Samplingtheoremandlow-passfilteringCONTENTSPAGESamplingtheorem0102Low-passfilteringSamplingtheorem01samplingtheoremTheidealsamplingprocessTheidealsamplingistoextracttheinstantaneousfunctionvalueofthesimulatedsignalunderthecontrolofthesamplingpulse.Sampling:theprocessofturningacontinuoustimesignalintoadiscretetimesignal.Thisdiscretetemporalsignaliscalledthesamplingsignal.SamplingtheoremThesamplingcircuitcanberegardedasanelectronicswitch,addingthecontinuoustimesignalX(t)totheinputendoftheelectronicswitch.TheswitchisbrieflyclosedeveryTsecond,andthecontinuoustimesignalX(t)isturnedontorealizeonesampling.SamplingtheoremSamplingtheorem1SamplingfrequencyThenumberofsamplesinunittime(persecond),knownasthesamplingfrequency,isgenerallyrepresentedbyfs.EqualtothereciprocalofthesamplingintervalTs.approach:2SamplingcycleSamplingperiodTs:referstothetimeintervalbetweeneverytwosamples,calledsamplingperiodTs,orsamplinginterval.Itisgenerallyrepresentedbytheterm"T".samplingtheorem“forinstance1)ForthesamplingperiodT=1millisecond=0.001seconds,thenfs=1/T=1/0.001=1000times/second.Industrialfrequencycyclessamplingpoints=20ms/Ts=20times2)SamplingperiodT=5/3ms,workingfrequencyperiodsamplingpoints=20ms/5/3=12times,12timeseach,at300intervalspickasample.3)SamplingperiodT=5/6ms,workingfrequencyperiodsamplingpoints=20ms/5/6=24times,24times,every150intervalspickasample.samplingtheoremThereciprocalofthesamplingintervalTsiscalledthesamplingfrequency,andthecorrectselectionofthesamplingfrequencyinvolveswhetherthemicrocomputer-protectedsamplingsignaltrulyreflectstheinputsignal.Thatistosay,whetherthediscretesignalcantrulyreflectthesampledcontinuoussignal,ifrequiredtoensurenottoloseinformation,andtosamplethelosersignalintact,thesamplingtheoremmustbesatisfied.3Samplingtheoremsamplingtheoremsamplingtheorem:Whensamplingthecontinuous-timesignalX(t),thesamplingfrequencymustbegreaterthantwicethehighestfrequencycomponentfmaxcontainedinthesampledoriginalsignal.N=fs>2fmaxsamplingtheoremForexample:thesmallcurrentgroundingsystemdetectiondevice,thesignaltobesampledis5timesthefrequencyofthecurrentsignal,howtochoosethesamplingfrequency?Because:thefrequencyofthesampledsignal:Therefore,thesamplingfrequencyshouldbeselectedatleastselected:Toensurethatthesampled5xfrequencycurrentsignalisnotrestoredwithoutdistortion.samplingtheoremTheintroductionofproblems:Inthetransientstateofthepowersystemofthefault,thevoltageandcurrentcontainhighfrequencycomponents.Ifallhighharmoniccomponentsaretobesampledwithoutdistortion,thesamplingfrequencywillbeveryhigh,highrequirementsforhardwarespeed,andthecostisincreased.Low-passfiltering02Low-passfilteringTheintroductionofproblems:Inthetransientstateofthepowersystemofthefault,thevoltageandcurrentcontainhighfrequencycomponents.Ifallhighharmoniccomponentsaretobesampledwithoutdistortion,thesamplingfrequencywillbeveryhigh,highrequirementsforhardwarespeed,andthecostisincreased.Limitthehighestsignalfrequencycomponentwithinacertainfrequencybandbeforesampling,thatis,limitthehighestfrequencyoftheinputsignaltoreducethesamplingfrequency,therebyreducingthespeedrequirementforhardwareontheonehand,andsamplingtherequiredhighestfrequencysignalontheotherhandNodistortionwilloccur.Functionoflow-passfilter(ALF):filterthefrequencycomponentabovefs/2intheinputsignaltoreducethesamplingfrequency.resolvent:Low-passfilteringreflectionquestion:

Whenthesamplingfrequencyofaprotectionmeasurementandcontroldeviceis1000Hz,whatisthesamplingcycle?

Howmanysamplingpointsdoestheprotectionmeasurementandcontroldevicehav