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1、BEIJING JIAOTONG UNIVERSITYThe Course Group of Signals and Systems,Beijing Jiaotong University.P.R.CHINA.Copyright 2020Signals and Systems“signals and systems”is an important course for E&Estudents.The era of information and intelligence hascome.The course has laid a theoretical foundation forinform
2、ation andintelligence.Itdealswithsignalrepresentation and system description in timedomain,frequencydomain,andcomplexfrequencydomainrespectively.Introduction to Signals and SystemsDefinition of SignalDefinition of SystemRelation between Signal and SystemCourse Contents and Teaching ObjectivesIntrodu
3、ction to Signals and SystemsDefinition:A signal is defined as a function of one or more variables that conveys information.Electrocardiogram(ECG)signalDefinition of SignalAudio signalOt(1)Mathematical expressionx(t)=sin(t),xk=0.5k(2)Graphical expressionOkk5.0=k xDefinition of Signal()sin()x tt=In th
4、is course,we will pay attention to one-dimensional signals defined as single-valued functions of time.The function value may be a real number,or a complex number.In either case,the independent variable(time)is a real number.Definition of SignalOtO()x ttsingle-valuedXx t()signalsCommunication signals
5、Radar signalsImage signalsAudio signalsBiomedical signalsTraffic signalsEarthquake signalsSonar signals Definition of SignalThere are many kinds of signalsDefinition of SignalDefinition of SystemRelation between Signal and SystemCourse Contents and Teaching ObjectivesIntroduction to Signals and Syst
6、emsDefinition of System A system is defined as an entity that can manipulate the input signals to accomplish some kind of function,thereby yieldingthe output signals.In other words,a system is an entity that can process the input signals,and generate the output signals.SystemInput signalOutput signa
7、l(excitation)(response)SystemInput signalOutput signal(excitation)(response)In most cases,we design or select the system,so that we can get the expected output signals,or effectively process the input signals such as denoising,extracting information,etc.Definition of System Some simple electric circ
8、uits)t(2Rv2R-+)t(v-+1R2R)t(2Ri)t(i1RVoltage divider+=v tvRtRR()()12R22+=i tiRtRR()()12R21Definition of SystemCurrent dividerHuman body systemdigestive systemnervous systemrespiratory systemcirculatory systemDefinition of SystemDefinition of SignalDefinition of SystemRelation between Signal and Syste
9、mCourse Contents and Teaching ObjectivesIntroduction to Signals and SystemsRelation between Signal and SystemDenoisingSystemReverberationSystem(I and You)(Town Story)Without the systems,the information in signals cannot be effectively extracted.Without the signals,systems will be of no use at all.Th
10、erefore,signals and systems are interdependent.Through the signal analysis and the system analysis,the relation between signal and system is revealed.We conduct the signal analysis by Signal Representation,the system analysis by System Description.Relation between Signal and SystemSystemInput signal
11、Output signal(excitation)(response)Definition of SignalDefinition of SystemRelation between Signal and SystemCourse Contents and Teaching ObjectivesIntroduction to Signals and SystemsCore Contents:Signal Representation System DescriptionSystemInput signalOutput signal(excitation)(response)Course Con
12、tents and Teaching Objectivesy(t)=x(t)*h(t)Y(jw)=X(jw)H(jw)Y(s)=X(s)H(s)Fourier TransformLaplace and z TransformSampling in timeSampling in FrequencySignalsContinuousTime-DomainTransformed-DomainDiscreteSystemsCourse Contents and Teaching ObjectivesCh1.Introduction to Signals and SystemsCh2.The sign
13、al analysis in time domainCh3.The system analysis in time domainCh4.The signal analysis in frequency domainCh5.The system analysis in frequency domainCh6.The C-T S&S analysis in complex-freq.domainCh7.The D-T S&S analysis in complex-freq.domainCh8.The state variable analysis for the systemsCh9.The a
14、pplications in biological neural networksCourse Contents and Teaching ObjectivesMastering the fundamental principles and theoriesMastering the analysis methods in all domainsUnderstanding the concept of signal TransformsTraining students ability of applying knowledgeCourse Contents and Teaching ObjectivesAcknowledgmentsMaterials used here are accumulated by authors for years with helpfrom colleagues,media or other sources,which,unfortunately,cannotbe noted specifically.We gratefully acknowledge those contributors.Introduction to Signals and Systems