Question

5. For each system, determine whether it is TI/TV and whether it is memoryless/dynamic. (b) y[k] = f[-k] + 5 n=k-2 nk-2

Answer 1

y (k) = f (2 k) input rightarrow output f (k) rightarrow f (2 k) f (k - k_0) rightarrow f (2 k - k_0) = y_actual (k) y_expected = f (2 k - 2 k_0) as y_actual notequal y_expected therefore time variant put k = + 1 y (1) = p(2) as it depend on future value therefore memory/Dynamic y (k) = f (- k) + 5 f (k) rightarrow f (- k) + 5 f (k - k_0) rightarrow f (- k - k_0) + 5 = y_actual (t) \r\n y_expected y (k - k_0) = x [- (k - k_0)] + 5 as y_actual notequal y_expected Time variant for k = -1 y (- 1) = f (+ 1) as it depend on future and past value therefore Dynamic \r\n y (k) = sigma_n = k - 2^k + 4 f (n) f (k) rightarrow sigm