标签: properties

Thetimeandfrequencydomainsarealternativewaysofrepresentingsignals.TheFouriertransformisthemathematicalrelationshipbetweenthesetworepresentations.Ifasignalismodifiedinonedomain,itwillalsobechangedintheotherdomain,althoughusuallynotinthesameway.Forexample,itwasshowninthelastchapterthatconvolvingtimedomainsignalsresultsintheirfrequencyspectrabeingmultiplied.Othermathematicaloperations,suchasaddition,scalingandshifting,alsohaveamatchingoperationintheoppositedomain.TheserelationshipsarecalledpropertiesoftheFourierTransform,howamathematicalchangeinonedomainresultsinamathematicalchangeintheotherdomain.CHAPTERFourierTransformProperties10Thetimeandfrequencydomainsarealternativewaysofrepresentingsignals.TheFouriertransformisthemathematicalrelationshipbetweenthesetworepresentations.Ifasignalismodifiedinonedomain,itwillalsobechangedintheotherdomain,althoughusuallynotinthesameway.Forexample,itwasshowninthelastchapterthatconvolvingtimedomainsignalsresultsintheirfrequencyspectrabeingmultiplied.Othermathematicaloperations,suchasaddition,scalingandshifting,alsohaveamatchingoperationintheoppositedomain.TheserelationshipsarecalledpropertiesoftheFourierTransform,howamathematicalchangeinonedomainresultsinamathematicalchangeintheotherdomain.Linearityo……

Alinearsystem'scharacteristicsarecompletelyspecifiedbythesystem'simpulseresponse,asgovernedbythemathematicsofconvolution.Thisisthebasisofmanysignalprocessingtechniques.Forexample:Digitalfiltersarecreatedbydesigninganappropriateimpulseresponse.Enemyaircraftaredetectedwithradarbyanalyzingameasuredimpulseresponse.Echosuppressioninlongdistancetelephonecallsisaccomplishedbycreatinganimpulseresponsethatcounteractstheimpulseresponseofthereverberation.Thelistgoesonandon.Thischapterexpandsonthepropertiesandusageofconvolutioninseveralareas.First,severalcommonimpulseresponsesarediscussed.Second,methodsarepresentedfordealingwithcascadeandparallelcombinationsoflinearsystems.Third,thetechniqueofcorrelationisintroduced.Fourth,anastyproblemwithconvolutionisexamined,thecomputationtimecanbeunacceptablylongusingconventionalalgorithmsandcomputers.CHAPTERPropertiesofConvolution7Alinearsystem'scharacteristicsarecompletelyspecifiedbythesystem'simpulseresponse,asgovernedbythemathematicsofconvolution.Thisisthebasisofmanysignalprocessingtechniques.Forexample:Digitalfiltersarecreatedbydesigninganappropriateimpulseresponse.Enemyaircraftaredetectedwithradarbyanalyzingameasuredimpulseresponse.Echosuppressioninlongdistancetelephonecallsisaccomplishedbycreatinganimpulseresponsethatcounteractstheimpulseresponseofthereverberation.Thelistgoesonandon.Thischapterexpandsonthepropertiesandusageofconvolutioninseveralareas.First,severalcommonimpulseresponsesarediscussed.Second,methodsarepresentedfor……

MostDSPtechniquesarebasedonadivide-and-conquerstrategycalledsuperposition.Thesignalbeingprocessedisbrokenintosimplecomponents,eachcomponentisprocessedindividually,andtheresultsreunited.Thisapproachhasthetremendouspowerofbreakingasinglecomplicatedproblemintomanyeasyones.Superpositioncanonlybeusedwithlinearsystems,atermmeaningthatcertainmathematicalrulesapply.Fortunately,mostoftheapplicationsencounteredinscienceandengineeringfallintothiscategory.ThischapterpresentsthefoundationofDSP:whatitmeansforasystemtobelinear,variouswaysforbreakingsignalsintosimplercomponents,andhowsuperpositionprovidesavarietyofsignalprocessingtechniques.CHAPTERLinearSystems5MostDSPtechniquesarebasedonadivide-and-conquerstrategycalledsuperposition.Thesignalbeingprocessedisbrokenintosimplecomponents,eachcomponentisprocessedindividually,andtheresultsreunited.Thisapproachhasthetremendouspowerofbreakingasinglecomplicatedproblemintomanyeasyones.Superpositioncanonlybeusedwithlinearsystems,atermmeaningthatcertainmathematicalrulesapply.Fortunately,mostoftheapplicationsencounteredinscienceandengineeringfallintothiscategory.ThischapterpresentsthefoundationofDSP:whatitmeansforasystemtobelinear,variouswaysforbreakingsignalsintosimplercomponents,andhowsuperpositionprovidesavarietyofsignalproces……

electronicstructureandmagne...,electronicstructureandmagnetoopticalpropertiesofsolids……