3. Nyquist sampling theorems X(n) X(j9) Q-9,≥g2 29 3①.Ω ON) X(j9) C23-2x<g 3203
3.Nyquist sampling theorems s −N N s −N N
Nyquist sampling theorems let x(t be a band lim ited signal with XC(9)=0.921N then x(t)is uniquely det er min ed by its samples xn]=xC(n7),n=0,+1,+2 ≥2N,atis (,=7)220m(=7)22/N Q2(/2: nyquist frequency 2Q2N: nyquist rate Q2>222N: oversampling Q2. <2Q: undersampling 18
c N c X j let x t be a band ited signal with ( ) = 0,| | ( ) lim undersampling oversampling nyquist rate nyquist frequency s N s N N s 2 : 2 : 2 : / 2 : [ ] ( ), 0, 1, 2, ( ) det min x n = x nT n = then x t is uniquely er ed by its samples c c s N s N s N N f T or f T if that is ) 2 1 ) 2 , ( 2 ( , = = − Nyquist sampling theorems:
Haojie) =g2 Ant ample AD Discrete-time D/A Compensated aliasing a reconstruction filter hold converter m(心心pt 50 HijO T T Figure 4.41 Digital processing of analog signals
Figure 4.41 Digital processing of analog signals c = s / 2 H ( j) aa
examples of sampling theorem (1) The highest frequency of analog signal which wav file with sampling rate 1 6kHz can show, is: 8kHZ The higher sampling rate of audio files, the better fidelity
examples of sampling theorem（1） 8kHz The highest frequency of analog signal ,which wav file with sampling rate 16kHz can show ， is： The higher sampling rate of audio files, the better fidelity
数字电话中的音频信号 CD中的音频信号 单个样本 单全样本: 每千分之 每1/1000 秒有8个抽 秒有44个 抽样 0时间(秒)0.00600070.01 0时间(秒)00060.0070.01