數(shù)字信號(hào)處理a(雙語)chapter6ztransforma140404課件

1、上講回顧Z變換的定義：Z變換和DTFT的關(guān)系：Z平面和收斂域上講回顧Z變換的定義： Z 變換收斂域的特點(diǎn)：收斂域是一個(gè)圓環(huán)，有時(shí)可向內(nèi)收縮到原點(diǎn)有時(shí)可向外擴(kuò)展到，只有序列(n)的收斂域是整個(gè)Z平面收斂域內(nèi)無極點(diǎn)，X(z)在收斂域內(nèi)每一點(diǎn)上都是解析函數(shù)。Z 變換表示法：級(jí)數(shù)形式、解析表達(dá)式 （注意:函數(shù)收斂域，缺一不可） Z 變換收斂域的特點(diǎn)：Chapter 6z-TransformChapter 6z-TransformChapter 6 z-TransformPart A: z-TransformPart B: The Inverse z-Transform and z-Transform

2、TheoremsPart C: Convolution(卷積) Part D: The Transfer FunctionChapter 6 z-TransformIntroduction6.1 Definition6.2 Rational z-Transforms(有理z變換)6.3 Region of Convergence（收斂域） of a Rational z-Transform Part A: z-TransformIntroduction Part A: z-TransfoPart A: IntroductionThe DTFT provides a frequency-doma

3、in (頻域) representation of discrete-time signals and LTI（線性時(shí)不變）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: IntroductionThe D

4、TFT pPart A: IntroductionIn 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

5、 in continuous time systems. ZT characterizes signals or LTI systems in complex frequency domain（復(fù)頻域）.Part A: IntroductionIn general6.1 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-Tra

6、nsform6.1 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-Transform6.1 Definition of z-Transform6.1 Definition of z-Transform6.1 Definition of z-Transform6.1

7、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-Transform6.1 Definition of z-Transform6.1 Definition of z-Transform6.1 Definition of z-Transform6.1 Definition

8、 of z-Transform6.1 Definition of z-TransformTable 6.1 Some commonly used z-transform pairsTable 6.1 Some commonly used zIntroduction6.1 Definition6.2 Rational z-Transforms(有理z變換)6.3 Region of Convergence（收斂域） of a Rational z-Transform Part A: z-TransformIntroduction Part A: z-Transfo6.2 Rational z-T

9、ransform6.2 Rational z-Transform6.2 Rational z-Transform6.2 Rational z-Transform6.2 Rational z-Transform6.2 Rational z-Transform6.2 Rational z-Transform6.2 Rational z-Transform6.2 Rational z-Transform6.2 Rational z-Transform6.2 Rational z-Transform6.2 Rational z-Transform6.2 Rational z-Transform6.2

10、Rational z-Transform6.2 Rational z-Transform零極點(diǎn)共軛成對(duì)出現(xiàn)、收斂域內(nèi)無極點(diǎn)需注意的是：求解零、極點(diǎn)時(shí)，為避免遺漏，需先將Z變換有理分式的分子和分母都轉(zhuǎn)換成Z的正數(shù)次冪，再進(jìn)行求解，詳見第26頁P(yáng)PT。6.2 Rational z-Transform零極點(diǎn)共軛成Introduction6.1 Definition6.2 Rational z-Transforms(有理z變換)6.3 Region of Convergence（收斂域） of a Rational z-Transform Part A: z-TransformIntroduction

11、 Part A: z-Transfo6.3 Region of convergence of a rational z-Transform6.3 Region of convergence of a6.3 Region of convergence of a rational z-Transform6.3 Region of convergence of a6.3 Region of convergence of a rational z-Transform6.3 Region of convergence of a6.3 Region of convergence of a rational

12、 z-Transform6.3 Region of convergence of a6.3 Region of convergence of a rational z-Transform6.3 Region of convergence of a有限長(zhǎng)序列的Z變換有限長(zhǎng)序列的Z變換有限長(zhǎng)序列的Z變換有限長(zhǎng)序列的Z變換例1：序列x（n）=（n）的Z變換 由于n1=n2=0，其收斂域?yàn)檎麄€(gè)閉域 Z平面，0|Z|例1：序列x（n）=（n）的Z變換 例2：矩形序列x（n）=RN（n） 有限項(xiàng)等比級(jí)數(shù)求和 6.3 Region of convergence of a rational z-Transfo

13、rm6.3 Region of convergence of a6.3 Region of convergence of a rational z-TransformZ變換的收斂域包括 點(diǎn)是因果序列的特征。6.3 Region of convergence of a6.3 Region of convergence of a rational z-Transform6.3 Region of convergence of a6.3 Region of convergence of a rational z-Transform6.3 Region of convergence of a6.3 R

14、egion of convergence of a rational z-Transform6.3 Region of convergence of a6.3 Region of convergence of a rational z-Transform6.3 Region of convergence of a6.3 Region of convergence of a rational z-Transform6.3 Region of convergence of a6.3 Region of convergence of a rational z-Transform6.3 Region of convergence of a6.3 Region of convergence of a rational z-Transform6.3 Region of convergence of a6.3 Region of convergence of a rational z-Transform6.3 Region of convergence of a6.3 Region of convergence of a rational z-Transformwhere6.3 Region of conv