《电路》（英文版）14-8 Definition of the Fourier transform

$14-8 Definition of the Fourier transform The exponential form of the Fourier series 2元 f()=∑A,em0(oo=2n) f(t)e un@ot LetT→>∞,0o=domd 0→0,n→0,n0+0 T2丌2丌 A,T→f()e-ar ∫ f(te dt Fourier transform off(o F(o)=f(Oe -jio dt ()=2Aemx1=∑r(omm 1 do (n0n→m,-= T 2丌 Inverse Fourier transform f(t) FGoje/do of Fga 2丌

§14-8 Definition of the Fourier transform The exponential form of the Fourier series   =−  = = n j n t n ) T f ( t ) A e (    2 0 0 − − = / 2 / 2 0 ( ) 1 T T j n t n f t e dt T A        2 2 1 , 0 0 d T Let T →  = d and = →  → , n → , n0 →   +  − − +  − −  A T → f t e dt = f t e dt j n t j t n   ( ) ( ) 0 Fourier transform of f (t)  +  − − F j = f t e dt j t ( ) ( ) , ) 2 1 ( , 0 → = T →  d T n       =−  =  n j n t n T f t A Te 1 ( )  0  + − =     f t F j e d j t ( ) 2 1 ( ) Inverse Fourier transform of F (j  )     2 ( ) d F j e n j t   =−  =