§36激画和阶跃画数的傅立叶变换
.F[()=∫a()emat =o0 ○O 6(t) F(j0) JO 6()=」1 2兀0 1eod=2兀 cos atdo P80-81象曼一勒贝格2-9和2-100 6()分1(t-to)<>e0
一 . F t t e dt j t − − = [ ( )] ( ) 1 0 = = − j e (t) t j F( j) 1 − − = = t e d t d j t cos 2 1 1. 2 1 ( ) (t) 1 0 ( ) 0 j t t t e − − P80-81黎曼－勒贝格2-99和2－100
F(j0) 0(10)
( ) 0 t −t 0 t F( j) ( j) 0 −t
二冲激偶的傅或叶变换 FTD()=160=÷Cmdo dt [S()]=2 (j@)elo 'do F7δ(t) dt dt 6()|=(01F7()=27()yn[6(o do
二.冲激偶的傅立叶变换 − = t e d j t 2 1 ( ) − = t j e d dt d j t ( ) ( ) 2 1 t j dt d FT = ( ) n n n t j dt d FT ( ) = ( ) ( ) 2 ( ) () n n n n d d FT t = j FT[ (t)] =1
三gn(t)的付立叶变换 +1t>0 f(t)=sgn( t) 1t<0 e.t >0 f2()= t<0 F2()=-Je)a+∫e-m)h j20 2 2 C+0 F(o=lim F2(j@) >0 0 2 2 lim 1→0a-+JO o(j)=m<0 2
三.sgn(t)的付立叶变换 f (t) = sgn(t) = +1 t>0 -1 t<0 f 2 (t) = ..... 0 − e t at − e .....t 0 at F j e dt e dt a j t a j t − + − − = − + 0 ( ) 0 ( ) 2 ( ) 2 2 2 + − = a j ( ) ( ) 2 0 F j limF j a→ = a j j a 2 2 2 2 0 lim = + − = → 2 F( j ) = ( j) = .... 0 2 − .... 0 2 1 −1