**1 Answer**

written 7.6 years ago by | • modified 4.2 years ago |

**1. Linear or non linear:**

Ans: $y_1(n) = 2x_1(n-1) + x_1(2n) \\ y_2(n) = 2x_2(n-1) + x_2(2n) \\ \therefore y_1(n) + y_2(n) = 2x_1(n-1) + 2x_2(n-1) + x_1(2n) + x_2(2n)….. (1) \\ Replacing \ \ x(n) by x_1(n) + x_2(n); \\ y(n) = 2x_1(n-1) + 2x_2(n-1) + x_1(2n) + x_2(2n)………...… (2) \\ from (1) (2), y(n) = y_1(n) + y_2(n)$

$\therefore$ **Linear System**

**2. Causal or non-causal**

Ans: the terms 2x(n-1)&x(2n) both indicate signals in future,

Thus, System is Non-Causal.

**3. Time variant or Time invariant**

Ans: y(n) = 2x(n-1) + x(2n)

$\therefore$, Delaying input by k units;

y(n,k) = 2x(n-1-k) + x(2n-k) …. . . . .. (1)

& replacing n by n-1;

y(n-k) = 2x(n-k-1) + x(2(n-k))

i.e., y(n-k) = 2x(n-1-k) + x(2n-2k)… . . ... (2)

from (1) & (2), y(n,k) y(n-k)

$\therefore$ **System is TimeVariant.**

**4. Static or Dynamic**

Ans: the terms 2x(n-1)&x(2n) both indicate signals in future/past,

**Thus, System is Dynamic.**