Summary 1.z[n]arbitrary length DTFT X(ejv) X(e“)= ∑ xnje-jwn n=-0 2.[n]periodic-DFS[附 N- [= ∑nw, Wv=e-i装 n= = ∑[njExlnjW n=-0 =DTFT{njRNin])l.=装 3.x[n]finite length (0,1,....N-1)DFT[] 网=m》州=∑+rW xIn]in]Rv(n] DFT of ln]DFS of [((n))N]DTFT {n The following figure summarizes this lecture. DTFT Finite Length Signal X(e) x[n] 1 X[k]DFT 1 Periodic Sequence (n] [附 DFS 6Summary 1. x[n] arbitrary length DTFT X(ejω ↔ ) ∞ e X −jωn (ejω) = � x[n] n=−∞ x[n] periodic DFS ˜ 2. ˜ ↔ X[k] N−1 Wnk X[k] = , � ˜ x˜[n] N N WN = e−j 2π n=0 ∞ Wnk = � x˜[n]RN [n] N n=−∞ = DT F T {x˜[n]RN [n] 2πk N }|ω= 3. x[n] finite length (0, 1, . . . , N − 1) ↔ DFT X[k] x˜[n] = x[((n))N ] = �x[n + rN] r x[n] = x˜[n]RN [n] DFT of x[n] = DFS of x[((n))N ] = DTFT {x[n] 2πk N }|ω= The following figure summarizes this lecture. 6