1、上讲回顾上讲回顾lZ变换的定义：变换的定义：lZ变换和变换和DTFT的关系：的关系：lZ平面和收敛域平面和收敛域nnzngzG)()()jjj nz enG zG eg n e Z 变换收敛域的特点：变换收敛域的特点：l收敛域是一个圆环，有时可向内收缩到原点收敛域是一个圆环，有时可向内收缩到原点有时可向外扩展到有时可向外扩展到，只有序列，只有序列(n)的收敛域的收敛域是整个是整个Z平面平面l收敛域内无极点，收敛域内无极点，X(z)在收敛域内每一点上在收敛域内每一点上都是解析函数。都是解析函数。lZ 变换表示法：级数形式、解析表达式变换表示法：级数形式、解析表达式 （注意（注意:函数收敛域，缺一
2、不可）函数收敛域，缺一不可）Chapter 6z-TransformChapter 6 z-TransformlPart A:z-TransformlPart B:The Inverse z-Transform and z-Transform TheoremslPart C:Convolution(卷积卷积)lPart D:The Transfer FunctionlIntroductionl6.1 Definitionl6.2 Rational z-Transforms(有理有理z变换变换)l6.3 Region of Convergence（收敛域）（收敛域）of a Rational z
3、-Transform Part A:z-TransformPart A:IntroductionlThe DTFT provides a frequency-domain(频域频域)representation of discrete-time signals and LTI（线（线性时不变）性时不变）discrete-time systems.lBecause of the convergence condition,in many cases,the DTFT of a sequence may not exist.lAs a result,it is not possible to ma
4、ke use of such frequency-domain characterization in these cases.Part A:IntroductionlIn general,ZT can be thought of as a generalization of the DTFT.ZT is more complex than DTFT(both literally and figuratively),but provides a great deal of insight into system design and behavior.lFor discrete-time sy
5、stems,ZT plays the same role of Laplace-transform does in continuous time systems.ZT characterizes signals or LTI systems in complex frequency domain（复频域）（复频域）.6.1 Definition of z-Transform6.1 Definition of z-Transform6.1 Definition of z-Transform6.1 Definition of z-Transform6.1 Definition of z-Tran
6、sform6.1 Definition of z-Transform6.1 Definition of z-Transform6.1 Definition of z-Transform6.1 Definition of z-Transform6.1 Definition of z-Transform6.1 Definition of z-Transform6.1 Definition of z-TransformImzjRez0平面zaz a6.1 Definition of z-Transform ImzjRez0平面zaz a6.1 Definition of z-TransformTab
7、le 6.1 Some commonly used z-transform pairslIntroductionl6.1 Definitionl6.2 Rational z-Transforms(有理有理z变换变换)l6.3 Region of Convergence（收敛域）（收敛域）of a Rational z-Transform Part A:z-Transform6.2 Rational z-Transform6.2 Rational z-Transform6.2 Rational z-Transform6.2 Rational z-Transform6.2 Rational z-T
8、ransform6.2 Rational z-Transform6.2 Rational z-Transform6.2 Rational z-Transforml零极点共轭成对出现、收敛域内无极点零极点共轭成对出现、收敛域内无极点l需注意的是：求解零、极点时，为避免遗漏，需注意的是：求解零、极点时，为避免遗漏，需需先将先将Z变换有理分式的分子和分母都转换成变换有理分式的分子和分母都转换成Z的正数次幂的正数次幂，再进行求解，详见第，再进行求解，详见第26页页PPT。11()1X Zaz ZZa lIntroductionl6.1 Definitionl6.2 Rational z-Transfo
9、rms(有理有理z变换变换)l6.3 Region of Convergence（收敛域）（收敛域）of a Rational z-Transform Part A:z-Transform6.3 Region of convergence of a rational z-Transform6.3 Region of convergence of a rational z-Transform6.3 Region of convergence of a rational z-Transform6.3 Region of convergence of a rational z-Transform6.
10、3 Region of convergence of a rational z-Transform有限长序列的有限长序列的Z变换变换有限长序列的有限长序列的Z变换变换例例1：序列：序列x（n）=（n）的）的Z变换变换 由于由于n1=n2=0，其收敛域为整个闭域，其收敛域为整个闭域 Z平面，平面，0|Z|0()()11nnX zn zz 例例2：矩形序列：矩形序列x（n）=RN（n）有限项等比级数求和有限项等比级数求和 112(1)0()()11nNnNnNnX zRn zzzzz 11(),0|1NzXzzz 0(1)1Naqq 6.3 Region of convergence of a r
11、ational z-Transform6.3 Region of convergence of a rational z-TransformZ变换的收敛域包括变换的收敛域包括 点是因果序列的特征。点是因果序列的特征。6.3 Region of convergence of a rational z-Transform6.3 Region of convergence of a rational z-Transform6.3 Region of convergence of a rational z-Transform6.3 Region of convergence of a rational
12、 z-Transform6.3 Region of convergence of a rational z-Transform6.3 Region of convergence of a rational z-Transform6.3 Region of convergence of a rational z-Transform6.3 Region of convergence of a rational z-Transform6.3 Region of convergence of a rational z-TransformwhereLLLLLLaaabbbaaabbbaaabbbsos21021022120222120212110121110122110221101)(zazaazbzbbzGkkkkkkLk6.3 Region of convergence of a rational z-TransformHomeworklProblems:6.2(a,b),6.5(a,b),6.7,6.8(a)(i,iv),6.13(a),6.16,6.44,6.81lMatlab Exercises:M6.1(a),M6.5
