Question

Hey I just need help on Problem 4 for the system (b-f) from Problem 2. Please explain steps by steps so I can understand properly, thanks

EE306 Hwi Problem 1 A discrete-time signal (efnl) is shown in the figure below. Sketch and label carefally euch of the following signals. (a) (n-1).(oa-3) (d) (xinl) (Imm pulie Rerans e Problem 2 Plot the impulse response of each of the following systems. Make sure to specify the amplitude value of every sample. Use the symbols...to signify that the impulse response remains constant until +oo or until -oo. (b) stlol)-(n cos(n-+l) a nl) (d) S(ainl) -(2ml) o) stcb)-e)-. i1 720 2 0 (System f is worth triple points.) Problem 3 (Tame- invanhmd For each of the systems of Problem 2, consider (vinl)- s((anl) and (0) derive (vn-Tol) in terms of (rin]), (ä) derive S((rn-nol) in terms of (xin)). System f is worth triple points.) Conclude whether the system is time-invariant or not. Problem 4 State whether each system of Problem 2 is linear or not. If not, explain why

Answer 1

(a) s[x(n)] = cos (x(n)) = cos [x_1 (n) + x_2 (n)] notequalto cos (x_1 (n)) + cos (x_2 (n)) non Linear \r\n (b) s[x(n)] = n cos (n + 1) x[n] s_3 [x(n)] = n cos (n + 1) [a_1 x_1 (n) + a_2 x_2 (n)] = n a_1 cos (n + 1) x_1 (n) + a_2 n cos (n + 1) x_2 (n) implies Linear = s_1 + s_2 (c) s[x(n)] = x(-n + 2) s_3 [x(n)] = x_1 (-n + 2) + x_2 (-n + 2) = s_1 + s_2 implies Linear (d) s[x(n)] = x[2n] s_3 [x(n)] = x_1 (2n) + x_2 (2n) = s_1 + s_2 implies Linear (e) y(n) = x(n) implies for a x(n) notequalto a y(n) [if a < 0] so it is non - Linear. (f) y(n) = Sigma^n + 1_k = -infinity x [k] y_3 (n) = Sigma^n + 1_k = -infinity x-1 [k] + Sigma^n + 1

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