傅里葉變換的性質

1、傅里葉變換的性質1)2()(22SadtejFtj)(jF02)(tG2t201傅里葉變換的性質2)()()()(22112211jFajFatfatfa)()(00jFettftj)()(00jFetftjtje0)()(21cos)(000jFjFttf)()(2sin)(000jFjFjttf)(21cos000tjtjeet)(21sin000tjtjeejt傅里葉變換的性質3)(1)(ajFatafatjeajFatatf0)(1)(0atjeajFaattf0)(1)(0)(2)(fjtF)()(jFtfatjeajFaattaftatfajFaatfjFtf0)(1)()()(1

2、)()()(00atjtjeajFatatfejFttfjFtf00)(1)()()()()(00傅里葉變換的性質4)()()()(sin)(cos)()()(jtjejFjXRtdttfjtdttfdtetfjF0cos)(2cos)()(tdttftdttfR0)(X0)(R0sin)(2sin)()(tdttftdttfX傅里葉變換的性質5tje0tje0)(21cos000tjtjeet)()(cos000t)(21sin000tjtjeejt)()(sin000 jt傅里葉變換的性質6)(0tetjjt1)()()()(21)(cos000tetetttjtj)(1)()(000jt

3、etj220000)()(2)(cosjtt傅里葉變換的性質7t22)(tf1)(jF2000)2()(SatG)(21cos)()(000tjtjeetGttGtf2)(22)(2)(00SaSajF)()(21cos)(010101FFttf傅里葉變換的性質8)(costtetjtet1)()(cos)(21tjtjtteetette22)()(1)(121)(cosjjjjttet傅里葉變換的性質9)()()()(jFjtfnn)(1)()0()()1(jFjFtf)()()(tytftf)(ty)(jY),()0()(1)()(YjYjdttytftFF),()(2)()()()()(

4、fjFftfdttftftF FF)()()()(1)(fftfjjFF0)()() 0(0dttfjFF)()(1)()(jFjtfnn)()()()()()0(fftfdttfdttyY)()()()(1)()(2)(ffjYjfjF)()(tfjY F傅里葉變換的性質100)()0(dttyY)(1)(tfjtf F F傅里葉變換的性質11)(tft011)(tft011)()2(1)(2 jeSajjF)(3)2(1)(2 jeSajjFjjeeSajjF2)2(1)()(tft0112)(tft011)(tft011)(tft011)1(傅里葉變換的性質12)(tQTt0TT1t0T

5、TT1T1T2)(tQT )(1)(2)(1)(TtTtTTtTtQT ,121)()(2TjTjeTTeTjFj)2()2(sin4)cos1 (2)(2222TTSaTTTTjF)(jFT0T2t0T1T1TT)(tQT傅里葉變換的性質13)()()()(jFtfjtnn)()(1)()0()1(jFtfjttf0)(21)0(djFf)()(1)1(jFtfjt)(21)(2 jt)(2jt21)()( jttjt1)()(傅里葉變換的性質1421)()(jtt21)()( jtt22|t)(tft0)(tft011)(tf t0)2()()(ttttt)(2)(ttf 2222)(2)

6、(, 2)()(jjFjFj傅里葉變換的性質15)()()()(2121jFjFtftf)(tQTt0TT1t0T12T)(1tGTT2Tt0T12T)(1tGTT2T)2()(1TSaTtGTT)2()2()(22TSaTTSaTjF傅里葉變換的性質16)()(21)()(2121jFjFtftfttGtf22cos)()()()(cos),(2)(2222tSatG)()()(2)(2221Satf)()sin()()sin()()()(222222SaSajF22222)(coscoscost)(tft2cos0111)(2)(2)2()(2SatGSatG令傅里葉變換的性質17ttSatfC0cos)()()()(