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1、School of Computer Science and Information School of Computer Science and Information 1.1 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 singl
2、e(1-D)independent variable which we call“time”.Continuous-Time signals:x(t),t-continuous values.Discrete-Time signals:x(n),n-integer values only.School of Computer Science and Information ExamplesElectrical signals voltages and currents in a circuit.Acoustic signals audio or speech signals.Video sig
3、nals intensity variations in an image.Biological signals sequence of bases in a gene.School of Computer Science and Information A Simple RC CircuitThe patterns of variation over time in the source voltage Vs and capacitor voltage Vc are examples of signals.School of Computer Science and Information
4、A Speech SignalSchool of Computer Science and Information A PictureSchool of Computer Science and Information Vertical Wind ProfileSchool of Computer Science and Information 1.2 SystemsFor the most part,our view of systems will be from an input-output perspective.A system responds to applied input s
5、ignals,and its response is described in terms of one or more output signals.School of Computer Science and Information ExampleRLC circuitSchool of Computer Science and Information By interconnecting simpler subsystems.We can build more complex systems.School of Computer Science and Information 1.3 T
6、ypes 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 function of certain time.We only know the probability of certain value.School of Computer Science and Information Exam
7、pleNoise Signal and Interfere SignalSchool of Computer Science and Information 2.Periodic Signal and Aperiodic SignaluPeriodic Signal Has the property that it is unchanged by a time shift of T.For example,A periodic continuous-time or discrete-time signal can be represented as:uAperiodic Signal Has
8、not the property that it is unchanged by a time shift of T.Notice:When T,then Periodic Signal Aperiodic Signal.School of Computer Science and Information ExamplePeriodic SignalSchool of Computer Science and Information 3.Continuous-time Signal and Discrete-time SignaluContinuous-time Signal The inde
9、pendent variable is continuous,and thus these signals are defined for a continuum of values of the independent variable.uDiscrete-time Signal The independent variable takes on only a discrete times,and thus these signals are defined only at discrete times.School of Computer Science and Information E
10、xampleContinuous-time SignalSchool of Computer Science and Information ExampleDiscrete-time SignalSchool of Computer Science and Information 4.Energy and Power Signals uEnergy(Continuous-time)Instantaneous power:Let R=1,soEnergy over t1 t t2:School of Computer Science and Information Total Energy:Av
11、erage Power:uEnergy(Discrete-time)Instantaneous power:School of Computer Science and Information Energy over n1 n n2:Total Energy:Average Power:School of Computer Science and Information uFinite Energy and Finite Power SignalFinite Energy Signal(P 0):Finite Power Signal(E ):School of Computer Scienc
12、e and Information Example(Finite Energy Signal)(Finite Power Signal)(Signals with neither finite total energy nor finite average power)School of Computer Science and Information 1.Sinusoidal Signal1.4 Typical SignalsSchool of Computer Science and Information Property:The Differential or Integral of
13、f(t)is also a sinusoidal signal with the same frequency.important formulas:School of Computer Science and Information 2.Real Exponential SignalSchool of Computer Science and Information Property:The Differential or Integral of f(t)is also a real exponential signal.Notice:When 0,f(t)is a growing func
14、tion with t.When 0,f(t)is a decaying function with t.When 0,f(t)is a constant function with t.School of Computer Science and Information 3.Complex Exponential SignalProperties:The real and imaginary of complex exponential signal are sinusoidal.For 0 they correspond to sinusoidal signal multiplied by
15、 a growing exponential.For 0 they correspond to sinusoidal signal multiplied by a decaying exponential.School of Computer Science and Information School of Computer Science and Information 4.Sampling SignalSchool of Computer Science and Information 5.Unit Step SignalSchool of Computer Science and In
16、formation 6.Unit Impulse SignalSchool of Computer Science and Information Properties:Relation Between Unit-Impulse and Unit-Step.Sampling Properties of(t).School of Computer Science and Information 7.Unit Impulse Even SignalProperties:School of Computer Science and Information 8.Unit Triangle Signal
17、Properties:School of Computer Science and Information 1.5 Basal Operation of Signals1.Plus and multiplication2.Time InversalSchool of Computer Science and Information School of Computer Science and Information School of Computer Science and Information 3.Time ShiftSchool of Computer Science and Info
18、rmation 4.FlexibilitySchool of Computer Science and Information ExampleSchool of Computer Science and Information School of Computer Science and Information 1.6 The Representation of Continuous-time Signals in Terms of ImpulsesSchool of Computer Science and Information Define:School of Computer Scie
19、nce and Information We have the expressionThereforeor School of Computer Science and Information School of Computer Science and Information 1.7 Discrete-time Signal1.The Concepts of Discrete-time SignalThe independent variable takes on only a discrete times,and thus these signals are defined only at
20、 discrete times.School of Computer Science and Information 2.Basal Operation of SequencesSchool of Computer Science and Information School of Computer Science and Information School of Computer Science and Information School of Computer Science and Information 3.Typical of Sequences(1)Unit Sample(2)
21、Unit Step SequenceSchool of Computer Science and Information School of Computer Science and Information(3)Unit Rectangle SequenceSchool of Computer Science and Information(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.S
22、chool of Computer Science and Information(a)1；(b)0 1；(c)-1 0；(d)-1School of Computer Science and Information(6)Sinusoidal SequenceSchool of Computer Science and Information(7)Complex Exponential SequenceProperty:The real and imaginary of complex exponential sequences are sinusoidal sequence.School o
23、f Computer Science and Information(8)Complex Exponential Signalthenin whichSchool of Computer Science and Information(a)Growing sinusoidal sequence；(b)Decaying sinusoidal sequenceSchool of Computer Science and Information 4.The Representation of Discrete-time Signal in Terms of Unit SamplesSchool of
24、 Computer Science and Information 1.8 Calculation of Convolution1.Calculation of Convolution IntegralSchool of Computer Science and Information ExampleSchool of Computer Science and Information School of Computer Science and Information When t0When 0t3School of Computer Science and Information 2.Cal
25、culation of Convolution SumSchool of Computer Science and Information Example 1Solution:School of Computer Science and Information Example 2If Discrete-times signals:To calculateSchool of Computer Science and Information School of Computer Science and Information In order to calculate the convolutio
26、n of two limited long sequences,we can put the two sequence in two lines,and then to calculate according to the common multiplication apart from the intermediate results not carrying.Finally,the results of convolution can be gotten by locating the intermediate together at the same list.Another way:S
27、chool of Computer Science and Information School of Computer Science and Information 3.The Properties of ConvolutionCT SignalsSchool of Computer Science and Information DT SignalsSchool of Computer Science and Information 4.Several important formulasCT SignalsSchool of Computer Science and Information DT Signals个人观点供参考，欢迎讨论个人观点供参考，欢迎讨论