9.1.1 Direct Evalutation of the Defination of DFT ◆Conjugate symmetry: WN-”=W=(W农）* RefX[k)->[RefnB Rew)-Imfxn}ImW] n=0 group terms in the summation for n and/(N-n): Refxn}RefWA"y Refxn']ReW n-0 n=2 n'=N-n,n=N-n' except n=0,N/2): N_ RefxN-n}ReWN-"l n= >[RefXnB ReW)+RefxN-nB Re(WSIN-n] →1 ->[(RefxrB+RefxN-nB)RefW] eWs 乘法次数减少近以一半 generally N=27 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 n kn kn Re Re Re I X k x n W x n W N N 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 0 2 2 [ ] [ ] N + n N N n N N k k n n Re Re Re Re x W x n n W − − = =       1 2 [ ] [ ] N n N N n k N n Re e x W R = −  − 乘法次数减少近似一半 except n=0,N/2):     1 2 [ ] N N n N kn Re e x n R W − =    n N n n N n   = = − − ， generally N=2r ( ) ( )* k k k N N N n N W W W − − n n = =