标签: s-domain

Thetwomaintechniquesinsignalprocessing,convolutionandFourieranalysis,teachthatalinearsystemcanbecompletelyunderstoodfromitsimpulseorfrequencyresponse.Thisisaverygeneralizedapproach,sincetheimpulseandfrequencyresponsescanbeofnearlyanyshapeorform.Infact,itistoogeneralformanyapplicationsinscienceandengineering.Manyoftheparametersinouruniverseinteractthroughdifferentialequations.Forexample,thevoltageacrossaninductorisproportionaltothederivativeofthecurrentthroughthedevice.Likewise,theforceappliedtoamassisproportionaltothederivativeofitsvelocity.Physicsisfilledwiththesekindsofrelations.Thefrequencyandimpulseresponsesofthesesystemscannotbearbitrary,butmustbeconsistentwiththesolutionofthesedifferentialequations.Thismeansthattheirimpulseresponsescanonlyconsistofexponentialsandsinusoids.TheLaplacetransformisatechniqueforanalyzingthesespecialsystemswhenthesignalsarecontinuous.Theztransformisasimilartechniqueusedinthediscretecase.CHAPTERTheLaplaceTransform32Thetwomaintechniquesinsignalprocessing,convolutionandFourieranalysis,teachthatalinearsystemcanbecompletelyunderstoodfromitsimpulseorfrequencyresponse.Thisisaverygeneralizedapproach,sincetheimpulseandfrequencyresponsescanbeofnearlyanyshapeorform.Infact,itistoogeneralformanyapplicationsinscienceandengineering.Manyoftheparametersinouruniverseinteractthroughdifferentialequations.Forexample,thevoltageacrossaninductorisproportionaltothederivativeofthecurrentthroughthedevice.Likewise,theforceappliedtoamassisproportionaltothederivativeofitsvelocity.Physicsisfilledwiththesekindsofrelations.Thefrequencyandimpulse……