数字信号处理a(双语)chapter6-ztransforma.ppt

上讲回顾,Z变换的定义：Z变换和DTFT的关系：Z平面和收敛域,Z 变换收敛域的特点：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，只有序列(n)的收敛域是整个Z平面收敛域内无极点，X(z)在收敛域内每一点上都是解析函数。Z 变换表示法：级数形式、解析表达式（注意:函数收敛域，缺一不可）,Chapter 6,z-Transform,Chapter 6 z-Transform,Part A:z-TransformPart B:The Inverse z-Transform and z-Transform TheoremsPart C:Convolution(卷积)Part D:The Transfer Function,Introduction6.1 Definition6.2 Rational z-Transforms(有理z变换)6.3 Region of Convergence（收敛域）of a Rational z-Transform,Part A:z-Transform,Part A:Introduction,The DTFT provides a frequency-domain(频域)representation of discrete-time signals and LTI（线性时不变）discrete-time systems.Because of the convergence condition,in many cases,the DTFT of a sequence may not exist.As a result,it is not possible to make use of such frequency-domain characterization in these cases.,Part A:Introduction,In 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.For discrete-time systems,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）.,6.1 Definition of z-Transform,6.1 Definition of z-Transform,6.1 Definition of z-Transform,6.1 Definition of z-Transform,6.1 Definition of z-Transform,6.1 Definition of z-Transform,6.1 Definition of z-Transform,6.1 Definition of z-Transform,6.1 Definition of z-Transform,6.1 Definition of z-Transform,6.1 Definition of z-Transform,6.1 Definition of z-Transform,6.1 Definition of z-Transform,6.1 Definition of z-Transform,Table 6.1 Some commonly used z-transform pairs,Introduction6.1 Definition6.2 Rational z-Transforms(有理z变换)6.3 Region of Convergence（收敛域）of a Rational z-Transform,Part A:z-Transform,6.2 Rational z-Transform,6.2 Rational z-Transform,6.2 Rational z-Transform,6.2 Rational z-Transform,6.2 Rational z-Transform,6.2 Rational z-Transform,6.2 Rational z-Transform,6.2 Rational z-Transform,零极点共轭成对出现、收敛域内无极点需注意的是：求解零、极点时，为避免遗漏，需先将Z变换有理分式的分子和分母都转换成Z的正数次幂，再进行求解，详见第26页PPT。,Introduction6.1 Definition6.2 Rational z-Transforms(有理z变换)6.3 Region of Convergence（收敛域）of a Rational z-Transform,Part A:z-Transform,6.3 Region of convergence of a rational z-Transform,6.3 Region of convergence of a rational z-Transform,6.3 Region of convergence of a rational z-Transform,6.3 Region of convergence of a rational z-Transform,6.3 Region of convergence of a rational z-Transform,有限长序列的Z变换,有限长序列的Z变换,例1：序列x（n）=（n）的Z变换 由于n1=n2=0，其收敛域为整个闭域 Z平面，0|Z|,例2：矩形序列x（n）=RN（n）有限项等比级数求和,6.3 Region of convergence of a rational z-Transform,6.3 Region of convergence of a rational z-Transform,Z变换的收敛域包括 点是因果序列的特征。,6.3 Region of convergence of a rational z-Transform,6.3 Region of convergence of a rational z-Transform,6.3 Region of convergence of a rational z-Transform,6.3 Region of convergence of a rational z-Transform,6.3 Region of convergence of a rational z-Transform,6.3 Region of convergence of a rational z-Transform,6.3 Region of convergence of a rational z-Transform,6.3 Region of convergence of a rational z-Transform,6.3 Region of convergence of a rational z-Transform,where,6.3 Region of convergence of a rational z-Transform,Homework,Problems:6.2(a,b),6.5(a,b),6.7,6.8(a)(i,iv),6.13(a),6.16,6.44,6.81Matlab Exercises:M6.1(a),M6.5,