第7章3傅氏變換性質(zhì)-資料下載頁
2025-08-01 17:46本頁面
【正文】 )ftite ??????? ?ite ??? ()ft?????????? ()ft dite ????????? ()ftite ?? ( ) dit??i? ????? ? ()ft ite ?? dt i?? ()F ?有限個 可去 間斷點 ()ft??F[ ] 2()i?? ()F ?F[ ] ()ft??? 3()i?? ()F ?F[ ] ()()nft ()ni?? ()F ?13 F[ ] F[ ] ()ft ()ft ite ?? dt????? ? ()F ??7. 積分性質(zhì) 如果 當 t ? ??時 ()f ? 0?則 t??? d?()f ?t??? d? 1i?? ()F ?復習 原函數(shù)微分性質(zhì) 則 ()ft?F[ ] i?? ()F ?F[ ] ()()nft ()ni?? ()F ?14 例 8 求函數(shù) ()ft ? sin 2?()H ? e??t??? d? 的 Fourier變換 解 F[ ] () tH t e ?? F[ ] () tH t e ?2iteF[ ] () tH t e ?2ite?sin2t()Ht te?F[ ] 22( 1 ) 4i???()ftF[ ] 1i???1 i??1 ?1 ( 2 )i ???1?1 ( 2 )i ???1?2(1 )i?? 4?212i? [1 ( 2 )i ???1 ]?1 ( 2 )i ???115 = F[ ] 例 9 設 F[ ] ()ft ()F ??試證明 若 ()ft 是奇函數(shù) 則 ()F ? 是奇函數(shù) 若 ()ft 是偶函數(shù) 則 ()F ? 是偶函數(shù) 證明 根據(jù)翻轉(zhuǎn)性質(zhì) F[ ] ()ft? ()F ???若 ()ft 是奇函數(shù) 則 ()ft? ()ft??()F ???F[ ] ()ft? ()ft? = — F[ ] ()ft()F ???若 ()ft 是偶函數(shù) 則 ()F ???F[ ] ()ft? = F[ ] ()ft ()F ?
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