1. Which of the following justifies the linearity property of z-transform?[x(n)↔X(z)].

A. x(n)+y(n) ↔ X(z)Y(z)

B. x(n)+y(n) ↔ X(z)+Y(z)

C. x(n)y(n) ↔ X(z)+Y(z)

D. x(n)y(n) ↔ X(z)Y(z)

2. What is the z-transform of the signal x(n)=[3(2n)-4(3n)]u(n)?

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

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

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

D. None of the mentioned

3. What is the z-transform of the signal x(n)=sin(jω0n)u(n)?

A. \(\frac{z^{-1} sin\omega_0}{1+2z^{-1} cos\omega_0+z^{-2}}\)

B. \(\frac{z^{-1} sin\omega_0}{1-2z^{-1} cos\omega_0-z^{-2}}\)

C. \(\frac{z^{-1} cos\omega_0}{1-2z^{-1} cos\omega_0+z^{-2}}\)

D. \(\frac{z^{-1} sin\omega_0}{1-2z^{-1} cos\omega_0+z^{-2}}\)

4. According to the Time-shifting property of the z-transform, if X(z) is the z-transform of x(n) then what is the z-transform of x(n-k)?

A. zkX(z)

B. z-kX(z)

C. X(z-k)

D. X(z+k)

5. What is the z-transform of the signal defined as x(n)=u(n)-u(n-N)?

A. \(\frac{1+z^N}{1+z^{-1}}\)

B. \(\frac{1-z^N}{1+z^{-1}}\)

C. \(\frac{1+z^{-N}}{1+z^{-1}}\)

D. \(\frac{1-z^{-N}}{1-z^{-1}}\)

6. If X(z) is the z-transform of the signal x(n) then what is the z-transform of anx(n)?

A. X(az)

B. X(az-1)

C. X(a-1z)

D. None of the mentioned

7. If the ROC of X(z) is r1<|z|<r2, then what is the ROC of X(a-1z)?

A. |a|r1<|z|<|a|r2

B. |a|r1>|z|>|a|r2

C. |a|r1<|z|>|a|r2

D. |a|r1>|z|<|a|r2

8. What is the z-transform of the signal x(n)=an(sinω0n)u(n)?

A.\(\frac{az^{-1} sin\omega_0}{1+2 az^{-1} cos\omega_0+a^2 z^{-2}}\)

B.\(\frac{az^{-1} sin\omega_0}{1-2 az^{-1} cos\omega_0- a^2 z^{-2}}\)

C.\(\frac{(az)^{-1} cos\omega_0}{1-2 az^{-1} cos\omega_0+a^2 z^{-2}}\)

D.\(\frac{az^{-1} sin\omega_0}{1-2 az^{-1} cos\omega_0+a^2 z^{-2}}\)

9. If X(z) is the z-transform of the signal x(n), then what is the z-transform of the signal x(-n)?

A. X(-z)

B. X(z-1)

C. X-1(z)

D. None of the mentioned

10. X(z) is the z-transform of the signal x(n), then what is the z-transform of the signal nx(n)?

A. \(-z\frac{dX(z)}{dz}\)

B. \(z\frac{dX(z)}{dz}\)

C. \(-z^{-1}\frac{dX(z)}{dz}\)

D. \(z^{-1}\frac{dX(z)}{dz}\)

11. What is the z-transform of the signal x(n)=nanu(n)?

A. \(\frac{(az)^{-1}}{(1-(az)^{-1})^2}\)

B. \(\frac{az^{-1}}{(1-(az)^{-1})^2}\)

C. \(\frac{az^{-1}}{(1-az^{-1})^2}\)

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

12. Sampling rate conversion by the rational factor I/D is accomplished by what connection of interpolator and decimator?

A. Parallel

B. Cascade

C. Convolution

D. None of the mentioned

13. Which of the following has to be performed in sampling rate conversion by rational factor?

A. Interpolation

B. Decimation

C. Either interpolation or decimation

D. None of the mentioned

14. Which of the following operation is performed by the blocks given in the figure below?

A. Sampling rate conversion by a factor I

B. Sampling rate conversion by a factor D

C. Sampling rate conversion by a factor D/I

D. Sampling rate conversion by a factor I/D

15. The Nth root of unity WN is given as _____________

A. ej2πN

B. e-j2πN

C. e-j2π/N

D. ej2π/N