9.1.1 Direct Evalutation of DFT Defination X[-∑Wg=∑ne2x n= =∑(Re{n+jImi(ReW}+jmw》 =>IReiAn那Rewy-mi}inW +j(Refxn}ImW+Imixn]ReW) k=0,1,2,…,N-1 Computational complexity in terms of real operations 4N2 real multiplications N(4N-2)real additions:N*2*(N+(N-1)6 9.1.1 Direct Evalutation of DFT Defination ◆Computational complexity in terms of real operations ◆4N2 real multiplications ◆N(4N-2) real additions : N*2*( N+(N-1) ) ( ) 1 0 2 / [ ] N n j N kn x n e  − = −     = 1 0 N kn n X k n x WN − = =          1 0 [ ] [ ] N kn kn N N n Re Re Im x n W x n W Im − = = −  (  [ ] [ ]       ) kn kn Re Im Im Re x n W x N N + j + n W k N = − 0,1,2, , 1 (    )(    ) 1 0 = [ ] [ ] N kn kn N N n Re Im Re Im x n x W W j n j − =  + +             1 0 [ ] [ ] N kn kn N N n Re Re Re I X k x n W x n W m Im − = = − 