Continuoustime Signal Sampling.ppt

continuous-timesignalsampling,elec309prof.siripongpotisuk,whydigitaldomain,uniformrepresentationofanalogsignalsi.e.,asequenceof0sand1s.operationofdigitalcircuitsnotdependentonprecisevaluesofthedigitalsignalsrequireonlybistablecircuitsandstoragemediumtoprocess,store,andtransmitsignalspossibilityofperfectsignalregenerationlowcostofdigitalprocessorhardware,benefits(continued),anydesirableaccuracyachievablebyincreasingthebinarywordlengthsubjecttocostlimitationthesamedigitalcomputertechnologyusedforgeneralinformationprocessingcanbeusedfordspapplicabilitytoverylowfrequencysignals(seismicapplications),disadvantages,increasedsystemcomplexity(a/dandd/a)limitedrangeoffrequenciesavailableforprocessingbecauseofthesamplingrequirementdigitalsystemsmostlyconstructedusingactivedevicesthatconsumeelectricalpoweradvantagesfaroutweighdisadvantages,analog-to-digitalconversion,discretizetheindependentvariableortimeofananalogsignal(sampling)discretizethedependentvariableoramplitudeofananalogsignalbyroundingofftothenearestinteger(quantization)eachquantizationlevelrepresentedusingbinaryencodingscheme(encoding),whysampling,necessaryfordigitalprocessingofanalogsignals,e.g.,x(t)takingsnapshotsofx(t)everytssecondseachsnapshotiscalledasampletsistheso-calledsamplinginterval,i.e.,thetimeintervalbetweeneachsample(second/sample)preferregularlyspacedsamples,thoughnotnecessary,analog-to-digitalconversion(a/d),mathematicaldescriptionofsampling,thesequenceofsamplesisgivenbyisthesamplingfrequencyorratetheunitofsamplingfrequencyissamples/second,butoftenexpressedintermsofhztomatchthehighestfrequencyinhzoftheanalogsignal,samplingintervalselection,bysampling,wethrowoutalotofinformationinbetweensamplesasetofsamplescanrepresentmorethanonedistinctsignal,samplingintervalselection,givenasetofsamplingpoints,underwhatconditionscanwereconstructtheoriginalctsignalsfromwhichthosesamplescame?inotherwords,allvaluesofx(t)betweensamplingpointsarelostbecauseofsamplingneedtoconsiderthefrequencycontentsofthectsignalbeingsampledfouriertransform,impulsesampling,frequency-domainanalysisofsampling,where,and,usingthemultiplicationpropertyofctft,thus,assumingx(t)isband-limited,i.e.,frequency-domainanalysisofsampling,nooverlapbetweenshiftedspectra!,reconstructionofthectsignalfromitssamples,ifthereisnooverlapbetweenshiftedspectra,wecanusealowpassfiltertoreconstructtheoriginalctsignal,originalspectrum,reconstructedspectrum,nyquistsamplingtheorem,practicalsampling,aliasingeffect,distortionoffilteredspectrumcausedbyaliasing,commonsamplesobtainedfromsamplingtwosinusoidsofdifferentfrequencies,anti-aliasingfilter,band-limitingoperationdoneontheanalogsignalbeforesamplingtopreventaliasingpassingitthroughananaloglowpassfilter,e.g.butterworth,chebyshev,ellipticalalternativelycalledguardfilterremoveallfrequencycomponentsoutsidetherange-fc,fcwherefcfd,signalreconstruction,threeinterpolationmethodsband-limitedinterpolationzero-order