信號(hào)與系統(tǒng)課件第一章

1、信號(hào)與系統(tǒng)課件第一章信號(hào)與系統(tǒng)課件第一章Ch1 Introduction (緒論緒論)本章重點(diǎn)本章重點(diǎn): What is a signal? 什么是信號(hào)? What is a system? 什么是系統(tǒng)? Classifications of signals 信號(hào)的分類(lèi) Basic operations of signals 信號(hào)的基本運(yùn)算 Basic signals 基本信號(hào) Properties of systems 系統(tǒng)的特性信號(hào)與系統(tǒng)課件第一章Ch1.1 What is a Signal (信號(hào)信號(hào))? A Speech signal Its amplitude varies with

2、 time, depending on the spoken word and who speaks it. Its a one-dimensional signal.x(t)信號(hào)與系統(tǒng)課件第一章What is a Signal? Electrocardiogram (ECG) Signal Represent the electrical activity of the heart. Its a one-dimensional signal.x(t)信號(hào)與系統(tǒng)課件第一章What is a Signal?I(x,y) An image is a function of two spatial

3、coordinates. Its a two-dimensional signal.信號(hào)與系統(tǒng)課件第一章What is a Signal (信號(hào)信號(hào))? Definitions A Signal is formally defined as a function of one or more variables that conveys information on the nature of a physical phenomenon.信號(hào)信號(hào)是一個(gè)或多個(gè)變量的函數(shù)，攜帶著某個(gè)物理現(xiàn)象的信息。信號(hào)與系統(tǒng)課件第一章Ch1.2 What is a System(系統(tǒng)系統(tǒng))?A System is

4、 formally defined as an entity that manipulates one or more signals to accomplish a function, thereby yielding new signals. Definitions 信號(hào)與系統(tǒng)課件第一章Ch1.3 Overview of Specific SystemsElements of a communication system. The transmitter changes the message signal into a form suitable for transmission ove

5、r the channel. The receiver processes the channel output (i.e., the received signal) to produce an estimate of the message signal.Examples: Communication Systems(通信系統(tǒng)通信系統(tǒng))信號(hào)與系統(tǒng)課件第一章(a) Snapshot of Pathfinder exploring the surface of Mars.(b) The 70-meter (230-foot) diameter antenna located at Canber

6、ra, Australia. The surface of the 70-meter reflector must remain accurate within a fraction of the signals wavelength. (Courtesy of Jet Propulsion Laboratory.)信號(hào)與系統(tǒng)課件第一章Examples: Control Systems(控制系統(tǒng)控制系統(tǒng))Block diagram of a feedback control system. The controller drives the plant, whose disturbed out

7、put drives the sensor(s). The resulting feedback signal is subtracted from the reference input to produce an error signal e(t), which, in turn, drives the controller. The feedback loop is thereby closed.信號(hào)與系統(tǒng)課件第一章Examples: Biomedical Signal Processing(生物信號(hào)處理生物信號(hào)處理)The traces shown in (a), (b), and (

8、c) are three examples of EEG signals recorded from the hippocampus of a rat. Neurobiological studies suggest that the hippocampus plays a key role in certain aspects of learning and memory. 信號(hào)與系統(tǒng)課件第一章(a) In this diagram, the basilar membrane in the cochlea is depicted as if it were uncoiled and stre

9、tched out flat; the “base” and “apex” refer to the cochlea, but the remarks “stiff region” and “flexible region” refer to the basilar membrane. Examples: Auditory Systems(聽(tīng)覺(jué)系統(tǒng)聽(tīng)覺(jué)系統(tǒng))(b) This diagram illustrates the traveling waves along the basilar membrane, showing their envelopes induced by incoming

10、 sound at three different frequencies.信號(hào)與系統(tǒng)課件第一章學(xué)習(xí)方法學(xué)習(xí)方法 理論與實(shí)際相結(jié)合，物理概念、數(shù)學(xué)概念和工程概念并重。 掌握信號(hào)與系統(tǒng)分析的基本思想和方法；注意問(wèn)題的提出、分析問(wèn)題和解決問(wèn)題的方法。 講、練、做相結(jié)合；加強(qiáng)計(jì)算機(jī)實(shí)踐環(huán)節(jié)，用 MATLAB進(jìn)行信號(hào)與系統(tǒng)的分析。信號(hào)與系統(tǒng)課件第一章本課程教學(xué)與學(xué)習(xí)的安排本課程教學(xué)與學(xué)習(xí)的安排1. 課堂教學(xué)：講解重點(diǎn)內(nèi)容和學(xué)生學(xué)習(xí)中遇到的疑難問(wèn)題。 2. 作業(yè)： 書(shū)面作業(yè)（理論）+ MATLAB上機(jī)作業(yè)（實(shí)踐）。3. 期中和期末考試：閉卷形式。主要考察學(xué)生對(duì)本門(mén)課的基本理論基本原理及重點(diǎn)內(nèi)容的掌握程度

11、。4.課程成績(jī)的組成： 由書(shū)面作業(yè)、MATLAB作業(yè)、期中考試和期末考試4部分組成。信號(hào)與系統(tǒng)課件第一章主要參考書(shū)主要參考書(shū)1 Simon H.,Barry V.V. Signals and Systems. John Wiley & Sons,Inc.19992 Edward W.K.,Bonnie S.H. Fundamentals of Signals and Systems Using MATLAB. Prentice-Hall International,Inc. 19973 A.V.Oppenheim. Signals and Systems 或中譯本（第2版）. 西安交通大學(xué)出版

12、社.4 鄭君里，應(yīng)啟珩等. 信號(hào)與系統(tǒng). 第2版. 高等教育出版社，2000. 信號(hào)與系統(tǒng)課件第一章主要參考書(shū)主要參考書(shū)5 吳湘淇等. 信號(hào)、系統(tǒng)與信號(hào)處理(上). 第2版. 電子工業(yè)出版社，20016 吳湘淇,郝曉莉等. 信號(hào)、系統(tǒng)與信號(hào)處理軟硬件 實(shí)現(xiàn).電子工業(yè)出版社，20027 陳后金等. 信號(hào)與系統(tǒng). 清華大學(xué)出版社， 20038 陳后金等. 信號(hào)與系統(tǒng)學(xué)習(xí)指導(dǎo)與習(xí)題精解. 清華大學(xué)出版社，2004信號(hào)與系統(tǒng)課件第一章Ch1.4 classifications of signals (信號(hào)的分類(lèi)信號(hào)的分類(lèi)) 1. continuous-time and discrete-time si

13、gnals 連續(xù)時(shí)間信號(hào)和離散時(shí)間信號(hào)2. periodic and non-periodic signals 周期信號(hào)和非周期信號(hào)3. deterministic and random signals 確定信號(hào)和隨機(jī)信號(hào)4. Energy and power signals 能量信號(hào)和功率信號(hào)信號(hào)與系統(tǒng)課件第一章Continuous-time and Discrete-time signals 連續(xù)時(shí)間信號(hào)和離散時(shí)間信號(hào)連續(xù)時(shí)間信號(hào)和離散時(shí)間信號(hào)(a) Continuous-time signal x(t). (b) Representation of x(t) as a discrete-

14、time signal xn.信號(hào)與系統(tǒng)課件第一章 Continuous-time and Discrete-time signals 連續(xù)時(shí)間信號(hào)和離散時(shí)間信號(hào)連續(xù)時(shí)間信號(hào)和離散時(shí)間信號(hào) Discrete-time signal: a signal if it is defined only at discrete instants of time. 離散時(shí)間信號(hào)：若信號(hào)僅在某些離散時(shí)刻處有定離散時(shí)間信號(hào)：若信號(hào)僅在某些離散時(shí)刻處有定義義, 用用xn表示。表示。Continuous-time signal: a signal if it is defined for all time t.

15、連續(xù)時(shí)間信號(hào)：若信號(hào)在所有時(shí)間連續(xù)時(shí)間信號(hào)：若信號(hào)在所有時(shí)間t 處都有定義處都有定義, 用用x(t)表示。表示。Definitions 信號(hào)與系統(tǒng)課件第一章 Continuous-time and Discrete-time signals 連續(xù)時(shí)間信號(hào)和離散時(shí)間信號(hào)連續(xù)時(shí)間信號(hào)和離散時(shí)間信號(hào)離散信號(hào)可以由連續(xù)信號(hào)取樣離散信號(hào)可以由連續(xù)信號(hào)取樣(sampling)得來(lái)：得來(lái)： xn=x(t)|t=nT =x(nT) T稱(chēng)為稱(chēng)為取樣間隔取樣間隔 信號(hào)與系統(tǒng)課件第一章periodic and non-periodic signals 周期信號(hào)和非周期信號(hào)周期信號(hào)和非周期信號(hào)(a) Square w

16、ave with amplitude A = 1 and period T = 0.2s.(b) Rectangular pulse of amplitude A and duration T1.信號(hào)與系統(tǒng)課件第一章Periodic and Non-Periodic Signals (周期信號(hào)與非周期信號(hào)周期信號(hào)與非周期信號(hào))A Periodic signals is a function of time that satisfies the condition: x(t+T) = x(t) for all t.Definition Fundamental Period: T0， the sm

17、allest value of T that satisfies the definition.,4 ,3 ,2,0000TTTTT Period：信號(hào)與系統(tǒng)課件第一章Periodic and Non-Periodic Signals (周期信號(hào)與非周期信號(hào)周期信號(hào)與非周期信號(hào))Definition Frequency)Hz(1Tf Fundamental Frequency)Hz(100Tf Angular Frequency) s/rad(220Tf信號(hào)與系統(tǒng)課件第一章Periodic and Non-Periodic Signals (周期信號(hào)與非周期信號(hào)周期信號(hào)與非周期信號(hào))(a) S

18、quare wave with amplitude A = 1 and period T = 0.2s.(b) Rectangular pulse of amplitude A and duration T1.信號(hào)與系統(tǒng)課件第一章Problem: Triangular wave alternative between 1 and +1 信號(hào)與系統(tǒng)課件第一章Periodic and Non-Periodic Signals (周期信號(hào)與非周期信號(hào)周期信號(hào)與非周期信號(hào))A discrete Periodic signals is a function of time that satisfies

19、the condition: xn+N = xn for integer n.Definition Fundamental Period: N， the smallest integer that satisfies the definition.信號(hào)與系統(tǒng)課件第一章Periodic and Non-Periodic Signals (周期信號(hào)與非周期信號(hào)周期信號(hào)與非周期信號(hào))Definition PeriodNFundamental Frequency)rad(2N信號(hào)與系統(tǒng)課件第一章(a) Discrete-time square wave alternative between 1 an

20、d +1. (b) Non-periodic discrete-time signal consisting of three nonzero samples.periodic and non-periodic signals (周期信號(hào)和非周期信號(hào)周期信號(hào)和非周期信號(hào))信號(hào)與系統(tǒng)課件第一章Deterministic and Random Signals確定性信號(hào)和隨機(jī)信號(hào)確定性信號(hào)和隨機(jī)信號(hào)(非確定性信號(hào)非確定性信號(hào))Definitions A random signal is a signal about which there is uncertainty before it occur

21、s.隨機(jī)信號(hào)：再出現(xiàn)之前具有不確定性的信號(hào)。隨機(jī)信號(hào)：再出現(xiàn)之前具有不確定性的信號(hào)。A deterministic signal is a signal about which there is no uncertainty with respect to its value at any time.確確定性信號(hào)：在任意時(shí)刻都有確定的值的信號(hào)定性信號(hào)：在任意時(shí)刻都有確定的值的信號(hào)。信號(hào)與系統(tǒng)課件第一章Deterministic and Random Signals確定性信號(hào)和隨機(jī)信號(hào)確定性信號(hào)和隨機(jī)信號(hào)xn0Nn信號(hào)與系統(tǒng)課件第一章Deterministic and Random Signal

22、s確定性信號(hào)和隨機(jī)信號(hào)確定性信號(hào)和隨機(jī)信號(hào)tttX(t)(1tx)(2tx)(3tx信號(hào)與系統(tǒng)課件第一章Energy and Power signals (能量信號(hào)和功率信號(hào)能量信號(hào)和功率信號(hào))Definitions: EnergyTTTdttxE2)(limAverage PowerTTTdttxTP2)(21limNNnnnxE2)(limNNnnnxNP2)(21lim信號(hào)與系統(tǒng)課件第一章Energy and Power signals (能量信號(hào)和功率信號(hào)能量信號(hào)和功率信號(hào))Definitions: Energy Signal E0Power Signal)0(P)(E P0信號(hào)與系統(tǒng)

23、課件第一章Energy and Power signals 能量信號(hào)和功率信號(hào)能量信號(hào)和功率信號(hào)Problem: Determine the total energy of the discrete-time signal.信號(hào)與系統(tǒng)課件第一章Energy and Power signals (能量信號(hào)和功率信號(hào)能量信號(hào)和功率信號(hào))Problem: Determine the average power of the square wave. amplitude A = 1 and period T = 4s, T0 = 1s.)(txtT0T0TT10信號(hào)與系統(tǒng)課件第一章Energy and

24、 Power signals (能量信號(hào)和功率信號(hào)能量信號(hào)和功率信號(hào))te2te2Energy signal? Power signal?信號(hào)與系統(tǒng)課件第一章Ch1.5 basic operations on signals信號(hào)的基本運(yùn)算信號(hào)的基本運(yùn)算 1. 基于從變量（信號(hào)本身或信號(hào)之間）的運(yùn)算 幅度變化； 相加和相乘； 連續(xù)信號(hào)的微積分，離散信號(hào)的差分與累加 2. 基于自變量的運(yùn)算 連續(xù)信號(hào)的翻轉(zhuǎn)、展縮和平移 離散信號(hào)的翻轉(zhuǎn)、展縮和平移信號(hào)與系統(tǒng)課件第一章operations performed on dependent variables (基于從變量的運(yùn)算基于從變量的運(yùn)算) 1. Am

25、plitude scaling (幅度比例變化) x(t) cx(t) xn cxn (c為常數(shù)) 波形不變，幅度成比例放大或縮小。 Example：x(t)=sin(210t) ; y(t)=5x(t)=5sin(210t) ; 信號(hào)與系統(tǒng)課件第一章operations performed on dependent variables (基于從變量的運(yùn)算基于從變量的運(yùn)算) 2. Addition (信號(hào)相加) y(t) = x1(t)+x2(t) y(n) = x1n+x2n3. Multiplication (信號(hào)相乘) y(t) = x1(t) x2(t) y(n) = x1n x2n信

26、號(hào)與系統(tǒng)課件第一章operations performed on dependent variables (基于從變量的運(yùn)算基于從變量的運(yùn)算)tdxty)()( 4. Differentiation(連續(xù)信號(hào)的微分) 5. integration（連續(xù)信號(hào)的積分）dttdxty)()(信號(hào)與系統(tǒng)課件第一章operations performed on dependent variables (基于從變量的運(yùn)算基于從變量的運(yùn)算)tdiCtv)(1)( Example：電感兩端的電壓與其電流為微分關(guān)系： Example： 電容兩端的電壓與其電流為積分關(guān)系：dttdiLtv)()(信號(hào)與系統(tǒng)課件第一

27、章operations performed on independent variables (基于信號(hào)自變量的運(yùn)算基于信號(hào)自變量的運(yùn)算) (a) continuous-time signal x(t)(b) version of x(t) compressed by a factor of 2,(c) version of x(t) expanded by a factor of 2.1.Time scaling（尺度展縮）: y(t)=x(at) a0 若0a1，則x(at)是x(t)擴(kuò)展1/a倍。 若a1， 則x(at)是x(t)壓縮a倍。 信號(hào)與系統(tǒng)課件第一章Time scaling（

28、尺度展縮）（尺度展縮） (a) discrete-time signal xn (b) version of xn compressed by a factor of 2, with some values of the original xn lost as a result of the compression.yn= xkn信號(hào)與系統(tǒng)課件第一章operations performed on independent variables (基于信號(hào)自變量的運(yùn)算基于信號(hào)自變量的運(yùn)算) (a) continuous-time signal x(t)(b) reflected version of

29、 x(t) about the origin. 2. reflection（ 翻轉(zhuǎn)）: y(t)=x(-t) x(-t)表示將x(t)以縱軸為中心作180翻轉(zhuǎn)。信號(hào)與系統(tǒng)課件第一章Reflection（ 翻轉(zhuǎn)）翻轉(zhuǎn)）Problem: Find the reflected version of xn and yn2. reflection（ 翻轉(zhuǎn)）: xn x-n xn以縱軸為中心作180翻轉(zhuǎn)信號(hào)與系統(tǒng)課件第一章operations performed on independent variables (基于信號(hào)自變量的運(yùn)算基于信號(hào)自變量的運(yùn)算) (a) continuous-time sign

30、al in the form of a rectangular pulse of amplitude 1.0 and duration 1.0, symmetric about the origin;(b) time-shifted version of x(t) by 2 time shifts. 3.Time shifting (時(shí)移 ): y(t) =x(tt0) x(tt0)表示信號(hào) x(t)右移t0單位； x(tt0)表示信號(hào)x(t)左移t0單位。信號(hào)與系統(tǒng)課件第一章Time shifting (時(shí)移時(shí)移 )n10nx-12 34-21-12Problem: Find the tim

31、e-shifted signal yn= xn+3 yn=xn k ，k0 xn+k，左移k單位； xn-k， 右移k單位。信號(hào)與系統(tǒng)課件第一章operations performed on independent variables (基于信號(hào)自變量的運(yùn)算基于信號(hào)自變量的運(yùn)算)abtaxbatx)()()()()(abtaxatxtxtx時(shí)移展縮翻轉(zhuǎn) 總結(jié)公式：信號(hào)與系統(tǒng)課件第一章operations performed on independent variables (基于基于信號(hào)自變量的運(yùn)算信號(hào)自變量的運(yùn)算)1t30 x(t)2)3(2(3)2(2)()( txtxtxtx右移縮翻轉(zhuǎn)1

32、t1x(2t)1.5x(2t+6)1.54t11t2x(t)3Example: 已知x(t)的波形如圖所示，試畫(huà)出x(2t)、 x(t/3)、 x(t+6) 、x(-t)、 x(62t)的波形。信號(hào)與系統(tǒng)課件第一章operations performed on independent variables (基于基于信號(hào)自變量的運(yùn)算信號(hào)自變量的運(yùn)算)n10nx-12 34-21-12Example: 已知x(n)的波形如圖所示，求xn+2、 x-n 、x-n-2、x-n/3、 x2n 的波形。信號(hào)與系統(tǒng)課件第一章Ch1.6 Basic Signals基本信號(hào)基本信號(hào)Exponential Sig

33、nals 指數(shù)信號(hào)指數(shù)信號(hào)Sinusoidal Signals 正弦信號(hào)正弦信號(hào)Exponential Damped Sinusoidal Signals 按指數(shù)按指數(shù)衰減的正弦信號(hào)衰減的正弦信號(hào)Step Signals 階躍信號(hào)階躍信號(hào)Impulse Signals 沖激信號(hào)沖激信號(hào)Derivatives of The Impulse 沖激信號(hào)的導(dǎo)數(shù)沖激信號(hào)的導(dǎo)數(shù)Ramp Function 斜坡函數(shù)斜坡函數(shù)信號(hào)與系統(tǒng)課件第一章Exponential Signals指數(shù)信號(hào)指數(shù)信號(hào) (a) Decaying exponential form of continuous-time signal.

34、(b) Growing exponential form of continuous-time signal.atBtxe)(信號(hào)與系統(tǒng)課件第一章Examples of Exponential Signals指數(shù)信號(hào)指數(shù)信號(hào)Lossy capacitor, with the loss represented by shunt resistance R. 信號(hào)與系統(tǒng)課件第一章Exponential Signals(指數(shù)信號(hào)指數(shù)信號(hào)) (a) Decaying exponential form of discrete-time signal.(b) Growing exponential form

35、 of discrete-time signal. nBrtx信號(hào)與系統(tǒng)課件第一章Sinusoidal signal(正弦信號(hào)正弦信號(hào)) (a) Sinusoidal signal Acos(t +) with phase=+/6 radians. (b) Sinusoidal signal Asin(t +) with phase=+/6 radians.Sinusoidal signal： x (t)=A cos(t + )信號(hào)與系統(tǒng)課件第一章Examples of Sinusoidal signal正弦信號(hào)正弦信號(hào)Parallel LC circuit, assuming that th

36、e inductor L and capacitor C are both ideal. 信號(hào)與系統(tǒng)課件第一章Sinusoidal signal正弦信號(hào)正弦信號(hào)Discrete-time sinusoidal signal.信號(hào)與系統(tǒng)課件第一章Relation between Sinusoidal and Complex Exponential Signals正弦信號(hào)和復(fù)指數(shù)信號(hào)的關(guān)系正弦信號(hào)和復(fù)指數(shù)信號(hào)的關(guān)系Complex plane, showing eight points uniformly distributed on the unit circle.信號(hào)與系統(tǒng)課件第一章Expone

37、ntially damped sinusoidal signal按指數(shù)衰減的正弦信號(hào)按指數(shù)衰減的正弦信號(hào)Exponentially damped sinusoidal signal Ae-at sin(t), with A = 60 and = 6.x (t)= Ae-at sin(t)， 0信號(hào)與系統(tǒng)課件第一章Step function 階躍函數(shù)階躍函數(shù)Continuous-time version of the unit-step function of unit amplitude.0 00 1)(tttuDefinitions:信號(hào)與系統(tǒng)課件第一章Step function(階躍函數(shù)階

38、躍函數(shù))(a) Rectangular pulse x(t) of amplitude A and duration of 1 s, symmetric about the origin. (b) Representation of x(t) as the difference of two step functions of amplitude A, with one step function shifted to the left by and the other shifted to the right by ; the two shifted signals are denoted

39、by x1(t) and x2(t), respectively. Note that x(t) = x1(t) x2(t).信號(hào)與系統(tǒng)課件第一章Examples of Step function 階躍函數(shù)階躍函數(shù)(a) Series RC circuit with a switch that is closed at time t = 0, thereby energizing the voltage source. (b) Equivalent circuit, using a step function to replace the action of the switch.信號(hào)與系統(tǒng)課

40、件第一章t)(t)1 (01=d )( tt(t)=0 , t0Definitions:Unit Impulse單位沖激信號(hào)單位沖激信號(hào)000 1kkk011k2k2信號(hào)與系統(tǒng)課件第一章(a) Evolution of a rectangular pulse of unit area into an impulse of unit strength (i.e., unit impulse). (b) Graphical symbol for unit impulse. (c) Representation of an impulse of strength a that results fro

41、m allowing the duration of a rectangular pulse of area a to approach zero.Examples of Unit Impulse沖激信號(hào)沖激信號(hào)信號(hào)與系統(tǒng)課件第一章(a) Series circuit consisting of a capacitor, a dc voltage source, and a switch; the switch is closed at time t = 0. (b) Equivalent circuit, replacing the action of the switch with a s

42、tep function u(t).Examples of Unit Impulse沖激信號(hào)沖激信號(hào)信號(hào)與系統(tǒng)課件第一章篩選特性篩選特性)()()()(000tttftttxProperties of Unit Impulse沖激信號(hào)的性質(zhì)沖激信號(hào)的性質(zhì)信號(hào)與系統(tǒng)課件第一章取樣特性取樣特性)(d)()(00txttttxttttxd)()(0ttttxd)()(00ttttxd)()(00)(0tx利用篩選特性Properties of Unit Impulse沖激信號(hào)沖激信號(hào)信號(hào)與系統(tǒng)課件第一章展縮特性展縮特性)0( )(1)(tt推論：沖激信號(hào)沖激信號(hào)是偶函數(shù)。根據(jù)(t)泛函定義證明取 a

43、 = 1 , 可得 (t) = (t)Properties of Unit Impulse沖激信號(hào)的性質(zhì)沖激信號(hào)的性質(zhì)信號(hào)與系統(tǒng)課件第一章The Time-scaling Property of Unit Impulse沖激信號(hào)的時(shí)間展縮沖激信號(hào)的時(shí)間展縮Steps involved in proving the time-scaling property of the unit impulse. (a) Rectangular pulse x(t) of amplitude 1/ and duration , symmetric about the origin. (b) Pulse x(t

44、) compressed by factor a. (c) Amplitude scaling of the compressed pulse, restoring it to unit area.信號(hào)與系統(tǒng)課件第一章與與的關(guān)系的關(guān)系ttt0 00 1d)()(tuttud)(d)(tProperties of Unit Impulse沖激信號(hào)的性質(zhì)沖激信號(hào)的性質(zhì)信號(hào)與系統(tǒng)課件第一章Problemstttd)4()sin() 1 (325d) 1(e)2(ttt642d)8(e) 3(ttttttd)22(e)4(222d) 13()3()5(tttt)2()32)(6(23ttt)22(e

45、)7(4tt) 1()(e )8(2ttut信號(hào)與系統(tǒng)課件第一章2/2)4sin(d)4()sin() 1 (ttt51 5325e/1ed) 1(e)2(ttt0d)8(e)3(642ttte21d) 1(21ed)22(e)4(tttttt0d) 3(3)3(d) 13()3()5(222222tttttttt)2(19)2() 3222()2() 32)(6(2323ttttt) 1(e21) 1(e21) 1(21e)22(e )7(4(-1) 444tttttt0) 1(0) 1() 1(e) 1()(e )8(-1) 22ttuttutsolution信號(hào)與系統(tǒng)課件第一章Defin

46、itions:Derivatives of The Impulse function沖激函數(shù)的導(dǎo)數(shù)（沖激偶）沖激函數(shù)的導(dǎo)數(shù)（沖激偶）) 1 (t)( t0tttd)(d)( 信號(hào)與系統(tǒng)課件第一章Properties: 0d)(tt)( )( tt)()( )( )()( )(00000tttftttftttf)( d)( )(00tfttttf(取樣特性)(篩選特性)0)( )( 1)( tt(展縮特性)Derivatives of The Impulse function沖激函數(shù)的導(dǎo)數(shù)（沖激偶）沖激函數(shù)的導(dǎo)數(shù)（沖激偶）信號(hào)與系統(tǒng)課件第一章Ramp function(斜坡函數(shù)斜坡函數(shù))0 00

47、 )(ttttr)()(tuttr或0nknkkukrn123012344rkkDefinitions:信號(hào)與系統(tǒng)課件第一章t1)(tr1)(d)(dtuttrtutrd)()(0t)(tu1Relation Between Unit Function and Ramp function階躍函數(shù)與斜坡函數(shù)的關(guān)系階躍函數(shù)與斜坡函數(shù)的關(guān)系信號(hào)與系統(tǒng)課件第一章01tf (t)121)2() 1()() 1()(trtrtrtrtf01tf (t)11) 1(2)(2) 1()(trtrtutf解：解：Problems信號(hào)與系統(tǒng)課件第一章tttd)(d)( ttutd)(d)(ttrtud)(d)(d

48、 )()(tutrd )()(ttud )( )(ttRelations of Impulse Function, Unit Function and Ramp function沖激函數(shù)、階躍函數(shù)與斜坡函數(shù)的關(guān)系沖激函數(shù)、階躍函數(shù)與斜坡函數(shù)的關(guān)系信號(hào)與系統(tǒng)課件第一章Ch1.7 Systems Viewed as Interconnections of Operations Block diagram representation of operator H for (a) continuous time and (b) discrete time.信號(hào)與系統(tǒng)課件第一章Discrete-time

49、-shift operator Sk, operating on the discrete-time signal xn to produce xn k.Ex: Moving-Average Systems滑動(dòng)平均系統(tǒng)：y(n)=x(n)+x(n-1)+x(n-2)/3 信號(hào)與系統(tǒng)課件第一章Two different (but equivalent) implementations of the moving-average system: (a) cascade form of implementation and (b) parallel form of implementation.Ex

50、: Moving-Average Systems滑動(dòng)平均系統(tǒng)：y(n)=x(n)+x(n-1)+x(n-2)/3信號(hào)與系統(tǒng)課件第一章Ch1.8 Properties of Systems 1.Stability (穩(wěn)定性） 2.Causality （因果性） 3. Invertibility （可逆性）4.Time-Invariance (時(shí)不變性)5. linearity (線(xiàn)性)信號(hào)與系統(tǒng)課件第一章1. Stability (穩(wěn)定性）穩(wěn)定性）穩(wěn)定系統(tǒng)：Bounded Input-Bounded Output（ 有界輸入產(chǎn)生 有界輸出，BIBO穩(wěn)定）yxMtyMtx)()(yxMnyMnx)

51、()( )(tx)(ty連續(xù)系統(tǒng))(nx)(ny離散系統(tǒng)不穩(wěn)定系統(tǒng)：系統(tǒng)的輸入有界而輸出無(wú)界。信號(hào)與系統(tǒng)課件第一章Stability (穩(wěn)定性）穩(wěn)定性） Ex: Moving-Average Systems (滑動(dòng)平均系統(tǒng)). Show that the System is BIBO stable: y(n)=x(n)+x(n-1)+x(n-2)/3.Solution： y(n) = x(n)+x(n-1)+x(n-2) /3 （Mx+Mx+Mx）/3=Mx y(n)有界，系統(tǒng)穩(wěn)定。Solution： x(n) Mx1， rn ， y(n)無(wú)界，系統(tǒng)不穩(wěn)定Ex: Unstable System

52、. y(n)=rnx(n) , r1信號(hào)與系統(tǒng)課件第一章Dramatic photographs showing the collapse of the Tacoma Narrows suspension bridge on November 7, 1940. (a) Photograph showing the twisting motion of the bridges center span just before failure. (b) A few minutes after the first piece of concrete fell, this second photogra

53、ph shows a 600-ft section of the bridge breaking out of the suspension span and turning upside down as it crashed in Puget Sound, Washington. Note the car in the top right-hand corner of the photograph.An Unstable System信號(hào)與系統(tǒng)課件第一章2.Causality （因果性）（因果性） 因果：輸出不領(lǐng)先于輸入，即現(xiàn)時(shí)刻的輸出僅取決于當(dāng)前時(shí)刻的輸入和（或）過(guò)去時(shí)刻的輸入 Ex: M

54、oving-Average Systems (滑動(dòng)平均系統(tǒng)) y(n)=x(n)+x(n-1)+x(n-2)/3Is this system causal? 信號(hào)與系統(tǒng)課件第一章Causality （因果性）（因果性） Series RC circuit driven from an ideal voltage source v1(t), producing output voltage v2(t).Ex: Consider the RC circuit. Is this system causal or non-causal?信號(hào)與系統(tǒng)課件第一章3. Invertibility (可逆性可逆性)The notion of system invertibility. Th