傅里叶变换性质及常用变换

傅立叶变换的性质正反变换2()()jftXfxtedt()()jtXxtedt2()()jftxtXfedf1()()2jtxtXed12()()xtxt12()()XfXf12()()XX*()xt*()Xf*()X()Xt()xf2()X02()jftxte0()Xff0(2)Xf()xat1()||fXaa1()||Xaa()xatT21()||fjTafXeaa1()||jTaXeaa()xtT2()jfTXfe()jTXe()()xtyt()()XfYf()()XY()()xtyt()()XfYf1()()2XY()nndxtdt(2)()njfXf()()njX()ntxt()2nnnjdXfdf()nnndjXd()txd()1(0)()22XfXfjf()(0)()XXj()*()xtytdt()*()XfYfdf1()*()2XYd2|()|xtdt2|()|Xfdf21()2Xd0()cos2xtft001()()2XffXff00()()XX0()sin2xtft00()()2jXffXff00()()jXX21()njtTnntnTeT1()nnfTT0002()()nnT()nTtnT2()jnTfnnnfTeT02()nn()xyR*()()XfYf*()()XY()R2()Xf2()X卷积()*()()()()()xtytxytdyxtd()*()()()()()xtytxtydxytd相关()*()()()*()xyRxtytdtytxtdt＝()()yx()xyR*()()ytxtdt*()yxR常见傅立叶变换()t11()f0()tt02jfte02jfte0()ff()rectt()sincf()sinct()rectf()t2()sincf2()sinct()f0cos(2)ft001()()2ffff0sin(2)ft00()()2jffff()sgnt1jf1t()jsgnf()ut11()22fjf1()22jtt()sgnf()()nt()njf'()tjf()(0)teut12jf()(0)tteut21(2)jf||(0)te222(2)f2te2fe()ntnT1()nnfTT