Question

2. Verify the time reversal property of the discrete Fourier transform. That is, given xn]Xk, then x-n, mod N] X[-k, mod N].

Answer 1

Answer: Güven the Joverse dõscorete fowier transform is x(m) - x(k) cu ar – 0 By the Inverse discorute tourier trans form the original sequence retrived is 1 x [n] = √ 2 x [ k] was so nezn . n=on then X(_n) : -+ 2x [] wet n - 0 The DFT of an n point signal is sex [n], n62n = {oil, ---- N-1} From O a x) = ☆ E xem) e var hon} M20 h:0 en - 0 Dis colete fourier transform pain is 1. Since X(K) = * = x(n) with | x (R). * (n) e-jun KT – (0) DFT spectrum (0)=[1:274w] if K-K+N *CK+N) = zame-jem (KAM) -42 x cm) e jen min) - 3200 * (K+n) = x(k) ė atinj = x(K) then [x] = 1 x [n] work in ke zn - ① where Ww = crear cos (29) +j sin () Some of DFT properties o periodicy : x[n] = [N+] © linearity : - 0,X,[n] + 22.22 [n] Time Reversal - [N-n] X [K] : * [k+M] ax. [K] + Q2X2 Ok] X (NK] From 0. a En, modn] 4. X[-k, mod]