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
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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 [ ] − =
