上游充大学 SHANGHAI JIAO TONG UNIVERSITY 证：若F(=,+π6(o)→ iw f(t)=.子-1[F(ω]=u(t) 0yro1oeda do oedw+3a0eaw 21 0 1 1 ( ) [ ( )] () d 2 1 1 () d d 2 2 1 1 sin () d d 2 2 1 1 sin d () 2 i t i t i t i t ft F e i e e i t e t u t ω ω ω ω ω πδ ω ω π ω πδ ω ω ω π π ω ω δω ω ω π ω ω ω π ω +∞ − −∞ +∞ +∞ −∞ −∞ +∞ +∞ −∞ −∞ +∞   = = +     = + = + = + = ∫ ∫ ∫ ∫ ∫ ∫ F 1 1 () () ( ) [ ( )] ( ) F i f t F ut ω πδ ω ω ω − =+ ⇒ = = 证：若 F