1. Find the z-transform, x(z), given x(n) = (0.3^n-1)u(n-1)+(0.55^n-2)u(n-2). a.

Question

1. Find the z-transform, x(z), given x(n) = (0.3^n-1)u(n-1)+(0.55^n-2)u(n-2).

a. z/(z-0.3)+z/(z-0.55)

b. 1/(z-0.3)+z/(z-0.55)

c. 1/(z-0.3)+1/z(z+-0.55)

d. z/(z-0.3)+z^2/z-0.55)

2. A system has the following transfer function. Determine its poles and zeroes and whether it is a stable or unstable system. H(z)=(z^2+3z+2.5z)/(z^2-1.6z+1.45)

a. zeros at z = 3,2.5: poles at -16, 1.45, unstable

b. zeros at z=-1.5 +/- j0.5; poles at -0.8 +/- j0.9, stable

c. zeros at z = -1.5 +/- j0.5; poles at 0.8 +/- j0.9, unstable

d. zeros at z = -1.5 +/- j0.5; poles at -0.9+/- j0.8, stable

Explanation / Answer

1)c. 1/(z-0.3)+1/z(z+-0.55)

2)b. zeros at z=-1.5 +/- j0.5; poles at -0.8 +/- j0.9, stable

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