精品課程大學物理-非周期信號的分解(存儲版)
【正文】 on in frequency ? if ? then )()]([ 11 wjFtfFT =)()]([ 22 wjFtfFT =)(*)(21)]()([ 2121 ww?jFjFtftfFT =?. determine the spectrum function of the cosine impulse t?tcos)(tG1EE )(tf2t2t2t2t2t2t相乘 ][ c o s t?tFTFTt?t?)( t?w?? FT )(wGt?2t?2)( wjF卷積 )( t?w?? ?t? ttGtf c o s).()( =)2()( wttw SaEjG = )()(t?w??t?w?? ??)(tG t?tc os??????=2)(1)2c o s (2)(?wt?wttwEjF乘 FT FT 卷 ]c o s)([ 0 ttfFT w)]()([21 00 w ?? FF)]([ tfFT ][co s0 tFT w00ww0w0w 卷積 ??12121利用卷積證明 0w0w11. Parseval’s Relation ww?djFdttf ???????= 22 )(21)(? ?? dttftfs o l u t i o n )()(：? ?????= dtdejFtf tj ])(21)[( ww?w? ????????????= ww?w ddtetfjF tj)()(21????= ?djFjF )()(21 *??????==? ww?dFdttfE 22 |)(|21)(dfjfF2)(????=)()( w? ?? ?? Ftfaf t bf t aF bF1 2 1 2( ) ( ) ( ) ( )? ? ?? ?w w)(2)( w? ? ?? ftFf at a F j a( ) ( )? ?? 1 w0tj0 )()( ww ejFttf ?? ??f t e F jt( ) [ ( )]? ? ?? j 0w w w 01． 對稱性 2． 線性特性 3． 對稱互易特性 4． 展縮特性 5． 時移特性 6． 頻移特性 (調制定理 ) )()( ** wFtf =f t f t F j F j1 2 1 2( ) ( ) ( ) ( )? ? ?? ?w w)]()([2 1)()( 2121 ww? jFjFtftf ?? ???d fdt j F jnnn? ?? ?( ) ( )w wf d j F j Ft ( ) ( ) ( ) ( )t t w w ? ? w?? ? ?? ?1 0t f t j dF jdn n n n( ) ( )? ?? ? ww?? ???? == ww? dFdttfE 22 |)(|2 1)(7． 卷積特性 8． 乘積特性 9． 時域微分特性 10． 積分特性 11． 頻域微分特性 12． 能量定理 167。 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
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