Question

10.16 Prove the time-shifting property stated in Eq. (10.24). Shift property If xj[k] * x2[k] = 8[k], then x] [k – ki] * x2[k – k2] = g[k – kj – k2] (10.24)

Answer 1

. Answer Ix, (arki ) * H₂ (krk 2) = y(K) taking zo transform. z" x1(z) xa (2) = Y(Z) (kitka) YCZ) = Z .xirz)(Z) 0 As 21(K) *H2(K) = g(K) so XI(Z) • X2(Z) = G(Z) So Y(Z) = Echthus) GCZ) taking inverse z transform- y (K) = g [4-(Kitka) ] y(K) = g(k-kirk2) Proved so | 2 (Krk) *H2 (ke-Up) = y(K) = g(K-K, -K2) /