Unit11FourierTransformsandFrequency-DomainDescriptionPart3SignalandSystemUnit11FourierTransformsandFrequency-DomainDescription?Backgrounds?Texttour?Languageinuse–Vocabulary–Structure–Reading/writingtechniques?Terminology–FouriertransformBackgroundsTerminologyFouriertransform?Inmathematics,theFouriertransform(oftenabbreviatedFT)isanoperationthattransformsonecomplex-valuedfunctionofarealvariableintoanother.Insuchapplicationsassignalprocessing,thedomainoftheoriginalfunctionistypicallytimeandisaccordinglycalledthetimedomain.Thedomainofthenewfunctionistypicallycalledthefrequencydomain,andthenewfunctionitselfiscalledthefrequencydomainrepresentationoftheoriginalfunction.Fouriertransform?TheFouriertransformanditsgeneralizationsarethesubjectofFourieranalysis.Inthisspecificcase,boththetimeandfrequencydomainsareunboundedlinearcontinua.ItispossibletodefinetheFouriertransformofafunctionofseveralvariables,whichisimportantforinstanceinthephysicalstudyofwavemotionandoptics.ItisalsopossibletogeneralizetheFouriertransformondiscretestructuressuchasfinitegroups.Theefficientcomputationofsuchstructures,byfastFouriertransform,isessentialforhigh-speedcomputing.?ContinuousFouriertransform?DiscreteFouriertransform?Convolutiontheorem卷积定理?Cross-correlation互相关?autocorrelation自相关?characteristicfunction?Laplacetransforms?differentialequations微分方程?nuclearmagneticresonance核磁共振?polarcoordinate极坐标?amplitude?phase?angularfrequency角频率?Euler'sformula?realnumber?complexnumbers?impulseresponse脉冲响应?eigenfunction特征函数?Outline–…Texttour?Vocabulary–spectrum,integral,linear,sinusoidal?Structure?Reading/writingtechniques–DLanguageinuseVocabularyspectrumindictionary?anorderedarrayofthecomponentsofanemissionorwave?光谱，频谱，波谱spectrumintext?IftheFouriertransformofasignalisdefined,thetransformiscalledthefrequencyspectrumofthesignal.?如果定义了信号的傅里叶变换，那么该变换称之为信号的