精品課程大學物理-非周期信號的分解-展示頁
2024-08-06 06:12本頁面
【正文】 dejF tj)(21 ? ??=tjnn TtjnTT edtetf00 ])(2[l i m 0 ww?w? ???=??=w?ww dedtetf tjtj? ??????= ])([21傅里葉變換對 傅 里 葉正變換： ???= dtetfjF tj ww )()( 傅里 葉反變換： ???= ww?w dejFtf tj)(21)( 物理意義：非周期信號可以分解為無 數(shù)個頻率為 w，復振幅為 (F(jw)/2?)dw 的復指數(shù)信號 ejw t的線性組合。 2. 聯(lián)系： tje wtjne 0wTTnFjF10 )(lim)( ww??=三 存在性：狄利赫利條件 傅立葉變換存在的充分條件 ?????dttf )(用廣義函數(shù)的概念，允許奇異函數(shù)也能滿足上述條件，因而象階躍、沖激一類函數(shù)也存在傅立葉變換 四 .頻譜密度函數(shù)的對稱性 是實函數(shù))(.1 tf是實偶函數(shù))(.2 tf)()()()()( w?w jejFjXRjF =?=)()(),()( w XXRR ==)()(,)()( w?w?ww == jFjF0)()(),()()( ==== ww XXRjFjF?w?w?ww ?=== 或0)()(),()( RjF(t)是實奇信號 )()()(,0)()( ww jXjFjFRR ====2)()(,)()( ?w?w?ww ?=== XjF(t)是任意實函數(shù) )()(),()( ww jXtfRtf oe ??(t)是因果信號 )()(0 tftft oe =? 時 ?)()(2)()(2)( ttfttftf oe ?? ==?)()(),()( ww jXtfRtf oe ?? )()]([2)( 1 tRFTtf ?w=)()]([2 1 tjXFT ?w=例：已知因果信號 )()()()( jXRjFtf ?=?。 properties of the continuoustime fourier transferm ? linearity ? Time shifting ? Time scaling ? Duality ? Frequency shifting ? Differentiation and Integration ? Convolution property ? Parseval’s Relation linearity If then ? ? )()( wjFtfFT ii =??===?????? niiiniii jFatfaFT11)()( wdetermine： )(tfThe fourier transform of )(tf2t2t tt12t)]()([)]()([)( 22 t?t??? tt ???= tttttf)](2)2/([)( wtwttw SaSaF ?=t?2w Time shifting if Then solution： ? ?)()()()(000)(0wwjFedxexfedxexfxfFTttxtjxjtjtxj?????====??? ? )()( 00 ww jFettfFT tj=?)()( wjFtf ?0)()( 0 tjejFttf ww ? Time scaling ? If ? then )()( wjFtf ? ??)(1)(ajFaatfw? ??)(1)()]([0 1ajFadxexfatfFTa axja ww ==? ???)(1)(1)]([0ajFadxexfaatfFTa axj ww ==? ???Compression(expand) in time is equal to expand(pression) in frequency f(t/2) 0 t)2(2 wFt2ttt?t?0w)2( tf0 4/t4/t t)2(21 wF2tt?4t?4pression expand 11w0Time shifting carries scaling ? ? atjeajFatatfFT0)(1)( 0ww =)(1)(1/)()(10)()]([000)(0/)(000ajFeadxexfeaatxtdxexfatatxadtetatftatfFTatjxjatjatxjtjawwwwww???????=====?=??? Duality ? if ? then ? ??= ww? w dejFtf tj)(2 1)(,)(21)( ? ??= ww?w dejFtf tj?= ? ? dtetFf tj w?w )(21)()(2)( w? ? ?? ftFsolution： )()( wjFtf ? ??)(2)( w? ? ?? fjtF)(tf )( wjFt?22t2t t?2)(tf
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