1、信号与系统信号与系统(第二版第二版)全册全册配套课件配套课件2Signals & Systems3课程说明课程说明教学计划教学计划学时学时: 80 学分学分: 5教学内容教学内容1. 课堂理论教学课堂理论教学(68学时学时)2. 课程设计课程设计(8学时学时)3. 课堂习题课课堂习题课(4学时学时)4课程说明课程说明参考书目参考书目: 信号与系统分析信号与系统分析吕幼新吕幼新 张明友张明友 电子工业出版社电子工业出版社信号与系统分析信号与系统分析闵大镒闵大镒 朱学勇朱学勇 电子科技大学出版社电子科技大学出版社5Chapter 1 Signals and Systems The mathemat
2、ical description and representations of signals and systems. Signals and Systems arise in a broad array of application. Chapter 1 Signals and Systems6Chapter 1 Signals and Systems(1) A simple RC circuitSource voltage Vs and Capacitor voltage Vc(2) An automobile7(3) A Speech SignalChapter 1 Signals a
3、nd Systems8(4) A PictureChapter 1 Signals and Systems9(5) Vertical Wind ProfileChapter 1 Signals and Systems10信号信号的描述的描述频率特性频率特性通信系统中通信系统中信息信息: 受信者预先不知道的消息受信者预先不知道的消息;信号信号: 携带消息的物理量携带消息的物理量;信号可表示成一个或多个自变量的函数信号可表示成一个或多个自变量的函数;tzyxf,电压电压电流电流 tv ti系统分析的两个共同的基本点：系统分析的两个共同的基本点：2. 系统：对给定的信号作出响应，并产生新的信号系统：
4、对给定的信号作出响应，并产生新的信号Chapter 1 Signals and Systems1. 信号（一个或多个自变量）信号（一个或多个自变量）时间特性时间特性11 1.1 Continuous-Time and Discrete- Time Signals连续时间信号和离散时间信号连续时间信号和离散时间信号 1.1.1 Examples and Mathematical Representation1. Continuous-Time Signals The independent variable is continuous0 t tf0 t tfChapter 1 Signals a
5、nd Systems12Chapter 1 Signals and Systems2. Discrete-Time Signals The independent variable is discrete nxn5012 3145641710811n is integer numberContinuous-time signalsDiscrete-time signals 1.1.2 Signal Energy and Powerv( t) voltage i( t) current13Chapter 1 Signals and Systemsi(t)+ v(t) -R1. Instantan
6、eous power瞬时功率瞬时功率 titvtp2. Total energy dttpEtt21 nxEnnn221 t dttvRdttpE21 n nxEn2 21 ttt21nnn tvR21 dttvRtt221114Chapter 1 Signals and Systems3. Time-averaged power平均功率平均功率 dttxTPTTT221lim 2 21limnxNPNNnN Energy signal0 PE Power signal EP Energy signal0 t tx0 t tx Power signal0 t txNeither energy,
7、nor power15Chapter 1 Signals and Systems1.2 Transformations of the independent variable1.2.1 Examples of transformations of the independent variable1. Time shift( 时移时移)0ttt 0nnn 0ttxtx 0nnxnx tx0 t1 t1Example 1 tx1/tt10tt 0 otherwisePlease indicate 0ttx 16Chapter 1 Signals and Systems0ttx tx 与与 波形相同
8、波形相同00 t相当于相当于 左移（超前）左移（超前） to tx2. Time reversal( 时域反折时域反折)tt nn tx0 t1 t1tx - t1 0 t1x(-t) is a reflection of x(t) about t=000 t tx相当于相当于 右移（延迟）右移（延迟） to173. Time- scaling( 尺度变换尺度变换)Chapter 1 Signals and Systems atxtxatt tx0 t1 t1 tx 20 t1/2 t1tx210 2t1 t1a1 信号压缩信号压缩a倍倍0a0Synthesize the signals pe
9、riodic tx1T1 tx2T2当当T1/T2为有理数时，为有理数时， 为周期的为周期的 tbxtax21 Example tttx 3sin2cos 11 T3/22 TT=22211TnTnT ContinuousT, N 0 period其中其中 n1,n2 互质互质其周期其周期20Chapter 1 Signals and Systems 1.2.3 Even and Odd Signals txtxtxtx EvenOdd nxnxnxnx EvenOdd txOdtxEvtx Even part of x(t) 偶部偶部 txtxtxEv 21Odd part of x(t)
10、奇部奇部 txtxtxOd 210 1 2 t tx1-2 -1 0 1 2 t txEv1/2-2 -1 0 1 2 t txOd1/2-1/221Chapter 1 Signals and Systems 1.3 Exponential and Sinusoidal Signals复指数信号和正弦信号复指数信号和正弦信号 1.3.1 Continuous-Time Complex Exponential and Sinusoidal Signals stCetx t1. Real Exponential Signals atCetx a is real atCetxa0a022Chapte
11、r 1 Signals and Systems2. Periodic Complex Exponential and Sinusoidal Signals Period tjTtjee00 , 2, 1, 0 k10 Tje 02 kT , 2, 1 k tjCetx0 t0 js 002 TFundamental Period 基本周期基本周期0 Fundamental Frequency kje 2 23Chapter 1 Signals and Systems Euler s relation( 尤拉关系尤拉关系)tjtetj00sincos0 tjtjeejt0021sin0 tjtj
12、eet0021cos0 tjeAtA0Recos0 Average Power020000TdteEtjTT 11000TTETP121lim20dteTPtjTTT E24Chapter 1 Signals and Systems Harmonic relationtje0 Basic Signal tjkket0 , 2, 1, 0k002 TCommon Period 0 Fundamental Frequency kTTk/00 kkkth harmonic25Chapter 1 Signals and Systems3. General Complex Exponential Sig
13、nals stCetx0 js jeCC tjteeCtx0 teCjteCtt00sincos 0,Retx 0,Retx26Chapter 1 Signals and Systems 1.3.2 Discrete-Time Complex Exponential and Sinusoidal Signals nCnx n nCenx where e2. Complex Exponential Signals and Sinusoidal Signals 0 je1PE1. Real Exponential Signals a real nanx njenx0 27 jnjjnjeAeAnA
14、0022cos0Chapter 1 Signals and Systemsnjnenj00sincos0 Euler s relation3. General Complex Exponential Signals nCnx 0 je jeCC njneCnx0 nCjnCnn00sincos28 1.3.3 Periodicity Properties of Discrete-Time Complex ExponentialsChapter 1 Signals and Systemstje0 nje0 Sampling1.nje 202.njnenj00sincos0 nnx0cos 2,
15、000变化变化2k时信号相同时信号相同njnjee 20nje0 29Chapter 1 Signals and Systems( a) 0=0 N=1 ( b) 0= /8 N=16 ( c) 0= /4 N=8 ( d) 0 = /2 N=4 ( e) 0 = N=2 低频低频高频高频( f) 0 =3 /2 N=4 ( g) 0 =7 /4 N=8 ( h) 0 =15 /8 N=16 ( i) 0 =2 N=1 nnx0cos Figure 1.27 2 , 000=2 k 时时, 信号频率低信号频率低0=(2 k+1) 时时, 信号频率高信号频率高303. Periodicity P
16、roperties Chapter 1 Signals and SystemsnjNnjee00 10Nje Nm 20Rational NumbermN02 Fundamental Period2 Nenj nje2is not periodic, 2, 1, 0mmje 2 310不同不同, ,信号不同信号不同. . 0相差相差2 k,信号相同信号相同. 0越大越大, ,频率越高频率越高. .0 =2 k 时时,频率低频率低; 0 =(2 k+1)时时,频率高频率高.对任意的对任意的0, ,信号均为周期的信号均为周期的. . 为有理数时为有理数时, , 信号为周期的信号为周期的. .Cha
17、pter 1 Signals and Systemstje0 nje0 2 , 00002 TmN02 2/0324. Harmonically related periodic exponentialsChapter 1 Signals and Systems njnjeenx 4332N1=3N2=8N= n1 N1= n2 N2=24 Fundamental Period nNjkken 2, 2, 1, 0k nNNkjNken 2=1 nnkNk nNjkken 21, 2 , 1 , 0NknNjNnNjkee 2233Chapter 1 Signals and Systems 1
18、.4 The Unit Impulse and Unit Step Functions单位冲激与单位阶跃函数单位冲激与单位阶跃函数 1.4.1 The Discrete-Time Unit Impulse and Unit Step SequencesUnit Impulse n 1n=00 n 0n01 nUnit Step nu1n 00 n 00 t 0? t = 00 t 0AC+- tvc tict=037Chapter 1 Signals and Systems dttdut tt 0limUnit Impulse Function dttdut 0 t(1) t t 0 t 0
19、1dtt 0 t t1 100dtt 21 0 t/21te- 0 t1 tf tft0,lim 38Chapter 1 Signals and Systems nxnnx 0 knkxnxk mnunm 1nunun t 0 t 0 1dtt 39Chapter 1 Signals and Systems0tt 0 t t010dttt 0 t0 t(1)0tt If s(t) is even , and 1dtts ktkstk lim dtut 0 t积分区间积分区间or , equivalently dttu0 0 tt积分区间积分区间40Chapter 1 Signals and S
20、ystems 1.4.3 The Properties of Unit Impulse Functions1. Sampling and Sifting properties tfttf 0If f(t) is continuous at the point of t=0 0fdtttf Sampling property Sifting property dtttf dttf 000 0 ,0,0 tf 0f dtttf 0041Chapter 1 Signals and Systems 设设 为在为在t=0连续的任意的普通函数连续的任意的普通函数 t dtttft 00 f dttft 0
21、 00 f tfttf 0In General 000tttftttf 00tfdttttf 0 t0 t(1)0tt 42Chapter 1 Signals and Systems2. Scaling propertyIf a is real, a 0 taat 1Specially a= -1 tt Even functionExample2 dttt2/22/sin d 2 4/sin0|4/sin21 42 4/t 2 1 43Chapter 1 Signals and Systems 1.4.4 信号的计算信号的计算1. 信号的加、减、乘、除信号的加、减、乘、除Example 3 t
22、f1t sin0t0t0 ttf sin2t sin0t0t0 tftf21t 2sin0t0t0 tftf21442. 信号的基本表示信号的基本表示Chapter 1 Signals and Systems- 0 t tP2- 0 ttu 0 ttu0 1 t 1 ttu1t0 1 t 0 t tu1-1 0 1 t1 tf-1 0 t1 11tut0 1 t 2 ttu20 1 2 t 1 11tut45Chapter 1 Signals and Systems3. 信号的微分、积分运算信号的微分、积分运算 2 1 0 1 2 3 4 tExample 1.7 x(t) is depict
23、ed in Figure 1.40(a),determinethe derivative of x(t).-1x(t) 0 1 2 3 4 t dttdx(2)(-3)(2) 422312tutututx dttdx12t 23t 42t 46Chapter 1 Signals and Systems 1.5 Continuous-time and discrete-time systemsSystem Be constituted by some unitsContact with some rule The systems functionSystem analysis （系统分析）（系统
24、分析）System synthesizes （系统综合）（系统综合）Research systemContinuous-timesystem ty txDiscrete-timesystem ny nx tytx txLty nynx nxLny47Chapter 1 Signals and Systems 1.5.1 Simple Examples of Systems dttdvCRtvtvticcs tvRCtvRCdttdvscc11Linear Constant-coefficientDifferential Equation Example 1.9 tv tfm tv dttdvm
25、tvtf tfmtvmdttdv1 Linear Constant-coefficientDifferential Equation Example 1.8 tvsR tiC tvc48Chapter 1 Signals and SystemsContinuous-Time System kkMkkkkNkkdttxdbdttyda00Discrete-Time System knxbknyaMkkNkk00N-order Linear Constant-coefficientDifferential Equation N-order Linear Constant-coefficientDi
26、fference Equation 49Chapter 1 Signals and Systems 1.5.2 Interconnection of SystemsSeries interconnection(级联级联)Parallel interconnection(并联并联)Feedback interconnection(反馈反馈)System 1System 2inputoutputSystem 1System 2inputoutputSystem 1System 2inputoutput50Chapter 1 Signals and Systems 1.6 Basic System
27、Properties 1.6.1 Systems with and without Memory有记忆、无记忆系统有记忆、无记忆系统无记忆系统无记忆系统: 在某时刻在某时刻(t)的输出仅仅与同时刻的输出仅仅与同时刻(t)的输入有关。的输入有关。 memoryless（无记忆）（无记忆）identity system ,memoryless 22 2 nxnxny txty summer kxnynk delay 1nxny integrate dxtytSystems with memory51Chapter 1 Signals and Systems 1.6.2 Invertibility
28、and Inverse Systems可逆系统与可逆性可逆系统与可逆性可逆系统可逆系统: 不同的输入导致不同的输出（一一对应）。不同的输入导致不同的输出（一一对应）。 System nx tx ty nyInverse System nxnw txtw tx txty2 ty txtw tytw21 kxnynk nx ny 1nynynw nxnw 0ny txty2noninvertible systems不可逆系统不可逆系统52Chapter 1 Signals and Systems 1.6.3 Causality （因果性）（因果性）因果系统因果系统: 在某时刻在某时刻(t)的输出只
29、取决于同时刻的输出只取决于同时刻(t)或以前或以前(t) 的输入。的输入。 (与该时刻以后的输入无关）与该时刻以后的输入无关） Systems without memory 1txty dxtytCausal systems因果系统因果系统不可预测系统不可预测系统物理上可实现物理上可实现 txtty1cos53Chapter 1 Signals and Systems非因果系统非因果系统: 适用于非时间自变量信号的处理适用于非时间自变量信号的处理. knxMnyMMk121 nxny txty2Not Causal 1.6.4 Stability （稳定性）（稳定性）Stable System
30、 Bty Mtx ttxty txety not stable stable54Chapter 1 Signals and Systems 1.6.5 Time Invariance （时不变性）（时不变性）时不变系统时不变系统: 系统参数不随时间改变系统参数不随时间改变(恒参系统恒参系统),系统的输出波系统的输出波形仅仅取决于输入波形形仅仅取决于输入波形,而与输入作用的时刻无关而与输入作用的时刻无关. txLtyIf 00ttyttxLTime invariant时不变时不变 Consider a continuous-time system Delay t0 tx0ttxL0ttxL tx
31、 tyLDelay t00tty= time invariantsystem time-varyingsystem55Chapter 1 Signals and SystemsExample 1.14 txtysinDelay t0 tx0ttxL0sinttx txL txsinDelay t00sinttxEqual Time invariantExample 1.15 nnxnyNot equal Time-varyingDelay n0 nx0nnxL0nnnxL nx nnxnyDelay n000nnxnn56Chapter 1 Signals and SystemsExample
32、 1.16 txty2Delay t0 tx0ttxL02ttx txL tx 2Delay t002ttxNot equal Time-varying 1.6.6 Linearity （线性）（线性） tv txm0 dttdvmtx1. Initial State （初始状态）（初始状态） dxmtvt 1输出取决于输入的全部历史输出取决于输入的全部历史57Chapter 1 Signals and Systems dxmvtvt0100tInitial State dxmv0102. Linearity Additivity Scaling tytftytf2211 tytytftf21
33、21 tytf taytaf tbytaytbftaf2121 Linear 58Chapter 1 Signals and Systems3. Linear SystemFull response ty tyx tftxLtyf,0Zero-input response Zero-state response Initial stateInput 0 , 0txLtyx , 0 tfLtyf Zero-input linearityWhen 0tf , 2 , 1 , 0 0nixxi 0 011ttyaxaixiniiini 0 0ttyxixi59Chapter 1 Signals an
34、d Systems Zero-state linearity If 00 x tytfainiiini110t tytfii0tExample 1.17 ttxtyExample 1.18 txty2Its a linear system.Its a nonlinear system.Its a nonlinear system.Example 1.19 nxnyRe60Chapter 1 Signals and SystemsExample 1.20 32nxny 32111nxnynx 32222nxnynx 322121nxnxnxnx nyny21 nonlinearConsider
35、nxnxnyny12122 nxnx12 nyny12Incrementally linear61Chapter 1 Signals and Systems ty ny nx tx线性线性系统系统 tyx nyx tyf nyf线性系统的三个特性线性系统的三个特性 tytf 微分特性微分特性 dttdydttdf 积分特性积分特性 dydftt 频率保持性：频率保持性：信号通过线性系统不会产生新的频率分量信号通过线性系统不会产生新的频率分量62Chapter 1 Signals and Systems作业：作业：1.14 1.15 1.16 1.171.21 (d) (e) (f) 1.22
36、(d) (g) 1.23 1.24 (a) (b) 1.26 (a) (b) 1.27 1.3163Chapter 2Linear Time-invariant Systems64 Chapter 2 LTI SystemsConsider a linear time-invariant system tytfiini, 2 , 1 iiinittfatf1Example 1 an LTI system0 2 t tf11 211tftf0 1 2 t ty11L 211tyty0 2 4 t1-10 2 4 t tf21L ty21 iiinittya ty1 65 Chapter 2 LT
37、I Systems2.1 Discrete-time LTI Systems : The Convolution Sum（卷积和）（卷积和）2.1.1 The Representation of Discrete-Time Signalsin Terms of impulses 11011nxnxnxnx knkxnxk Sifting Property离散时间信号的冲激表示离散时间信号的冲激表示 knkx Example 210 1 2123 nxn66 Chapter 2 LTI Systems2.1.2 The Discrete-Time Unit Impulse Responses a
38、nd the Convolution-Sum Representation of LTI Systems 1. The Unit Impulse Responses单位冲激响应单位冲激响应 knkxnxk Let nhknk nhkxnynxkkLet nhn0 knhnhk0Time-Invariant nLnh , 0 0Unit Impulse Responses67 Chapter 2 LTI Systems2. Convolution-Sum （卷积和）（卷积和） nhn knhkn Time Invariant knhkxknkx Scaling knhkxknkxkk Addit
39、ivity nx ny knhkxnyk Convolution-Sum（卷积和）（卷积和）系统在系统在n时刻的输出包含所有时刻输入脉冲的影响时刻的输出包含所有时刻输入脉冲的影响k时刻的脉冲在时刻的脉冲在n时刻的响应时刻的响应 nhnx68 Chapter 2 LTI Systems3. 卷积和的计算卷积和的计算 图解法图解法例例2.3 nuanxn nunh ?nhnx knhkxnhnxk图解法步骤：图解法步骤： khnhkh 反折反折 平移平移knhn 求乘积求乘积 knhkx 对每一个对每一个n求和求和 knhkxnhnxk循环循环 nuaan11169 Chapter 2 LTI S
40、ystemsExample 2.4 otherwise , 0 40 , 1 nnx otherwise , 0 60 , a nnnh10aDetermine the output signal nySolution (a) n0 微分微分n0, 222 bsbetbIf b0, txhas no Laplace transform.bjb bsbRe345 Chapter 9 The Laplace Transform tx sX maxRes tx tx minResProperty 7: If the Laplace transform of is rational, is right
41、 sided, is left sided,Example 9.8 211sssXj12j21 2Res 1Re2sj12 1Resleft sidedtwo sidedright sided346 Chapter 9 The Laplace TransformBasic Laplace Pairs tx sXPoles ROC t1none sRes1 tu 0Restu 0Ress1 tueat asRetueat asReas1as10s0sasas347 Chapter 9 The Laplace Transform9.3 The Inverse Laplace Transform F
42、 tetxsX desXetxtjt21 deesXtxtjt21jsjdds :jjs :ROC dsesXjtxstjj21defininga0j j j348 Chapter 9 The Laplace TransformExample 9.9 211sssXDetermine the inverse Laplace transform for all possible ROC. 21 11sssXSolution:j12 1Res 11s 1Res tuet 21 s 2Res tuet2 tuetuetxtt2 1Re s349 Chapter 9 The Laplace Trans
43、formj21 1Re2s 11s 1Restuet 1Re2 s 21 s 2Res tuet2 tuetuetxtt2j12 2Res 2Re s 11s 1Restuet 21 s 2Restuet2 tuetuetxtt2350 Chapter 9 The Laplace Transform9.4 Geometric evaluation of the Fourier transform几何求值几何求值from the Pole-Zero plot ROC0 jssXjX 11iniimissMsX 11iniimijjMjXijiijijPole vector:ijiieAjZero
44、 vector:ijiieBjiAiBii351 Chapter 9 The Laplace TransformnmjnmeAAABBBMjX2121 2121 2121nmAAABBBMjX nmjX21212/1j 21Re 2/11sssXExample 9.12 2/11jjX2/1j 11AjX 1jX352 Chapter 9 The Laplace Transform 0 /1Re 11sssH 0 /1Re /1/1sjjH9.4.1 First-Order System txtyty tuetht/1time constant (时间常数）时间常数）controls the
45、speed of response of first-order systems/1j353 Chapter 9 The Laplace Transform9.4.2 Second-Order System 0, 1 . 12121sssH 21,maxResj22A2 121jjjH tueCtueCthtt2121111A 121AAjH 21jH中的快速反应项中的快速反应项 th中的慢速反应项中的慢速反应项 th354 Chapter 9 The Laplace Transform 21 21 . 222nnsssH 2/1 , 2 221n2sssH 1Re 111sjsjssHjj1
46、2A2j111A 111jjjjjH 121AAjH 21jH355 Chapter 9 The Laplace Transform9.4.3 All-Pass Systems （全通系统）（全通系统）Constant jHFirst-Order Systemj11j1A11j1B 11jjjH零极点相对于零极点相对于j轴对称轴对称 11jjjH112 1tgjHjH全通系统：零极点个数相同，且相对于全通系统：零极点个数相同，且相对于j轴对称。轴对称。 11BA 356 Chapter 9 The Laplace Transform9.5 Properties of the Laplace T
47、ransform9.5.1 Linearity of the Laplace Transform sbXsaXtbxtaxL2121 sXtxL111RRoc sXtxL222RRoc 21RRRoc357 Chapter 9 The Laplace TransformExample 9.13 1Re 2112ssssX 1Re 111sssXj12j1 2121ssXsXsX 2Re s tuetxt2j2358 Chapter 9 The Laplace Transform9.5.2 Time Shifting 0L0stesXttx sXtxLRRoc RRoc Example kTtt
48、xk0 1Lt sRe LskTekTt sRe kTtk0ksTke0LsTe11Poles:10 , 2,kTkjskjpole-zero plotTj2Tj2359 sXtxL Chapter 9 The Laplace Transform9.5.3 Shifting in s-Domain 0L0ssXetxtsRRoc 0Re sRRocROC的边界平移的边界平移j2r 21Rersr1rj 0201ReReResrssr 01Re sr 02Re sr 360 Chapter 9 The Laplace Transform 0Re 1Lsstu tueat 1Las asRe00j
49、s When 0L0jsXetxtjRRoc tuetj0 10Ljs 0Res tuetj0 10Ljs 0Res tut0cos00L2/1 2/1jsjs361 Chapter 9 The Laplace Transform 202L0cossstut 0Res 2020L0sinstut 0Res tuteat0cos202Lasas asRe tuteat0sin2020Las asRe362 Chapter 9 The Laplace Transform9.5.4 Time Scaling sXtxLRRoc asXaatx/1LaRRoc 1Re 11sstueLt tuet22
50、 12/121sL 21s 2Res tuet2363 Chapter 9 The Laplace Transform 122 set 1Re1s1j1 442 2 set 2Re2s2j2 4/112 21 set 21Re21s21j21364 Chapter 9 The Laplace TransformsXtxLRRocWhen 1a asastueLatRe 1 1astueLat 1as as Re9.5.5 Conjugation sXtxLRRoc sXtxLRRoc txtx sXsX365 Chapter 9 The Laplace Transform9.5.6 Convo
