4 The continuous time Fourier transform When t>∞,x()-32,x() 丌 do T→∞ So a,T (t)e o dt=X(o (t)=lin foot T→>∞ lim Xoko roOt ∑X(kOo)e/m 7 Xoe4 The continuous time Fourier transform When T→ ,      ⎯ ⎯→ = ⎯ ⎯→ ⎯ ⎯→ → → → T T T k d T x t x t 0 0 2 ( ) ( ) ~ So ( ) ( )  a T x t e dt X j j t k = =  + − −     + − + =− → + =− → + =− → = = = =             X j e d X j k e e T X j k x t a e j t k j k t k j k t T k j k t k T ( ) 2 1 2 lim ( ) ( ) lim ( ) lim 0 0 0 0 0 0 0