2,时域循环移位的DFT 若yn)=x(0-m)R(n)试求y(m)的DFT:Y(k) Y(k)=DFTly(n)]=2x((n-m)NR(n)WN N-1 ∑x(7-m)WN=∑"x(n1)WWm N-1-m n= Y(k)=W∑ x((nUNN W∑x(n)Wk=WY(k) n'=0 n'=0 故FT[x(n-m)]=WX(k) 3,频域循环移位定理 若Y(k)=X(k-1)·R(k) U y(n)=IDFT[X((k-DNR(k]=WN x(n) 其中X(k)=DFT[x(n)]0≤k≤N-12，时域循环移位的DFT 若 y(n) x((n m)) R (n) N N = −  试求 y(n) 的DFT ： Y(k) DFT [x((n m)) ] W X(k) km 故 − N = N   − −  =−  − = = − =  N m n m k m N kn N N N n k n x n m NWN x n W W 1 1 0 (( )) (( )) 若 Y(k) X((k l)) R (k) N N = −  则 其中 X (k) = DFT[x(n)] 0  k  N −1 y(n) IDFT [X ((k l)) R (k)] W x(n) nl N N N − = − = 3，频域循环移位定理  − = = = − 1 0 ( ) [ ( )] (( )) ( ) N n k n N N WN Y k DFT y n x n m R n ∴ ( ) (( )) ( ) ( ) 1 0 1 0 Y k W x n W W x n W W X k km N N n kn N km N N n kn N N km = N   =   = − =  − = 