The z transform of the sequence - impulse response of the

Question

Question 1
Which one of the following is the Z- transform of x[n] = 2ⁿu[-n] + (1/4)ⁿ u(n-1)

(A) (-2z^-1)/(1-2z^-1) - 1/4.(z^-1/1-1/4z^-1), 1/4<|z|<2

(B) (2z^-1)/(1-2z^-1) + 1/4.(z^-1/1-1/4z^-1), 1/4<|z|<2

(C) (-2z^-1)/(1-2z^-1) + 1/4.(z^-1/1-1/4z^-1), 1/4<|z|<2

(D) (2z^-1)/(1-2z^-1) - 1/4.(z^-1/1-1/4z^-1), 1/4<|z|<2

Question 2

The Z transform of the sequence

is

(A) (z/2)/(1-z/2) + z²/(z² - 1/4) + (z/3)/(z²-1/9); 1/2<|z|<2

(B) (z/2)/(z/2 -1) + z²/(z² - 1/4) + (z/3)/(z²-1/9); 1/2<|z|<2

(C) (z/2)/(z/2 -1) + z²/(1/4 - z²) + (z/3)/(z²-1/9); 1/2<|z|<2

(D) Z transform is not possible

Question 3

If Z transform of x(n) is X(z) and Xz = 12z2/(3z² + 2z -1) then initial value of x(n) is ________.

Question 4

The impulse response of the LTI system is

h(n) = δ(n-5) - (-0.5)ⁿ u(n) - 8(2)ⁿ u(-n-3)

The transfer function of the LTI system is

(A) H(z) = z^-5 - 1/(1 + 0.5z^-1) + 2z²/(1- 2z^-1), 1/2 < |z| < 2

(B) H(z) = z^-5 + 1/(1 + 0.5z^-1) - 2z²/(1- 2z^-1), 1/2 < |z| < 2

(C) H(z) = z^-5 + 1/(1 + 0.5z^-1) + 2z^-2/(1- 2z^-1), 1/2 < |z| < 2

(D) H(z) = z^-5 + 1/(1 + 0.5z^-1) - 2z^-2/(1- 2z^-1), 1/2 < |z| < 2

Question 5

The Z transform pair (1/2)ⁿ u(n) ↔^zr X(z), and y(n) ^zr↔ y(z). If Y(z) = [X(z)]² then y(n) is

(A) (1/2)²ⁿ u(n)

(B) n(1/2)ⁿ⁺¹ u(n)

(C) n(1/2)²ⁿ u(n)

(D) (n+1)(1/2)ⁿ u(n)