外文资料翻译信号与系统Word文件下载.docx

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Discrete-timesignals,alsoreferredtoassequences,aredenotedbyfunctionswhoseargumentsareintegers.Forexample,x（n）representsasequencethatisdefinedforintegervaluesofnandundefinedfornon-integervalueofn.Thenotationx（n）referstothediscretetimefunctionxortothevalueoffunctionxataspecificvalueofn.Thedistinctionbetweenthesetwowillbeobviousfromthecontest.

Somesequencesandclassesofsequencesplayaparticularlyimportantroleindiscrete-timesignalprocessing.Thesearesummarizedbelow.

Theunitsamplesequence,denotedbyδ（n）=1,n=0，δ（n）=0,otherwise

（1）

Thesequenceδ（n）playarolesimilartoanimpulsefunctioninanaloganalysis.

Theunitstepsequence,denotedbyu（n）,isdefinedas

U（n）=1,n≧0u（n）=0,otherwise

（2）

Exponentialsequencesoftheform

X（n）=

（3）

Playaroleindiscretetimesignalprocessingsimilartotheroleplayedbyexponentialfunctionsincontinuoustimesignalprocessing.Specifically,theyareeigenfunctionsofdiscretetimelinearsystemandforthatreasonformthebasisfortransformanalysistechniques.When︳α︳=1,x（n）takestheform

x（n）=A

（4）

Becausethevariablenisaninteger,complexexponentialsequencesseparatedbyintegermultiplesof2πinω（frequency）areidenticalsequences,I.e:

（5）

Thisfactformsthecoreofmanyoftheimportantdifferencesbetweentherepresentationofdiscretetimesignalsandsystems.

Ageneralsinusoidalsequencecanbeexpressedas

x（n）=Acos（

n+Φ）（6）

whereAistheamplitude,

thefrequency,andΦthephase.

Incontrastwithcontinuoustimesinusoids,adiscretetimesinusoidalsignalisnotnecessarilyperiodicandifitistheperiodicandifitis,theperiodis2π/ω0isaninteger.

Inbothcontinuoustimeanddiscretetime,theimportanceofsinusoidalsignalsliesinthefactsthatabroadclassofsignalsandthattheresponseoflineartimeinvariantsystemstoasinusoidalsignalissinusoidalwiththesamefrequencyandwithachangeinonlytheamplitudeandphase.

Systems:

Ingeneral,asystemmapsaninputsignalx（n）toanoutputsignaly（n）throughasystemtransformationT{.}.Thedefinitionofasystemisverybroad.withoutsomerestrictions,thecharacterizationofasystemrequiresacompleteinput-outputrelationshipknowingtheoutputofasystemtoacertainsetofinputsdosenotallowustodeterminetheoutputofasystemtoothersetsofinputs.Twotypesofrestrictionsthatgreatlysimplifythecharacterizationandanalysisofasystemarelinearityandtimeinvariance,alternativelyreferredasshiftinvariance.Fortunately,manysystemcanoftenbeapproximatedbyalinearandtimeinvariantsystem.Thelinearityofasystemisdefinedthroughtheprincipleofsuperposition:

T{ax1（n）+bx2（n）}=ay1（n）+by2（n）（7）

WhereT{x1（n）}=y1（n）,T{x2（n）}=y2（n）,andaandbareanyscalarconstants.

TimeinvarianceofasystemisdefinedasTimeinvariance

T{x（n-n0）}=y（n-n0）（8）

Wherey（n）=T{x（n）}and

isaintegerlinearityandtimeinvarianceareindependentproperties,i.e,asystemmayhaveonebutnottheotherproperty,bothorneither.

Foralinearandtimeinvariant（LTI）system,thesystemresponsey（n）isgivenby

y（n）=

（9）

wherex（n）istheinputandh（n）istheresponseofthesystemwhentheinputisδ（n）.Eq（9）istheconvolutionsum.

Aswithcontinuoustimeconvolution,theconvolutionoperatorinEq（9）iscommutativeandassociativeanddistributesoveraddition:

Commutative:

x（n）*y（n）=y（n）*x（n）（10）

Associative:

[x（n）*y（n）]*w（n）=x（n）*[y（n）*w（n）]（11）

Distributive:

x（n）*[y（n）+w（n）]=x（n）*y（n）+x（n）*w（n）（12）

Incontinuoustimesystems,convolutionisprimarilyananalyticaltool.Fordiscretetimesystem,theconvolutionsum.InadditiontobeingimportantintheanalysisofLTIsystems,namelythoseforwhichtheimpulseresponseifoffinitelength（FIRsystems）.

Twoadditionalsystempropertiesthatarereferredtofrequentlyarethepropertiesofstabilityandcausality.Asystemisconsideredstableintheboundedinput-bounderoutput（BIBO）senseifandonlyifaboun