信号与系统-课件-(第三版)

1、Signals and SystemsChapter 1Signals and SystemsChapter 11.1 SignalsSignals are functions of independent variables that carry information. The independent variables can be continuous or discrete.The independent variables can be 1-D, 2-D, , n-D.For this course: Focus on a single (1-D) independent vari

2、able which we call “time”. Continuous-Time signals: x(t), t-continuous values.Discrete-Time signals: x(n), n-integer values only.1.1 SignalsSignals are functiExamplesElectrical signals voltages and currents in a circuit.Acoustic signals audio or speech signals.Video signals intensity variations in a

3、n image. Biological signals sequence of bases in a gene.ExamplesElectrical signals vA Simple RC CircuitThe patterns of variation over time in the source voltage Vs and capacitor voltage Vc are examples of signals.A Simple RC CircuitThe patternA Speech SignalA Speech SignalA PictureA PictureVertical

4、Wind ProfileVertical Wind Profile1.2 SystemsFor the most part, our view of systems will be from an input-output perspective.A system responds to applied input signals, and its response is described in terms of one or more output signals.1.2 SystemsFor the most part,ExampleRLC circuitExampleRLC circu

5、itBy interconnecting simpler subsystems. We can build more complex systems.By interconnecting simpler sub1.3 Types of Signals1. Certain Signal and Random SignalCertain Signal Can be represented mathematically as a function of certain time.Random Signal Cant be represented mathematically as a functio

6、n of certain time. We only know the probability of certain value.1.3 Types of Signals1. CertaiExampleNoise Signal and Interfere SignalExampleNoise Signal and Interf2. Periodic Signal and Aperiodic SignalPeriodic Signal Has the property that it is unchanged by a time shift of T. For example, A period

7、ic continuous-time or discrete-time signal can be represented as:Aperiodic Signal Has not the property that it is unchanged by a time shift of T. Notice:When T,then Periodic Signal Aperiodic Signal.2. Periodic Signal and AperiodExamplePeriodic SignalExamplePeriodic Signal3. Continuous-time Signal an

8、d Discrete-time SignalContinuous-time Signal The independent variable is continuous, and thus these signals are defined for a continuum of values of the independent variable.Discrete-time Signal The independent variable takes on only a discrete times, and thus these signals are defined only at discr

9、ete times.3. Continuous-time Signal and ExampleContinuous-time SignalExampleContinuous-time SignalExampleDiscrete-time SignalExampleDiscrete-time Signal4. Energy and Power Signals Energy (Continuous-time)Instantaneous power:Let R=1, soEnergy over t1 t t2:4. Energy and Power Signals EnTotal Energy:Av

10、erage Power:Energy (Discrete-time)Instantaneous power:Total Energy:Average Power:EneEnergy over n1 n n2:Total Energy :Average Power:Energy over n1 n n2:Total Finite Energy and Finite Power SignalFinite Energy Signal (P 0) :Finite Power Signal (E ) :Finite Energy and Finite PowerExample(Finite Energy

11、 Signal)(Finite Power Signal)(Signals with neither finite total energy nor finite average power)Example(Finite Energy Signal)(1. Sinusoidal Signal1.4 Typical Signals1. Sinusoidal Signal1.4 TypicProperty:The Differential or Integral of f (t) is also a sinusoidal signal with the same frequency.importa

12、nt formulas :Property:important formulas :2. Real Exponential Signal2. Real Exponential SignalProperty:The Differential or Integral of f(t) is also a real exponential signal.Notice:When 0, f (t) is a growing function with t.When 0, f (t) is a decaying function with t.When 0, f (t) is a constant func

13、tion with t.Property:Notice:3. Complex Exponential SignalProperties:The real and imaginary of complex exponential signal are sinusoidal.For 0 they correspond to sinusoidal signal multiplied by a growing exponential.For 0 they correspond to sinusoidal signal multiplied by a decaying exponential.3. Co

14、mplex Exponential SignalP信号与系统-课件-(第三版)4. Sampling Signal4. Sampling Signal5. Unit Step Signal5. Unit Step Signal6. Unit Impulse Signal6. Unit Impulse SignalProperties:Relation Between Unit-Impulse and Unit-Step. Sampling Properties of (t). Properties:Relation Between Un7. Unit Impulse Even SignalPr

15、operties:7. Unit Impulse Even SignalPr8. Unit Triangle SignalProperties:8. Unit Triangle SignalPropert1.5 Basal Operation of Signals1. Plus and multiplication2. Time Inversal1.5 Basal Operation of Signals信号与系统-课件-(第三版)信号与系统-课件-(第三版)3. Time Shift3. Time Shift4. Flexibility4. FlexibilityExampleExample

16、信号与系统-课件-(第三版)1.6 The Representation of Continuous-time Signals in Terms of Impulses1.6 The Representation of ContDefine:Define:We have the expressionThereforeor We have the expressionTherefor信号与系统-课件-(第三版)1.7 Discrete-time Signal1.The Concepts of Discrete-time SignalThe independent variable takes o

17、n only a discrete times, and thus these signals are defined only at discrete times.1.7 Discrete-time Signal1.The 2. Basal Operation of Sequences2. Basal Operation of Sequence信号与系统-课件-(第三版)信号与系统-课件-(第三版)信号与系统-课件-(第三版)3. Typical of Sequences(1) Unit Sample(2)Unit Step Sequence3. Typical of Sequences(1

18、) Uni信号与系统-课件-(第三版)(3)Unit Rectangle Sequence(3)Unit Rectangle Sequence(5) Exponential SequenceNotice:For |1, x(n) is a growing sequence.For |1, x(n) is a decaying sequence. For |1, x(n) is a constant sequence. (5) Exponential SequenceNotice(a) 1；(b) 01；(c) -10；(d) 1；(b) 01；(c) -10；(6) Sinusoidal Se

19、quence(6) Sinusoidal Sequence(7) Complex Exponential SequenceProperty:The real and imaginary of complex exponential sequences are sinusoidal sequence.(7) Complex Exponential Sequen(8) Complex Exponential Signalthenin which(8) Complex Exponential Signal(a) Growing sinusoidal sequence；(b) Decaying sin

20、usoidal sequence(a) Growing sinusoidal sequenc4. The Representation of Discrete-time Signal in Terms of Unit Samples4. The Representation of Discr1.8 Calculation of Convolution1. Calculation of Convolution Integral1.8 Calculation of ConvolutionExampleExample信号与系统-课件-(第三版)When t0When 0t3When t0When 0t3When t32. Calculation of Convolution Sum2. Calculation of Convolution Example 1Soluti