由x(n)=Re[v(m)得 X(k)=DFTIX, (n)= DFTRelw(n)=Wen(k) WW((K))N+W((N-KDNIrn(k) 由x2(m)=Imw(n)得 X(k)=DFTIx, (n]= DFT(Imw(n==Won(k) 2 W(K)N-W((N-k)R(k)
1 由 得 x n w n ( ) Re[ ( )] = 1 1 ( ) [ ( )] {Re[ ( )]} ( ) X k DFT x n DFT w n W k = = = ep 1 * [ (( )) (( )) ] ( ) 2 = + − W k W N k R k N N N 2 由 得 x n w n ( ) Im[ ( )] = 2 2 1 ( ) [ ( )] {Im[ ( )]} ( ) X k DFT x n DFT w n W k op j = = = 1 * [ (( )) (( )) ] ( ) 2 W k W N k R k N N N j = − −
、解:由题意X(k)=DFT[x(m)],Y()=DFTy(n) 构造序列z(k)=X(k)+jY(k) 对z(k)作一次N点F可得序列(n) E(n)=IDFT Z(k)I 又根据DF/的线性性质 =(n)=IDFT Z(k )=IDFTLX(k)+jY(k IDFTLX()+jIDFTLY(K) x(n)+jy(n 而x(n),y(m)都是实序列x(n)=Re[(n)] y(m)=m[=(n)
解：由题意 X k DFT x n Y k DFT y n ( ) = = ( ) ( ) ( ) ， 构造序列 Z k X k jY k ( ) = + ( ) ( ) 对 Z k( ) 作一次N点IFFT可得序列 z n( ) 又根据DFT的线性性质 = + IDFT X k jIDFT Y k ( ) ( ) 而 x n( ) ， y n( ) 都是实序列 ( ) ( ) ( ) ( ) Re Im x n z n y n z n = = z n IDFT Z k ( ) = ( ) z n IDFT Z k IDFT X k jY k ( ) = = + ( ) ( ) ( ) = + x n jy n ( ) ( )