1. Which of the following method is used to find the inverse z-transform of a signal?

A. Counter integration

B. Expansion into a series of terms

C. Partial fraction expansion

D. All of the mentioned

2. What is the inverse z-transform of

X(z)=\(\frac{1}{1-1.5z^{-1}+0.5z^{-2}}\) if ROC is |z|>1?

A. {1,3/2,7/4,15/8,31/16,….}

B. {1,2/3,4/7,8/15,16/31,….}

C. {1/2,3/4,7/8,15/16,31/32,….}

D. None of the mentioned

3. What is the inverse z-transform of

X(z)=\(\frac{1}{1-1.5z^{-1}+0.5z^{-2}}\) if ROC is |z| < 0.5?

A. {….62,30,14,6,2}

B. {…..62,30,14,6,2,0,0}

C. {0,0,2,6,14,30,62…..}

D. {2,6,14,30,62…..}

4. What is the inverse z-transform of X(z)=log(1+az-1) |z|>|a|?

A. x(n)=(-1)n+1 \(\frac{a^{-n}}{n}\), n≥1; x(n)=0, n≤0

B. x(n)=(-1)n-1 \(\frac{a^{-n}}{n}\), n≥1; x(n)=0, n≤0

C. x(n)=(-1)n+1 \(\frac{a^{-n}}{n}\), n≥1; x(n)=0, n≤0

D. None of the mentioned

5. What is the proper fraction and polynomial form of the improper rational transform

X(z)=\(\frac{1+3z^{-1}+\frac{11}{6} z^{-2}+\frac{1}{3} z^{-3}}{1+\frac{5}{6} z^{-1}+\frac{1}{6} z^{-2}}\)?

A. 1+2z-1+\(\frac{\frac{1}{6}z^{-1}}{1+\frac{5}{6} z^{-1}+\frac{1}{6} z^{-2}}\)

B. 1-2z-1+\(\frac{\frac{1}{6} z^{-1}}{1+\frac{5}{6} z^{-1}+\frac{1}{6} z^{-2}}\)

C. 1+2z-1+\(\frac{\frac{1}{3} z^{-1}}{1+\frac{5}{6} z^{-1}+\frac{1}{6} z^{-2}}\)

D. 1+2z-1–\(\frac{\frac{1}{6} z^{-1}}{1+\frac{5}{6} z^{-1}+\frac{1}{6} z^{-2}}\)

6. What is the partial fraction expansion of the proper function

X(z)=\(\frac{1}{1-1.5z^{-1}+0.5z^{-2}}\)?

A. \(\frac{2z}{z-1}-\frac{z}{z+0.5}\)

B. \(\frac{2z}{z-1}+\frac{z}{z-0.5}\)

C. \(\frac{2z}{z-1}+\frac{z}{z+0.5}\)

D. \(\frac{2z}{z-1}-\frac{z}{z-0.5}\)

7. What is the partial fraction expansion of

X(z)=\(\frac{1+z^{-1}}{1-z^{-1}+0.5z^{-2}}\)?

A. \(\frac{z(0.5-1.5j)}{z-0.5-0.5j} – \frac{z(0.5+1.5j)}{z-0.5+0.5j}\)

B. \(\frac{z(0.5-1.5j)}{z-0.5-0.5j} + \frac{z(0.5+1.5j)}{z-0.5+0.5j}\)

C. \(\frac{z(0.5+1.5j)}{z-0.5-0.5j} – \frac{z(0.5-1.5j)}{z-0.5+0.5j}\)

D. \(\frac{z(0.5+1.5j)}{z-0.5-0.5j} + \frac{z(0.5-1.5j)}{z-0.5+0.5j}\)

8. What is the partial fraction expansion of X(z)=\(\frac{1}{(1+z^{-1})(1-z^{-1})^2}\)?

A. \(\frac{z}{4(z+1)} + \frac{3z}{4(z-1)} + \frac{z}{2(z+1)^2}\)

B. \(\frac{z}{4(z+1)} + \frac{3z}{4(z-1)} – \frac{z}{2(z+1)^2}\)

C. \(\frac{z}{4(z+1)} + \frac{3z}{4(z-1)} + \frac{z}{2(z-1)^2}\)

D. \(\frac{z}{4(z+1)} + \frac{z}{4(z-1)} + \frac{z}{2(z+1)^2}\)

9. What is the inverse z-transform of

X(z)=\(\frac{1}{1-1.5z^{-1}+0.5z^{-2}}\) if ROC is |z|>1?

A. (2-0.5n)u(n)

B. (2+0.5n)u(n)

C. (2n-0.5n)u(n)

D. None of the mentioned

10. What is the inverse z-transform of

X(z)=\(\frac{1}{1-1.5z^{-1}+0.5z^{-2}}\) if ROC is |z|<0.5?

A. [-2-0.5n]u(n)

B. [-2+0.5n]u(n)

C. [-2+0.5n]u(-n-1)

D. [-2-0.5n]u(-n-1)