3 Fourier Series Representation of Periodic Signals (2) Representation for Real Signal Real periodic signal: X(t=X(t 在￠ So ak-a k x()=a+∑ koot+a-k ∑ 2 Relate] Let()ak=Ake aaOt (koot+Bk) x(t)=ao+>2Ak cos(koot+0k)3 Fourier Series Representation of Periodic Signals (2) Representation for Real Signal Real periodic signal: x(t)=x*(t) So a*k=a-k  + =− = k j k t x t ak e 0 ( )    + = − − + = = + = + + 1 0 1 0 2Re[ ] ( ) [ ] 0 0 0 k j k t k j k t k k j k t k a a e x t a a e a e    Let (A) ( ) 0 0 , k k j k t k j k t k j k k a A e a e A e    + = =  + =  = + + 1 0 0 ( ) 2 cos( ) k k k x t a A k t 