对称特性·DFS(X*[K]) = X[-m]DFT(x[K]}= X*[(-m)]R[m].DFS(*[-k] = X*[m]DFT(x[(-k)JR[K]} = X[m]当x[K]是实序列时X[m] = X*[(-m)~]R[K]4.循环卷积N定义[K][K]=x[(n)]x,[(k-n)]R[k(n=0x[k],N=443-21P0123h[k]1032301x[k]①[]0231
对称特性 [ ] ~ [ ]} ~ •DFS{x k = X −m DFT{x [k]} X [( m) ]R [m] = − N N [ ] ~ [ ]} ~ DFS{x k X m • − = [ ] ~ DFT{x [( k)N ]RN [k]} X m − = 当 x[k]是实序列时 X[m] X [( m) ]R [k] = − N N 4.循环卷积 定义 [ ] 1 x k [ ] 2 x k [( ) ] [( ) ] [ ] 1 2 1 0 x n x k n R k N N N N n = − − = h[k] 0 1 2 3 1 x[k],N=4 0 1 2 3 1 2 3 4 x[k] 4 h[k] 0 1 2 3 4 1 2 3
11231123011f012310123卷积定理DFT(x[K] x2[K]= X,[m]X2[m]DFT(s[Kk]x[K]= 一X[m]?X,[m]N
卷积定理 DFT [ ] [ ] [ ] [ ] DFTx1 [k] N x2 [k]= X1 [m]X2 [m] x1 k N x2 k = X1 m X2 m [ ] [ ] 1 DFT [ ] [ ] 1 2 X1 m N X2 m N x k x k = [ ] [ ] 1 DFT [ ] [ ] 1 2 X1 m N X2 m N x k x k = 0 1 2 3 1 0 1 2 3 1 0 1 2 3 1 0 1 2 3 1