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1、<p><p>&lt;p&gt;&amp;lt;p&amp;gt;&amp;amp;lt;p&amp;amp;gt;SymbolicanalysisanddesignofcommunicationsystemsusingcomputeralgebrasystemsProf.DrMiroslavLutovacDrDejanTo?i?SchoolofElectricalEngineeringattheUniversityofBelgradeSerbiaOvervie
2、w?Getbacktobasicunderstanding?Numericvs.SymbolicComputation?Computerasasymbolprocessor?Schematicasasymbolicobject?Programsasknowledgerepositories?Astepbystepexample:QAM?BenefitsfromsymbolictechniquesJamesKaiser-50yearsofSP&amp;amp;amp;#216;Ithasbecomesoeasytodosomuchcomputationusingcomputers
3、thatpeoplewillpresskeysonthekeyboardwithoutthinkingwhattheyaredoing&amp;amp;amp;#216;ItssoeasytogenerateatremendousamountofgarbagethatyouvegottounderstandwhatitisyouredoingFiftyYearsofSP(1998)page54JamesKaiser:“backtobasics”&amp;amp;amp;#252;Soitisveryimportantthatwegetbacktobasicund
4、erstandinggetamuchbettergroundingofwhatscienceunderliesthephenomenonwearelookingat&amp;amp;amp;#252;Imeanthisworldisnotanidealworld&amp;amp;amp;#252;Itstime-varyingandnonlinearFiftyYearsofSP(1998)page54JamesKaiser:“understandtools”qYoungpeopleoranybodyreallywhoareusingthesetoolshaveg
5、ottothoroughlyunderstandwhatassumptionsunderliethetoolthattheyareusingqThatwilltellthemwhattheycanexpecttogetoutFiftyYearsofSP(1998)page54Numericalambiguity:0.3-0.1=0.2a=0.3-0.1a=0.2000b=0.2b=0.2000a=bans=00.30.10.2MATLABCommandWindowWhyis0.3-0.10.2sym(0.8-0.6d)ans=.20000000000000006661338147750939s
6、ym(0.2d)ans=.20000000000000001110223024625157sym(0.3-0.1d)ans=.19999999999999998334665463062265sym(0.6-0.4d)ans=.19999999999999995559107901499374MATLABCommandWindowNumericvs.SymbolicComputation(210)=(1-810)ans=0sym(210)=sym(1-810)ans=1a=1a=a-0.2a=a-0.2a=a-0.2a=a-0.2a=a-0.2a=5.5511e-017a0a0Numericisf
7、alseSymbolicistrueNumericsimulationmightfailSymboliccomputationfindsexactsolutionAlgebraicloop?Symbolicanalysisofsystemsisinherentlyimmunetotheproblemimposedbyalgebraicloopsoccurringwhentwoormoreblockswithdirectfeed-throughoftheirsafeedbackloop?Numericsimulationsofalgebraicloopsconsiderablyreducethe
8、speedofasimulationandmaybeunsolvable?SymbolicsimulationsuccessfullyandaccuratelycomputestherequiredresponseitfindstheexactsolutionComputerasasymbolprocessor?Computershavebecomerecognizedassymbolprocessors(OppenheimandNawab1992)?Programcanbeviewedasasetofinstructionsanipulatingsymbols?Numbersareonlyo
9、neofthekindsofsymbolsthatthecomputercanhandleSchematicasasymbolicobjectqSystemmodelisasymbolicobjectqItcontainsalldetailsfordrawingsymbolicsolvingsimulatingandimplementing:?Analyzetheschematicasthesymbolicobject?Identifysymbolicsystemparameters?Knowledgeembeddedintheschematicobjectcanbeusedtogenerat
10、eimplementationcodeortoderivetransferfunctionFromschematictosystempropertysystem=&amp;amp;amp;quot;Multiplier&amp;amp;amp;quot;6063k1&amp;amp;amp;quot;Delay&amp;amp;amp;quot;45471&amp;amp;amp;quot;Adder&amp;amp;amp;quot;788598891120&amp;amp;amp
11、;quot;&amp;amp;amp;quot;08&amp;amp;amp;quot;X&amp;amp;amp;quot;&amp;amp;amp;quot;Output&amp;amp;amp;quot;98&amp;amp;amp;quot;Y1L&amp;amp;amp;quot;.&amp;amp;amp;quot;Line&amp;amp;amp;quot;68781.Findtransferfunction2.Simplifyexpre
12、ssions=H1(H1.z-1z)+H2(H2.z-1z)FullSimplifyComputerasintelligenceamplifier?Symbolprocessorwiththeappropriateprogramsisusableonamuchwiderrangeoftaskssuchasintelligenceamplifieroraugmentingourabilitytothink?Programminghasbecomeataskofknowledgeaccumulationtellingthecomputerwhattoknowwhentouseandhowtoapp
13、lytheknowledgeinsolvingproblemsWhattoknow-HowtoapplyqWHATTOKNOW:symbolicobjectthatcontainsaprocedureforautomatedgenerationoftheschematicforanarbitrarynumberofpartsqHOWTOAPPLY:drawsystemsolvesymbolicallysimulateandimplementsystem?Automaticallygeneratesystemparameters?Automaticallygenerateschematicwit
14、hsymbolicornumericparameters?Solvesymbolically:findthetransferfunctionimpulseresponseorpropertyofthesystemfromtheschematic?Automaticallygenerateimplementationcode?SimulateforspecifiedsymbolicparametervaluesWhattoknow-WhentouseqWHATTOKNOW:symbolicobjectthatcontainsaprocedureforautomatedgenerationofth
15、eschematicforanarbitrarynumberofpartsqWHENTOUSE:qWhenLaplaceorz-transcannotbefoundqWhennumericcomputationsfailqWhensymbolicexpressionshavealargenumberofparametersqWhenderivationbyhandisverytimeconsuminganddifficultqWhensymbolicoptimizationcanreducethenumberofparametersusedinnumericoptimizationKnowle
16、dgerepositories?Programsareviewedasknowledgerepositories?Programsshouldbewrittentocommunicate?notsimplytocomputeProgramsasknowledgerepositories1.drawbasicpartofsystem2.draw3.drawoutput(generateschematicbyreplicatingthebasicpart)numberOfStages=7adaptiveSystem=TranslateSchematic.adaptiveSystem=Joinada
17、ptiveSystem.DoadaptiveSystem=JoinadaptiveSystem.aK-ToExpression&amp;amp;amp;quot;a&amp;amp;amp;quot;StringJoin.knumberOfStages4.writecode5.SaveasfunctionaddknowledgeofasystemschematicSpecinpsouts=SchematicFunctionparamsx0y0optionsAutomateddrawingofsystemsnumStages=3p=UnitSymbolicSequ
18、encenumStages+1k0parameterSymbols=JoinbpFlattenhsSysteminpCoordsHSoutCoordsHS=HighSpeedIIR3FIRHalfbandFilterSchematicparameterSymbolsShowSchematichsSystemInvokefromtheknowledgerepositoryProgramswrittentocommunicatesystem=&amp;amp;amp;quot;Multiplier&amp;amp;amp;quot;6063k1&am
19、p;amp;amp;quot;Delay&amp;amp;amp;quot;45471&amp;amp;amp;quot;Adder&amp;amp;amp;quot;78.1120&amp;amp;amp;quot;&amp;amp;amp;quot;08&amp;amp;amp;quot;X&amp;amp;amp;quot;.&amp;amp;amp;quot;Line&amp;amp;amp;quot;6878Solve:findtransferfunctionofalloutputsY3LXY3HXProvingthepropertyofthesystems=H1(H1.z-1z)+H2(H2.z-1z)FullSimplifyDerivingnewpropertys=H1(H1.z-1z)+H2(H2.z-1z)FullSimplifySolves=&amp;amp;lt;/p&amp;amp;gt;&amp;lt;/p&amp;gt;&lt;/p&gt;</p></p>
