《7 信号与系统 周建华 光电学院教学课件》由会员分享，可在线阅读，更多相关《7 信号与系统 周建华 光电学院教学课件（23页珍藏版）》请在金锄头文库上搜索。
1、,7 Sampling,Emphases in this chapter: Impulse-train sampling. sampling theorem. the effect of undersampling: aliasing referring to: figure 7.2 7.3 7.4 formula 7.17.6,7 Sampling,7.1 Representation of a Continuous-time Signal by its Samples: The Sampling Theorem,7. Sampling,7 Sampling,7 Sampling,7.1.1
2、 Impulse-train Sampling,(1) Sampling,We wish to sample x(t).,a. Time domain:,7 Sampling,p(t): sampling function T: sample period s=2/T: Sample frequency,Figure 7.2,b. Frequency domain:,7 Sampling,7 Sampling,Figure 7.3,(2) (Shannon) Sampling theorem Let x(t) be a band-limited signal with X(j )=0 for
3、| M . Then x(t) is uniquely determined by its samples x(nT),n=0,1,2, only if s2 M, where s=2/T . 2M is called Nyquist Rate. ( Minimum distortionless sampling frequency ),7 Sampling,(3) Recovery,System for sampling and reconstruction:,7 Sampling,7 Sampling,Lowpass filter,Figure 7.4,7 Sampling,samplin
4、g,Lowpass filter,7 Sampling,例题： 已知某连续时间信号x(t)的持续时间为1分钟，它的频谱分量包含有直流到1000Hz分量，为便于计算机处理，对x(t)进行抽样以构成离散信号，求满足抽样定理的最少理想抽样点数。,7 Sampling,解：,7 Sampling,例题：已知信号x(t)，分别以抽样时间间隔T1，T2进行理想抽样，试画出抽样后所得序列的频谱图。,7 Sampling,解：因为x(t)的频谱X(j)如图所示：,当,，刚好没有重叠现象。,当,，有重叠现象。,7 Sampling,7 Sampling,Example: Consider the followi
5、ng system, with,7 Sampling,Question: Specify the range of value for the sampling period T which ensures that r1(t) is recoverable from r2(t). if T=0.05 second, sketch the spectrum of r1(t) and r2(t). Sketch and dimension a filter H2(j) so that y(t)=r1(t).,7 Sampling,Solution:,(a),7 Sampling,(b),7 Sampling,(c ),In order to y(t)=r1(t), then,以后内容不要求。,Problems: 7.1 7.2 7.3 7.6 7.9,7 Sampling,
