信号与系统课件第五章.ppt

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1、CHAPTER 5 THE DISCRETE-TIME FOURIER TRANSFORM5.0 INTRODUCTIONDiscrete-timeFouriertransformandinverseFouriertransform.Similaritiesanddifferencesbetweencontinuous-timeanddiscrete-timeFouriertransforms.5.1 REPRESENTATION OF APERIODIC SIGNALS:THE DISCRETE-TIME FOURIER TRANSFORM As,N N10N2NnN10N2xnnDefin

2、ingafunction:Thus,Consequently,As,discrete-time Fourier transformdiscrete-time inverse Fourier transformDifferencesbetweenthecontinuous-timeanddiscrete-timeFouriertransformare:periodicity ofthediscrete-timetransformandthefinite intervalofintegrationinthesynthesisequation.Indiscretetime,Low frequenci

3、es arethevaluesofneareven multiple of;high frequenciesarethosevaluesofnearodd multiples of.2 022020nx1n0nx2nExample 5.1Considerthesignal1/(1)1/(1+)202202100-11/(1+)1/(1)20 2202Example 5.2Considerthesignal0 xnn(1+)/(1)(1)/(1+)202for02M1/Ns 2spectrumofsampledsignalwiths2MIndiscrete-timecase,theresulto

4、fsamplingtheoremalsoexist.Example 5.14Considerasequence xnwhoseFouriertransformDeterminethelowestrateatwhichxnmaybesampledwithoutaliasing.Sincethecorrespondingsamplingfrequencyis2/4=/2.SothatThusFromthesamplingtheorem,weknow5.10 SUMMARY TheFouriertransformforperiodicdiscrete-timesignals;TheFouriertr

5、ansformforaperiodicdiscrete-timesignals;Convenientwaytoobtainthefrequencyresponseandsampleresponseofadiscrete-timeLTIsystem;Fourieranalysismethod(alsoreferredtofrequency-domainanalysis)(whichistousedtochangealinearconstant-coefficientdifferenceequationtoanalgebraicform);Thedifferencebetweenthecontinuous-timeFouriertransformandthediscrete-timeFouriertransform(thediscrete-timeFouriertransformofanaperiodicsignalisalwaysperiodicwithperiod2);ThepropertiesoftheFouriertransform(howdifferentcharacteristicsofsignalsarereflectedintheirtransforms);Samplingofdiscrete-timesignals.