Question

3) For each of the following systems with input xfin] and output y/nl, determine whether it is linear, time invariant, causal, and/or stable. lineax - time-varient

Answer 1

y(n) = x(n) - 0.005 v^2 x(n - 2) linearity: - x_1(t) gives y_1 (t) x_2(t) gives y_2(t) then x_1(t) + x_2(t) y_1(t) + y_2(t) i, e y(t) = y_1(t) + y_2(t) x_1(x) y_1(n) = x_1(n) - 0.005n^2 x_1(n - 2) x_2(n) y_2(n) = x_2(n) -0.005n^2 x_2(n - 2) y(t) = x_1(n) + x_2(n) - 0.005n^2(x_1(x -2) + x_2(n - 2) = y_1(t) + y_2(t) Therefore is linear \r\n time invariant A system is time Invariant, If the input and output characteristics don't change with time x(t) y(t) x(t -t_0) y(t -t_0) y(t) Vertical-bar _x(t - rt_0) = y(t) Vertical-bar _t = t -t_0 y(n) = x(n) - 0.005n^2 x (n -2) y(n, k) = x (n - k) - 0.005(n - k)^2 x ((v - k) - 2 eq (1) is varying input eq(2) is varying output eq(1) eq(2) so it is time variant Canal: - A System is causal, IF the present output depends of the input . but not on future values. y(n) = x(n) - 0.005n^2 x(n - 2) clearly

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