIT tt32-[D:11音频视频w异常停止时奏幻想空间221hWAW File Edit Search Project View Format Column Macro Advanced Window Help ◆口日日|舀|蛐川| 回的阳日田号|。|? 异幂停止时奏想到间2twAL 0oooo0h:52494646B816000057415645666D7420:RIFF?.. AVEIRo Filte Refresh 00000010h: 10 00 00 010 44AC0000 r,,D? 00000020h: 02 00 10 0Q 64 6174 61 8C OE 00 00 E5 F5 FF F7:.. data?.98? 030h:18 FA F FB98 FD FF FE170131034Ao5B106;.??.1.J.? 日0 pen Fi1e 0000040h:cA08cA0FcA169712170FFE 13E418TE17:??22.,?2~ 自p频视频异彩ooss:0764156415E418171DcA1D7E1EcA24:..,? 000:z33642A4Ak2164157E099704B2FrB2r1;23o3-32.2 0O00080h:B2E3FrE24BE232D9cBo7FD1E5D218D0;层?偎?彦 000000a0h c210C218c218C216c2cc277c318c9::289 00000090h: AB CD 65 C8 7F C3 CB C2 18 C2 18 C2 18 C2 18 C2: K 2E 22? 0o000Oboh:B2}EFr44BDB4BE24BEsE5EE32F57FB;畚融路鈇殄?3 00000c0h:cA011708170FFE139719cA1DB1223126:?,,.??2?18 00000doh: B1 29 CA 2B 97 2E 4A 2F B1 30 FE 2F FE 2F E4 2D 222J/22 000000e0h:TE2cFE283126FE21cA1D31184A13B10D:~,?15??1.J.? oo0oroh:1708cAo17FB32F598E4BE9B2E318DE;..?鯛额椴? 000010h:TFD898D365cF32cBB2C7E5c4cBc218c2:四航緲清乃?? 0000110h: 18 C2 18 C2 18 C2 7F C3 98 C5 65 C8 ES CB 18 D0 .??235152? 0000120h:FFD498Dk32E07FE67FEp7FF432FcE403:詞??? 00000130h:97BE4113118311F31267E2c7E33B137:??1,1.1~,~3? 00000140h: 97 3C 4A 3D FE 3D FE 3D FE 3D FE 3D FE 3D FE 3D ?J=2?222? 00000150h: FE 3D FE 3D FE 3D FE 3D FE 3D CA 39 9735 FE 2F :22222222 oo00160h:172BCA247E1E7E177E107E93103E5Fc;,+?~,~,~,~,1.妩 o0000170h:4BF?Frpo65 EB 7F E698 E1 CB DE FF DB32p9:K節?導崴??3 0o00180h:65D6FFD44Bp4FFp465p67rpa98Dk6spp;e訥?誅越? ooo0190h:EsEo18Es4BE9EsEE32 FS CB FA6400B106:避.錕殄?跛殷 000001a0h:FEC4A134A1AE41F7E25B129972E1732:?J,J.?~??.2 000001b0h:4A361739973c973c4A3D4A3D4A3D313B:J6.9?7J=J=J=1 0001ch:cA394A367E33972EB1291724311F3118;?J6~3??,氵1.1 oo001dh:E411E4oAE403E5 FC E5 F598Er4BE9rrE2:??妩艴槜κ? ooo1eh:65 DD CB D7Esp2B2cE32cB6sc84Bc6E5c4;e菟族也?到棋? 0000h:7Fc332c4E5c4B2C77 F CA FF CD7FD165D6;口?腻牟???裡? 200h: 4B DB 98 E1 E5 E7 32 EE 32 F5 7F FB 7E 02 CA 08: KME 222/8.2 00o00210h:CAoF1716171DFE21E426172B4A2F1732:? ?,+J/,2 00000220h:97354A36B137FE364A3631341732972E:?J6?2J614.2? 00000230h:172BTE2597204A1AB1144Aoc97044BFE;,+≈?J,2J.?K oo24h:B2F84BF0E5E798E1rFB6sD6cBDo4BcD;缠p疱綢?躇炙蘿 可匚 Pos: OH, 0, CO 开命多囵@‖圈1-,国回第章一回第章1异常,國!,〖多⑨s13-4
7 Display the wav speech signal in ULTRAEDIT
Display the way speech signal in COoLEDit 网 y“y心vE 国画回网幽四国哪醒画國国 回回回百四四圆四回画国国四四回回 The whole waveform O.9 毆圆0:00.357 Favorit口 ption=置 i ndow H1p 原國幽时四冖醒Fxl 国■ local Blowup 曰毆O:00.249m1
8 The whole waveform local Blowup Display the wav speech signal in COOLEDIT Display the wav speech signal in
2.1.2 Classification of sequence Right-side x[n]=0, for -o<n<N eft-side xn]=0,forN<n≤+∞ WO-SIde xn]≠0,for-∞0<n<+∞ Finite-length x[n]=0, outside of m1≤n≤N2 Causal xn=0, for n<0 Noncausal xn]≠0,orn<0
9 2.1.2 Classification of sequence Right-side x[n] = 0, for − n N x[n] = 0, for N n + x n for n [ ] 0, − +1 2 x[n] = 0,outsideof N n N x[n] = 0, for n 0 x[n] 0, for n 0 Left-side Two-side Finite-length Noncausal Causal
2.1.3 Basic sequences I Unit sample sequence 0 H≠0 n 2. The unit step sequence ≥0 0n<0 3. The rectangular sequence RIn 0≤n<N-1 other N-1 n
10 1. Unit sample sequence 2.1.3 Basic sequences 2．The unit step sequence 0 0 0 1 [ ] = = n n n 0 0 0 1 [ ] = n n u n 1 u[n] 0 n 1 δ[n] 0 n 3．The rectangular sequence 1 R[n] 0 N-1 n other n N R n N 0 1 0 1 [ ] − =