第七章课件奥本海姆本信号与系统 .pptVIP

7 Sampling 采样 Main Content 7.0 Introduction 7.1 Representation of A Continuous-Time Signal by Its Samples: The Sampling Theorem (p.516)（用信号样本表示连续时间信号：采样定理） 7.1.1 Impulse-train sampling (冲激串采样) 7.2 Reconstruction of A Signal From Its Samples Using Interpolation (p.522)（利用内插由样本重建信号） 7.3 The Effect of Undersampling: Aliasing （欠采样的效果：混叠现象） (p.527) Problems * * * * * * * The sampling theorem (抽样定理); Reconstruction of a signal from its samples using interpolation(利用内插从采样信号中重建信号); The effect of undersampling : aliasing(欠采样的效果：混叠现象） What is sampling? A continuous-time signal is represented by its values, or samples, at points equally spaced in time. The importance of the sampling Under certain conditions a c-t signal can be completely recovered from a sequence of its samples . Due to the dramatic development of digital technology, we can use d-t system technology to implement c-t systems and process c-t signals: We exploit sampling to convert a c-t signal to a d-t signal, process the d-t signal using a d-t system and then convert back to continuous time. In the absence of any additional conditions , could a signal be specified by a sequence of equally spaced samples? NO! T? In addition, we can get different sequences if a signal is sampled at different regular intervals . In time domain: Sampling function :Sampling period In frequency domain: is a periodic function of consisting of a superposition of shifted replicas of , scaled by Sampling theorem Let be a band-limited signal with for Then is uniquely determined by its samples , if where Nyquist rate（奈奎斯特率） Exact recovery of a c-t signal from its samples using an ideal lowpass filter Example 1(supplementary): Solution: Consider a c-t signal whose Fourier transform has the property that for . The signal lasted for 2 minutes. Determine the minimum sample points numbe