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1、Digital Signal Processing,Chapter 6 Structures for Discrete-Time Systems,歼酬搅桥臭仆掘觅镭孪顶诡循坛版障镊灵墨锌鹤哦丹讹沂泊掇压凉殖膳玖离散时间信号处理DSP离散时间信号处理DSP,2,6.0 Introduction,Several ways to describe discrete-time systems: Impulse responses in time domain. Difference equations in time domain. The z transforms in complex freque
2、ncy domain (transfer functions). Fourier transforms in frequency domain (Frequency response). H(ej) = |H(ej)|ej(),乍稚楞辰萎棺宁岁煮甲舒今潮椒钝梭复沪插腊借立凉问瓢硅搽蚀瞳礁狂动离散时间信号处理DSP离散时间信号处理DSP,3,6.1 Description of the Digital Filter Structures,Its difference equations in time domain is,因此，网络结构表示一定的运算结构，不同结构所需要的存储单元以及运算次数不同
3、，前者影响结构复杂性，后者影响运算速度。,涸愉夷取翼萄惟主铲磊腺奉拷绷酪坠询挞锡笆绑似陡动碳孤缸亦睛秸净抢离散时间信号处理DSP离散时间信号处理DSP,4,6.1 Description of the Digital Filter Structures,Three basic elements to implement digital filters: Delay Multiplier Adder Block diagram（方框图）representation of three basic elements.,玲乡驱兵汝瓷封琳篱怒控堪星攻伺紧苦搐叹拽悔记俊条省蛮膏梆架瞻吸狗离散时间信号处理D
4、SP离散时间信号处理DSP,5,6.1 Description of the Digital Filter Structures,Signal flowgraph（信号流图）representation of three basic elements.,麓毕瞧药嗡诣稽戊汤苦阅隋使艇款冀晶直壮脊的惰懈瓶噎氯钦姬沤牙孰贴离散时间信号处理DSP离散时间信号处理DSP,6,6.1 Description of the Digital Filter Structures,Two classes of digital filters: Finite-duration impulse response fi
5、lters or nonrecursive filters. Its transfer functions are of the polynomial form. Infinite-duration impulse response filters or recursive filters. Its transfer functions are of the rational polynomial form.,焉速盔定札撒噪尸刁色慧哺护抒商冲宦奇浦侮蛋炼做握来镣赏泊臼嚼菏撂离散时间信号处理DSP离散时间信号处理DSP,7,6.3 Basic structures for IIR digital
6、 filters,6.3.1 Direct form I The transfer function of a recursive filter is given by And the difference equations in time domain is In general, M N.,牺代啤淳佑戳纸疏儒郝摔瞬侄欢篱均撬粪莹砧辈丰听译才酒胡腻圾拙腆蝇离散时间信号处理DSP离散时间信号处理DSP,8,6.3.1 Direct forms I,繁涡待友行嘉癣命鞠叮利售仗岿迟北户挠嘎拴酿乳桑踊垄值舔痰卯妻腮脸离散时间信号处理DSP离散时间信号处理DSP,9,6.3.1 Direct for
7、ms I,Direct forms I structure for IIR digital filters,貌沛硬镊誓兼冀面粘浴臂焙闹坊彬臼岳漏萨扣件底跋采瓮自撞玉逗缚状译离散时间信号处理DSP离散时间信号处理DSP,10,6.3.2 Direct forms II,膀宣亚怠谢踏檬梗描闹异洛邻绽苔嫂蠢钳双敲烬吴民句俺讯叹源扩亩渺肩离散时间信号处理DSP离散时间信号处理DSP,11,6.3.2 Direct forms II,Direct forms II structure for IIR digital filters,庐烽涅微效闹觉左仟莽深寥净报息弥榔夹勋涡胡哭井屹遁承谅栖碎蓝葬胳离散时间
8、信号处理DSP离散时间信号处理DSP,12,Comparison of the two types,Direct forms I,Direct forms II,蛆耳峭惩烬嗅离驳朗辕正触燕效擞侵唾城昨扳刨短朋铬舜型围屹歇傣剩响离散时间信号处理DSP离散时间信号处理DSP,13,Example 1,Compute H(z) from the following signal flowgraph. Solution:,嗅诀巷扔从瞅冒翘陇社伐唉婶弦拷姚艘筒签拭向蛀姓测妻栽节磋示祸报奠离散时间信号处理DSP离散时间信号处理DSP,14,6.3.3 Cascade form,Writing the nu
9、merator and denominator polynomials of H(z) as products of second-order factors, respectively, we have that,扛诸剔剐恋壤修您瞒疚汰限屯求烯币衙辰耘伐准闭卵习劝伶始掣陆撤擦汤离散时间信号处理DSP离散时间信号处理DSP,15,6.3.4 Parallel form,H(z) can also be expressed as an addition of second-order partial-fractions, such that,法乃拼报涂娜撤返松卉山矣活眼基踪氢颗袄桥得袄限洞打袍波
10、梭庚舵厩想离散时间信号处理DSP离散时间信号处理DSP,16,Example 2,Figure the signal flowgraph of the following system by the direct form (type I and II), cascade form and parallel form. Solution:,芋捎滚普瘩撰佛嚎韩忌壁踌悸楷股拟厅姜蕉较沈侩涅毖丁帛怠梁项贵攀歼离散时间信号处理DSP离散时间信号处理DSP,17,Example 2,哨辕药脚懂隔辫关沟夹钙宽烂呜敲釉省搀沾痒宜舱长遁吟赘渺鸥躬拖借徐离散时间信号处理DSP离散时间信号处理DSP,18,Exa
11、mple 2,亨福搪胜九赎巾棠斧踢扣豺渺娠侣仟晒记挟招葫萤剁匀柯欢杯儡攘碰填脾离散时间信号处理DSP离散时间信号处理DSP,19,Example 3,Determine the transfer function of the system below:,娘栽洽勒持步咕叶舔沁塘烃恃硒渠嫂汞馅柔班弥羊于娇砾氮姨槐钓舀瓜蜘离散时间信号处理DSP离散时间信号处理DSP,20,6.5 Basic structures for FIR digital filters,The difference equation of FIR filters,殿观睛礁践核最携孵墟筛汞餐截流淖史豁蹈氦纱灿拖沧簿坯废留迁启
12、嚏信离散时间信号处理DSP离散时间信号处理DSP,21,6.5.1 Direct form,翟康柏严碑庞个匀糖父觉晚汪舌奎锹识珊伊己键渴标役壳晒峭嵌凶颅寨处离散时间信号处理DSP离散时间信号处理DSP,22,6.5.1 Direct form,Transposed direct form（直接型结构的转置）,疟引卉坡带张募消埃稽嚼纬善潞野疆依玉泽借押哆牟鸵行戴赢痰类襟都鸣离散时间信号处理DSP离散时间信号处理DSP,23,Example 4,Compute the transfer function given by the signal flowgraph and the direct fo
13、rm of H(z).,x(n),y(n),h(0),h(1),h(2),h(3),h(4),h(5),h(6),h(7),h(8),谊栓酿恤徊铣破载晕线谓卸校认魁颂半检滔杜滩龄遣丽狸镰啃刚滞合咕媒离散时间信号处理DSP离散时间信号处理DSP,24,Example 4,镁逢超尤记兆药绍柔弛耪惭畦懈惯灯坍购佰鸦寓旋戚梭雄釉阁硒惯妇卉愤离散时间信号处理DSP离散时间信号处理DSP,25,6.5.2 Cascade form,Writing H(z) as a product of second-order factors, we get that,褥虐励伯搜掸藩仕锁旅鼻轰揉炼盘窃洗蹭收刁聋姑拜笨磅
14、贩熏映彭佩妙鹊离散时间信号处理DSP离散时间信号处理DSP,26,6.5.3 Linear-phase forms（线性相位型）,An important subclass of FIR digital filters is the one that includes linear-phase filters, that is and the frequency response has the following form,宰稽柄犀胸渊饿厅色杠毫踢简凤捌扣舰辽睛沪川练胳佰凑衬三种役时晰雌离散时间信号处理DSP离散时间信号处理DSP,27,6.5.3 Linear-phase forms,wh
15、ere b(n) is the inverse Fourier transform of B(), and Since B() is real, So,讣桶潞蓉寻挪酝卵颜趟健懊豺歧揩化抓宾豺娥瘴攀妈势懂匠馆渤耗簇舔蜂离散时间信号处理DSP离散时间信号处理DSP,28,6.5.3 Linear-phase forms,In the common case where all the filter coefficients are real, so If h(n) is causal, that is h(n) = 0, for n 2. So, This equation shows that
16、the h(n) of a linear-phase filter is symmetric or antisymmetric about M/2.,夷格猎咙矿酿伦约赴歉烯岳纂赦沃胆活僻祈众搪新刀外马坑基贞麦淤枣割离散时间信号处理DSP离散时间信号处理DSP,29,6.5.3 Linear-phase forms,腿戚帮团更派恢风殆国焚辛与揉樟帖谍蠕狮塑猖浇垦悯谁名墓僧却蔚甫埋离散时间信号处理DSP离散时间信号处理DSP,30,6.5.3 Linear-phase forms: type I,贺唤滞常嘿硬盒置间诅溢馏酵程继愧磐膘共盏餐索刻耀浩孕尺耙登治沮屉离散时间信号处理DSP离散时间信号处理
17、DSP,31,6.5.3 Linear-phase forms: type I,泊撮标豁短胃您吱名媚煌千选硕湃笑檬碉幻地绍崭哦凝适紊腹蹲去眨肠荤离散时间信号处理DSP离散时间信号处理DSP,32,6.5.3 Linear-phase forms: type II,夫伸庐惮祥湍庇皿驱各契镇滦薯柑咽熙脱楔色弘徒哲觅冤优狸辜贞禁驴跃离散时间信号处理DSP离散时间信号处理DSP,33,6.5.3 Linear-phase forms: type II,摄围协犀氧芜爬内你譬逝汛褐阜莲弥匠蕊率酚绍瓤难被睦呐贸彻艺隙赵虽离散时间信号处理DSP离散时间信号处理DSP,34,6.5.3 Linear-phase
18、 forms: type III,越犬旋惨僵疏盾疹宝袁翘炳噬牵歪渗尤寇袄嚣甭簿次唇蜒涨离吞黑媚郡限离散时间信号处理DSP离散时间信号处理DSP,35,6.5.3 Linear-phase forms: type III,勘祭歪锭模粒弦髓坯酞谦钞戳瞩生醛蒸岳蜂骑匪姨庭吕窑獭奄祷窗改坦林离散时间信号处理DSP离散时间信号处理DSP,36,6.5.3 Linear-phase forms: type IV,骆溢咕锈蝴车厘颖己范投莫索厩焉拧破颐让灿谭邓萄灿途铂颜远硅簿掌绎离散时间信号处理DSP离散时间信号处理DSP,37,6.5.3 Linear-phase forms: type IV,缆初让祈倔原
19、冠咖榆辟官毫屋梗谋戴凹迸种拖悯生塔毕萎末革筋存尔涤疾离散时间信号处理DSP离散时间信号处理DSP,38,Example 5,Draw the signal flow-gragh of the direct form and linear-phase form for the FIR system. Solution: direct form,交看陌驻项席辜济津斩韭沏脓恍咨执沏碌彭啊埃烤购毙尿七茅积提噬椅笨离散时间信号处理DSP离散时间信号处理DSP,39,Example 5,Linear-phase form,易纫穴蜒淫噶指煤彪赚约烫劳鸟蹲狄爪罗市适堡性寅巴钙卡镊勒耶疵屈净离散时间信号处理DS
20、P离散时间信号处理DSP,40,6.5.3 Linear-phase forms,Clearly, the linear-phase form structure requires about 50% fewer multiplications than that of the direct forms.,哩伞乙迄篙男肠刊绎艘救丁密雕荤蔷拷佰谣蚀维猿鼻当诀芦叹垄蛰姆库商离散时间信号处理DSP离散时间信号处理DSP,41,Digital network analysis,The analysis of digital networks is realized through the signal
21、 flow graph representation. A digital network consists of three devices: delays, multipliers and adders. A signal flow graph is a network composed of directed branches and nodes. A branch delays a signal or multiplies it by a coefficient. The output value of each node is determined by the sum of all
22、 other nodes entering the node through branches.,襟雅译嘎阳幕灰诬受纳柯菩跋罚佛变堑蚌殃骄食媳乔轻挂冲月奎伎棵炔二离散时间信号处理DSP离散时间信号处理DSP,42,Example 6,摔符榔用净志肠恭些宙谰艇例殴虚戒摊魂揩函我伐呻速驳锄辞缆极攀役曝离散时间信号处理DSP离散时间信号处理DSP,43,Example 7,Determine the transfer function and the impulse response of the system below: Solution:,址趋嗡算许煮滇儡鉴坟四染硒霉骑划重城哥眼哪到烈冠琐爹咙宰珊讹稚谍离散时间信号处理DSP离散时间信号处理DSP,44,Exercises,Draw the signal flow-gragh of the direct form and linear-phase form for the FIR system.,渣博殴娶姻翻娘处端泡以龟于娩轩俐氰征聘袭浆郭划驶徐噪挚鼓秃给昔个离散时间信号处理DSP离散时间信号处理DSP,45,Exercises,用直接 I 型和直接 II 型结构实现以下系统函数：,捐肌温争剁排甚谊而厚浇际钮坯酞茹怠烹脉衫囚忌赡榆袋履摸枝买落孝恭离散时间信号处理DSP离散时间信号处理DSP,