信号与系统英文版课件：Chap1 Signals and Systems Basics

1、Signals and SystemsAutumn 2015TextbookA. V. Oppenheim, A. S. Willsky, and S. H. Nawab, Signals and Systems, 2nd Ed., Prentice Hall,1999.Contains many practical examplesSelective readingJ. R. Buck, M. M. Daniel and A. C. Singer, Computer Exploration in Signals and Systems Using MATLAB, 刘树棠(译), 西安交通大学

2、出版社, 2000.Homework & MatlabEssential for understanding the contentTest how well you have learnedHelp practice and master thingsHomework AssignmentAssign homework before chapter starts Collect before new chapter starts (no late homework will be accepted)Matlab PracticeNumerically manipulate signals a

3、nd model systemsSolve practical problemsEvaluationHomework & In-class participation: 10% Matlab practice & project: 20% Midterm exam: 20%Final exam: 50%About This CourseProfessionally-Related Core CourseA bridge between the professional and the fundamental Important for students in related majorsImp

4、ortant for many practical systems4000 out of 5000 UESTC undergraduates take this courseSignificant ImportanceTest subject of M.S./Ph.D. entrance examUseful throughout your study and research processCourse OutlineChap 1: Signals and Systems BasicsChap 2: Linear Time-Invariant SystemsChap 3: Fourier S

5、eries Representation of Periodic SigsChap 4: The Continuous-Time Fourier TransformChap 5: The Discrete-Time Fourier TransformChap 6: Time and Freq Characterization of Sig & SysChap 7: SamplingChap 8: Communication SystemsChap 9: Laplace TransformChap 10: Z TransformSignals and Systems BasicsChapter

6、1Topics Covered1.0 Introduction1.1 Continuous-Time and Discrete-Time Signals1.2 Transformations of the Independent Variable 1.3 Exponential and Sinusoidal Signals 1.4 The Unit Impulse and Unit Step functions 1.5 Continuous-time and Discrete-Time Systems1.6 Basic System Properties Homework #11.9 (b)

7、(c), 1.14, 1.15, 1.16, 1.17, 1.19 (b) (d), 1.20, 1.21 (b), 1.22 (c) (f), 1.23, 1.24, 1.27 (a) (f), 1.31Intro to Signals and Systems Conceptssystemsignal insignal outcomponentone thinganother thingA mathematical way of describing how a (physical, mathematical, or computational) component transforms o

8、ne thing to another. Example: CameraA camera is a system that receives lights from different sources and reflected from objects and produces a photograph. systemsignal insignal outExample: CameraIf the input signal changes, the output may change accordingly. systemsignal insignal outExample: Circuit

9、Voltages and currents are examples of signals, and a circuit itself an example of a system.v(t)i(t)circuitsystemsignal insignal outExample: CircuitVoltages and currents are functions of time.i(t)v(t)v(t)i(t)circuitsystemsignal insignal outExample: Cell PhoneCell phone system with sound in and out is

10、 another example. x(t)y(t)x(t)y(t)cell phones and towerssystemsignal insignal outOther ExamplesAx(t)amplifierintegratorx(t)wirex(t)mappingx(t)y(t)systemsignal insignal outLarge Area of ApplicationsThe concepts of signals and systems arise in a wide variety of fields, such as electronics, optics, mec

11、hanics, biology, finance, and so forth. mappingx(t)y(t)systemsignal insignal outSignalA tool that carries information.Can be represented as a mathematical function of one or more variables.i(t)v(t)Signals v(t) and i(t) are represented as functions of time variable t.Example: Traffic SignalsThe curve

12、 of a signal as a function of time is often called the waveform of the signal. red (STOP)green (GO)01Example: Sinusoidal SignalsThe amplitude A, angular frequency , and initial phase can carry information. E.g. In binary digital communicationssuppose we employ A to carry informationDIGIT 0digit 1Exa

13、mple: Sinusoidal SignalsThe amplitude A, angular frequency , and initial phase can carry information. E.g. In binary digital communicationssuppose we employ to carry informationDIGIT 0digit 1Example: Sinusoidal SignalsThe amplitude A, angular frequency , and initial phase can carry information. E.g.

14、 In binary digital communications suppose we employ to carry informationDIGIT 0digit 1Example: Frequency Shift Key SignalFSK signal is widely used in binary digital communicationsDIGIT 0digit 1DIGIT 0digit 1Example: Periodic Pulse SignalUse magnitude A, period T, and pulse width T1 to carry informat

15、ion.Example: Image SignalThe color of a pixel (i.e. picture element - a single point in a raster image) is an image signal, which can be represented by a binary function f (x, y) with variables x and y denoting the coordinates of the pixel.Causal SignalA signal f(t) is called a causal signal ifE.g.f

16、orAnticausal SignalA signal f(t) is called an anticausal signal ifE.g.forFinite Duration SignalA signal f(t) is called a finite duration signal if where t1 t2 are both finite numbers.E.g.forRight-Sided SignalA signal f(t) is called a right-sided signal if where t1 is a finite number.E.g.forcasual si

17、gnal right-sided signal Left-Sided SignalA signal f(t) is called a left-sided signal if where t2 is a finite number.E.g.foranticasual signal left-sided signal Two-Sided SignalA signal f(t) is called a two-sided signal if for any positive finite number t0E.g.forClassification of SignalsContinuous-tim

18、e signal vs discrete-time sigDeterministic signal vs random signalReal signal vs complex signalPeriodic signal vs aperiodic signalFinite-energy signal vs finite power signalContinuous-Time SignalA signal f(t) is called a continuous-time (CT) signal if the range of its variable t is continuous.E.g. f

19、 (t) = 0 f (t) = 1 f (t) = cos(t + ) Continuous-Time SignalA signal f(t) is called a continuous-time (CT) signal if the range of its variable t is continuous.E.g. f (t) is a continuous-time signal, but not a continuous functionContinuous-Time SignalA signal f(t) is called a continuous-time (CT) sign

20、al if the range of its variable t is continuous.In practice, CT signal is also called analog signal. Discrete-Time SignalA signal f(t) is called a discrete-time (DT) signal if the range of its variable t is discrete, i.e. t is defined at discrete points (usually integers)E.g. average temperature of

21、a month stock index image signal, etc.DT signal is also called DT sequenceDiscrete-Time SignalA signal f(t) is called a discrete-time (DT) signal if the range of its variable t is discrete, i.e. t is defined at discrete points (usually integers)E.g. Is the traffic signal x(t) a DT signal? CT signalS

22、amplingDT signal can be obtained from CT signal via sampling.CT signalDT signalDeterministic Sig vs Random SigSignal that can be expressed as a deterministic function is a deterministic signal. E.g. f (t) = t3 + 2tA random signal cannot be expressed as a deterministic function. The value of a random

23、 signal at any given time is a random variable.Mainly focus on deterministic signals. Real Signal vs Complex Signalreal signalsA real signal can be expressed as a real function. E.g. f (t) = a(t) cos0t+(t)A complex signal can be expressed as a complex function E.g. f (t) = a(t) exp j(t) = a(t) cos(t

24、) + j a(t) sin(t)Eulers relationReal Signal Ex - Gate Signalsignal widthReal Signal Ex - Sampling SignalSinc function:Real Signal Ex - Triangular Pulse SigPeriodic Signal vs Aperiodic SignalFor a CT signal f(t), if there exists a positive number T such that f(t+T) = f(t), then f(t) is a periodic sig

25、nal. The smallest T is called the (fundamental) period.For a DT signal fn, if there exists a positive integer N such that fn+N = fn, then fn is a periodic signal. The smallest N is called the (fundamental) period.Otherwise, the signal is aperiodic. For a CT signal f(t), if there exists a positive nu

26、mber T such that f(t+T) = f(t), then f(t) is a periodic signal. The smallest T is called the (fundamental) period.Periodic Signal Ex - Pulse TrainThe pulse train x(t) is a periodic signal with period T.Periodic Signal Ex - CT Cx ExpCT sinusoidal signal f(t) is periodic with period T = 2 / 0CT comple

27、x exponential signal f(t) is periodic with period T = 2 / 0Periodic Signal Ex - DT Compl ExpDT sinusoidal signal fn is periodic iff 0N = 2 k 0 = 2k / N k and N both integers, so (2k / N) is a rational number 0 must be rational multiples of for the DT sinusoidal signal to be periodic with period (N =

28、 2 k / 0) DT complex exponential signal is periodic iff 0 equals rational multiples of Periodic Signal Ex Given a DT signal , determine if it is a periodic signal? If yes, determine the period. Solution: Since , the second term is periodic with period N1=2. Since , the third term is periodic with pe

29、riod N2=4. fn is a periodic signal, the period N is the least common multiple of N1 and N2, i.e. N = 4. Instant Power and Signal Energy Instant power CT signal f(t) DT signal fnSignal energy CT signal f(t) DT signal fnInfinite-Energy-and-Power SignalAverage power CT signal f(t) DT signal fn Finite-e

30、nergy signalFinite-power signalInfinite-energy-and-power signalExampleConsider a CT signal (1) Is it periodic? If yes, determine its period. (2) Is it a finite-energy or finite-power signal?Solution: (1) For t 0, f (t+T) = sin (t+T)/2. It seems that f (t) is periodic with period T = 4. However, we c

31、an easily find a counter example when t 0t0 1)stretch(a t0). E.g. Are these system memoryless? Causal? memorylesscausalcausalwith memorycausalwith memorynoncausalwith memoryStabilityA system is stable if finite inputs lead to finite outputs. E.g. Is the system stable? Stable SystemyesnoTime Invarian

32、ceConceptually, a system is time invariant if the behavior and characteristics of the system are fixed over time.If y(t) is the output of a time-invariant system when the input is f(t), then y(t-t0) will be the output when the input is f(t-t0). Time-invariant SystemThe response to a delayed input equals the delayed response.LinearityA system is linear if it has both the additivity property and the homogeneity property.Additivity: If f1(t) - y1(t) and f2(t) - y2(t), then f