傅里叶变换的性质及常用函数的傅里叶变换

表6.3常用的连续傅里叶变换对及其对偶关系deFtftj)(21)(dtetfFtj)()(连续傅里叶变换对相对偶的连续傅里叶变换对重要连续时间函数)(tf傅里叶变换)(F连续时间函数)(tf傅里叶变换)(F重要√)(t11)(2√√)(tdtdjt)(2ddj)(tdtdkkkj)(kt)(2kkkddj√)(tu)(1jtjt21)(21)(u)(ttu21)(ddj0,10,1)sgn(tttj20,1t0,0,)(jjF√)(0tt0tjetje0)(20√t0cos)]()([00)()(00tttt0cos2tt0sin)]()([00j)()(00tttt0sin2tj√tttf,0,1)()2(Sa)(WtSaWWWF,0,1)(√√ttttf,0,1)()2(2Sa)2(22WtSaW,0,1)(√0}Re{),(atueatja1jt10),(2ue0}Re{,aeta222aa22t0,e√0}Re{),(cos0attueat202)(jaja√0}Re{),(sin0attueat2020)(ja0}Re{),(atuteat2)(1ja0,)(12jt)(2ue0}Re{),()!1(1atuketatkkja)(1√lTlTtt)()(kTkT)2(2√2)(te2)2(e√ttutu0cos)]2()2([]2)0(2)0([2SaSaktjkkeF0kkkF)(202连续傅里叶变换性质及其对偶关系deFtftj)(21)(dtetfFtj)()(1(0)()2fFd(0)()Fftdt连续傅里叶变换对相对偶的连续傅里叶变换对重要名称连续时间函数)(tf傅里叶变换)(F名称连续时间函数)(tf傅里叶变换)(F重要√线性)()(21tftf)()(21FF√尺度比例变换0),(aatf)(1aFa对偶性)(tf)(g)(tg)(2f√√时移)(0ttf0)(tjeF频移tjetf0)()(0F√时域微分性质)(tfdtd)(Fj频域微分性质)(tjtf)(Fdd√时域积分性质tdf)()()0()(FjF频域积分性质)()0()(tfjttfdF)(√时域卷积性质)(*)(thtf)()(HF频域卷积性质)()(tptf)(*)(21PF√√对称性)(tf)(*tf)(*tf)(F)(*F)(*F奇偶虚实性质)(tf是实函数)()(tfOdtfo)()(tfEvtfe)(ImFj)(ReF希尔伯特变换)()()(tutftf)()()(jIRF1*)()(IR√时域抽样nnTttf)()(kTkFT)2(1频域抽样nntf)2(100kkF)()(0√帕什瓦尔公式dFdttf22)(21)(取反----------取反共轭----共轭取反共轭取反---