9.1.1 Direct Evalutation of the Defination of DFT ◆Conjugate symmetry: WN-m=Wm=(W农)* Re(X[I-∑Ren)ReW Im{n)ImW】 group terms in the summation for n and (N-n): (except n=0,N/2): IRefxiuil Re+Re(x{N-nBRetm] ->[(Re(xrb+Re(N-nb)ReW ReWN" similarly, >[Imfxn)ImW+Im{N-n)ImWN 乘法次数减少近以一半 L-ImW" >[(Im{xn)-Im{xN-nB)ImW8 9.1.1 Direct Evalutation of the Defination of DFT ◆Conjugate symmetry: group terms in the summation for n and (N-n):             1 0 [ ] [ ] N kn kn N N n Re Re Re I X k x n W x n W m Im − = = −          1 1 2 [ ] [ ] [ ] N N n N kn N n k Re Re Re x x W n N n W Re − = −  + − (    )   1 1 2 [ ] [ ] N n N kn R e e e R x x W n R N n − = = + −  N  kn Re W          1 1 2 [ ] [ ] [ ] N N + n N kn N n k Im Im x W n N n Im Im x W − = − − −  (    )   1 1 2 [ ] [ ] N n N kn Im Im x n N n x W Im − = =− −  −  N  kn −Im W similarly, 乘法次数减少近似一半 (except n=0,N/2): ( ) ( )* k k k N N N n N W W W − − n n = =