數(shù)字信號(hào)處理(第二章[3].離散時(shí)間信號(hào)和系....ppt

1、1 / 30,z-Transform,The DTFT provides a frequency-domain representation of discrete-time signals and LTI discrete-time systems DTFT 為離散信號(hào)和系統(tǒng)的頻域表達(dá)和分析提供了一種有效的手段 Because of the convergence condition, in many cases, the DTFT of a sequence may not exist 但某些情況下，DTFT 可能并不存在（收斂） As a result, it is not possib

2、le to make use of such frequency-domain characterization in these cases 此時(shí)利用 DTFT 并不能完成對(duì)信號(hào)的準(zhǔn)確描述和分析,Beijing Institute of Technology,Ignore,2 / 30,z-Transform,z-transform may exist for many sequences for which the DTFT does not exist z-變換等效于對(duì)信號(hào)作特定漸弱預(yù)處理后的DTFT，它可以描述和分析某些DTFT不存在的信號(hào) Moreover, use of z-tra

3、nsform techniques permits simple algebraic manipulation 更重要的是：利用z-變換可以允許比較簡(jiǎn)單的代數(shù)運(yùn)算 Consequently, z-transform has become an important tool in the analysis and design of digital filters 鑒于此，z-變換在數(shù)字濾波器的分析和設(shè)計(jì)中發(fā)揮著重要的作用 z-transform reduces to its DTFT on the unit-circle, provided the latter exists 如果序列的DTF

4、T存在，它即是其單位圓上的z-變換,Beijing Institute of Technology,Ignore,3 / 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-變換的收斂域包括單位圓，則其DTFT存在 The existence of the DTFT dose NOT always imply the existence of the z-transform DTFT存

5、在并不意味著其z-變換也存在 Rational z-transform can be expressed as ratios of two polynomials in z-1, leading to the concept of zeros & poles 有理z-變換可以表示成兩個(gè)關(guān)于z-1的多項(xiàng)式，由此產(chǎn)生的極點(diǎn)和零點(diǎn)的概念,Beijing Institute of Technology,Ignore,4 / 30,z-變換及其性質(zhì)（2.-7、-10）,annular region,Beijing Institute of Technology,5 / 30,z-變換及其性質(zhì)（2.-7、

6、-10）,(5) 序列特性與收斂區(qū)域,Beijing Institute of Technology,6 / 30,Some remarks,The z-transform of two sequences may be identical even though the two parent sequences are different 兩個(gè)不同序列的z-變換可能相同 Only way a unique sequence can be associated with a z-transform is by specifying its ROC 只有指定收斂域后，z-變換才對(duì)應(yīng)一個(gè)唯一的序列

7、 Without the knowledge of the ROC, there is no unique relationship between a sequence and its z-transform,Beijing Institute of Technology,Ignore,7 / 30,常用序列的z-變換,Beijing Institute of Technology,Ignore,8 / 30,常用序列的z-變換,Beijing Institute of Technology,Ignore,9 / 30,z-變換的性質(zhì),Beijing Institute of Technol

8、ogy,Ignore,10 / 30,z-變換的性質(zhì),Beijing Institute of Technology,Ignore,11 / 30,2.9 逆z-變換,Beijing Institute of Technology,Ignore,12 / 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

9、sinusoidal discrete-time signals of different angular frequencies 大部分實(shí)際離散時(shí)間信號(hào)都可以表示成很多甚至無(wú)限多個(gè)具有互異角頻率正弦離散信號(hào)的組合 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 系統(tǒng)對(duì)單個(gè)正弦

10、離散信號(hào)的響應(yīng)之后，我們可以基于系統(tǒng)的線性疊加性質(zhì)確定其對(duì)更復(fù)雜信號(hào)的響應(yīng),Beijing Institute of Technology,Ignore,13 / 30,LTI DTS in the transform domain,特征信號(hào),example,特征函數(shù),復(fù)常數(shù),Beijing Institute of Technology,Ignore,14 / 30,On frequency response,two common system specifications,Beijing Institute of Technology,15 / 30,example,頻率選擇濾波器: fr

11、equency-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 無(wú)畸變通過(guò)某些頻率段信號(hào)并濾除其它非興趣頻率段之信號(hào)分量 Such systems are called Digital Filters 數(shù)字濾波器,Beijing Institute of Technology,16 / 30,頻率選擇濾波器: frequency-selective filter,Beijing Institute of Technology,17 / 30,傳遞（系統(tǒng)）