电子科技大学DSP复习要点

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1、Somekeypoints1.Anyarbitraryinputsequencex[n]canbeexpressedasalinearcombinationofdelayedandadvancedunitsamplesequences2.•LinearTime-Invariant(LTI)SystemAsystemsatisfyingboththelinearityandthetime-invarianceproperty.•Ify1[n]istheoutputduetoaninputx1[n]andy2[n]istheoutputduetoaninputx2[n]t

2、henforaninputx[n]=ax1[n]+bx2[n]theoutputisgivenbyy[n]=ay1[n]+by2[n]•Hence,theabovesystemislinear.•Abovepropertymustholdforanyarbitraryconstantsaandbandforallpossibleinputsx1[n]andx2[n].•Forashift-invariantsystem,ify1[n]istheresponsetoaninputx1[n],thentheresponsetoaninputx[n]=x1[n-n0]iss

3、implyy[n]=y1[n-n0]wheren0isanypositiveornegativeinteger•Theaboverelationmustholdforanyarbitraryinputanditscorrespondingoutput•Theabovepropertyiscalledtime-invarianceproperty,orshift-invariantproterty-Forexample,Down-samplingistime-variant3．ConvolutionintimedomainIfasignalinputstoasystem

4、withtheimpulseresponse,theoutputsignalThemainideaofthemethodisthataninputsignalisrepresentedas(decomposed)thesumofbasicsignal:,theresponseofLTIsystemisthesynthesisofbasicresponse.4.Discrete-TimeSignalsIntheTransformDomain(1)FromFTTODTFTandDFT•TheDTFTX(ejw)ofasequencex[n]isacontinuousfun

5、ctionofw•Itisalsoaperiodicfunctionofwwithaperiod2p.DTFTistheFourierTransformofdiscrete-timesequence.Itisdiscreteintimedomainanditsspectrumisperiodical.(2)RelationshipsZTandDTFTandDFTAfinite-lengthsequence.when,Thatmeans:TheZTontheunitcircleinZ-planeistheDTFTof.Thesamplesontheunitcirclei

6、nZ-plane,,aretheDFTof.5.TheConceptofFilteringOneapplicationofanLTIdiscrete-timesystemistopasscertainfrequencycomponentsinaninputsequencewithoutanydistortion(ifpossible)andtoblockotherfrequencycomponents。Inanotherwords,thesinusoidalcomponentsoftheinput,someofthesecomponentscanbeselective

7、lyheavilyattenuatedorfilteredwithrespecttotheothers。Forexample,asignalisinputtedtoalowpassfilter.Ifwechangethefrequencyresponseofthefilter,theoutputsignalwillbechanged(asshowninfollowingfigure).6.AnalogLowpassFilterSpecifications•passbandedgefrequency：•stopbandedgefrequency：•Pe