数字信号处理(第二章[3].离散时间信号和系....ppt

Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,/,30,Cllllllick to edit Master title style,z-Transform,The DTFT provides a frequency-domain representation of discrete-time signals and LTI discrete-time systems,DTFT,为离散信号和系统的频域表达和分析提供了一种有效的手段,Because of the convergence condition,in many cases,the DTFT of a sequence may not exist,但,某些情况下，,DTFT,可能并不存在（收敛）,As a result,it is not possible to make use of such frequency-domain characterization in these cases,此时利用,DTFT,并不能完成对信号的准确描述和分析,Beijing Institute of Technology,Ignore,/,30,z-Transform,z-transform may exist for many sequences for which the DTFT does not exist,z-,变换等效于对信号作特定渐弱预处理后的,DTFT,，它可以描述和分析某些,DTFT,不存在的信号,Moreover,use of z-transform techniques permits simple algebraic manipulation,更重要的是：利用,z-,变换可以允许比较简单的代数运算,Consequently,z-transform has become an important tool in the analysis and design of digital filters,鉴于此，,z-,变换在数字滤波器的分析和设计中发挥着重要的作用,z-transform reduces to its DTFT on the unit-circle,provided the latter exists,如果序列的,DTFT,存在，它即是其单位圆上的,z-,变换,Beijing Institute of Technology,Ignore,/,30,z-Transform,The DTFT of a sequence converges uniformly if and only if the ROC of the z-transform includes the unit circle,如果序列的,z-,变换的收敛域包括单位圆，则其,DTFT,存在,The existence of the DTFT dose NOT always imply the existence of the z-transform,DTFT,存在并不意味着其,z-,变换也存在,Rational z-transform can be expressed as ratios of two polynomials in z,-1,leading to the concept of zeros&poles,有理,z-,变换可以表示成两个关于,z,-1,的多项式，由此产生的极点和零点的概念,Beijing Institute of Technology,Ignore,/,30,z-,变换及其性质（,2.-7,、,-10,）,annular region,Beijing Institute of Technology,/,30,z-,变换及其性质（,2.-7,、,-10,）,(5),序列特性与收敛区域,Beijing Institute of Technology,/,30,Some remarks,The z-transform of two sequences may be identical even though the two parent sequences are different,两个不同序列的,z,-,变换可能相同,Only way a unique sequence can be associated with a z-transform is by specifying its ROC,只有指定收敛域后，,z,-,变换才对应一个唯一的序列,Without the knowledge of the ROC,there is no unique relationship between a sequence and its z-transform,Beijing Institute of Technology,Ignore,/,30,常用序列的,z-,变换,Beijing Institute of Technology,Ignore,/,30,常用序列的,z-,变换,Beijing Institute of Technology,Ignore,/,30,z-,变换的性质,Beijing Institute of Technology,Ignore,/,30,z-,变换的性质,Beijing Institute of Technology,Ignore,/,30,2.9,逆,z-,变换,c,Beijing Institute of Technology,Ignore,/,30,LTI DTS in the transform domain,Most discrete-time signals encountered in practice can be represented as a linear combination of a very large,maybe infinite,number of sinusoidal discrete-time signals of different angular frequencies,大部分实际离散时间信号都可以表示成很多甚至无限多个具有互异角频率正弦离散信号的组合,Thus,knowing the response of the LTI system to a single sinusoidal signal,we can determine its response to more complicated signals by making use of the superposition property,了解,LTI,系统对单个正弦离散信号的响应之后，我们可以基于系统的线性叠加性质确定其对更复杂信号的响应,Beijing Institute of Technology,Ignore,/,30,LTI DTS in the transform domain,T(,),Eigen function,xn,gyn,g,:complex const.,frequency response,特征信号,example,特征函数,复常数,Beijing Institute of Technology,Ignore,/,30,On frequency response,two common system specifications,Beijing Institute of Technology,/,30,example,频率选择滤波器,:frequency-selective filter,One application of an LTI discrete-time system is to,pass,certain frequency components in an input sequence without any distortion(if possible)and to,block,other frequency components,无畸变通过某些频率段信号并滤除其它非兴趣频率段之信号分量,Such systems are called,Digital Filters,数字滤波器,Beijing Institute of Technology,/,30,频率选择滤波器,:frequency-selective filter,Beijing Institute of Technology,/,30,传递（系统）函数,:,transfer function or system function,（,1,）稳定：在单位圆上收敛，即存在频率响应,（,2,）因果：,（,3,）因果稳定：,notes,1,Beijing Institute of Technology,/,30,总结：,Digital system,ANALOG DOMAIN,Filter,Antialiasing,DIGITAL DOMAIN,A/D,Digital Processing,ANALOG DOMAIN,D/A,Filter,Reconstruction,某些部分可能不需要：,-Filter+A/D,(ex:economics);,-D/A+filter,(ex:digital output wanted).,General scheme,Beijing Institute of Technology,*,本门课程之 重点所在,*,Digital Processing,/,30,