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KaiHuangEmbeddedSystemHardware(III)
ADDASamplingTheorem8/25/2024Kai.Huang@SYSU2Outline
8/25/2024Kai.Huang@SYSU3EmbeddedSystemHardwareEmbeddedsystemhardwareisfrequentlyusedinaloop(“hardwareinaloop“)CourseScope
8/25/2024Kai.Huang@SYSU4EmbeddedSystemHardwareEmbeddedsystemhardwareisfrequentlyusedinaloop(“hardwareinaloop“)
8/25/2024Kai.Huang@SYSU5EmbeddedSystemHardwareEmbeddedsystemhardwareisfrequentlyusedinaloop(“hardwareinaloop“)
ADDASamplingTheorem8/25/2024Kai.Huang@SYSU6Outline
Digitalcomputersrequirediscretesequencesofphysicalvalues?Sample-and-holdcircuitsDiscretizationoftimes:DT?DVDiscretetimedomain8/25/2024Kai.Huang@SYSU7
Clockedtransistor+capacitor;Capacitorstoressequencevaluese(t)isamapping???h(t)isasequenceofvaluesoramapping???Sample-and-holdcircuits8/25/2024Kai.Huang@SYSU8
Wouldwebeabletoreconstructinputsignalsfromthesampledsignals??approximationofsignalsbysinewaves.Doweloseinformationduetosampling?8/25/2024Kai.Huang@SYSU9
Target:squarewave
withperiodp1=4with?k:pk=p1/k:periodsofcontributionstoe’Approximationofasquarewave(1)K=3K=18/25/2024Kai.Huang@SYSU10
Approximationofasquarewave(2)K=7K=58/25/2024Kai.Huang@SYSU11
Approximationofasquarewave(3)K=9K=118/25/2024Kai.Huang@SYSU12
8/25/2024Kai.Huang@SYSU13Approximationofperiodicfunctions
8/25/2024Kai.Huang@SYSU14Fouriertransform
Lete1(t)ande2(t)besignalsDefinition:AtransformationTrofsignalsislineariffInthefollowing,wewillconsiderlineartransformations.?Weconsidersumsofsinewavesinsteadoftheoriginalsignals.Lineartransformations8/25/2024Kai.Huang@SYSU15
Periodsofp=8,4,1Indistinguishableifsampledatintegertimes,ps=1Aliasing8/25/2024Kai.Huang@SYSU16
Reconstructionimpossible,ifnotsamplingfrequentlyenoughHowfrequentlydowehavetosample?Nyquistcriterion(samplingtheory):Aliasingcanbeavoidedifwerestrictthefrequenciesof
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