This set of Digital Signal Processing Multiple Choice Questions & Answers (MCQs) focuses on “Rational Z Transform”.

1. What are the values of z for which the value of X(z)=0?

a) Poles**b) Zeros**

c) Solutions

d) None of the mentioned

2. What are the values of z for which the value of X(z)=∞?**a) Poles**

b) Zeros

c) Solutions

d) None of the mentioned

3. If X(z) has M finite zeros and N finite poles, then which of the following condition is true?

a) |N-M| poles at origin(if N>M)

b) |N+M| zeros at origin(if N>M)

c) |N+M| poles at origin(if N>M)**d) |N-M| zeros at origin(if N>M)**

4. If X(z) has M finite zeros and N finite poles, then which of the following condition is true?**a) |N-M| poles at origin(if N < M)**

b) |N+M| zeros at origin(if N < M)

c) |N+M| poles at origin(if N < M)

d) |N-M| zeros at origin(if N < M)

5. Which of the following signals have a pole-zero plot as shown below?

a) a.u(n)

b) u(an)**c) a ^{n}u(n)**

d) none of the mentioned

6. Which of the following signals have a pole-zero plot as shown below?(Let M=8 in the figure)

a)

x(n)=an, 0≤n≤8 =0, elsewhere

**b)**

x(n)=an, 0≤n≤7 =0, elsewhere

c)

x(n)=a-n, 0≤n≤8 =0, elsewhere

d)

x(n)=a-n, 0≤n≤7 =0, elsewhere

7. The z-transform X(z) of the signal x(n)=a^{n}u(n) has:

a) One pole at z=0 and one zero at z=a

b) One pole at z=0 and one zero at z=0

c) One pole at z=a and one zero at z=a**d) One pole at z=a and one zero at z=0**

8. What is the nature of the signal whose pole-zero plot is as shown?

a) Rising signal

b) Constant signal**c) Decaying signal**

d) None of the mentioned

9. What are the values of z for which the value of X(z)=0?

a) Poles**b) Zeros**

c) Solutions

d) None of the mentioned

10. If Y(z) is the z-transform of the output function, X(z) is the z-transform of the input function and H(z) is the z-transform of system function of the LTI system, then H(z)=?**a) Y(z)X(z)**

b) X(z)Y(z)

c) Y(z).X(z)

d) None of the mentioned

11. What is the system function of the system described by the difference equation y(n)=0.5y(n-1)+2x(n)?

a) 21+0.5z−1

b) 0.51+2z−1

c) 0.51−2z−1**d) 21−0.5z−1**

12. What is the unit sample response of the system described by the difference equation y(n)=0.5y(n-1)+2x(n)?

a) 0.5(2)^{n}u(n)**b) 2(0.5) ^{n}u(n)**

c) 0.5(2)

^{n}u(-n)

d) 2(0.5)

^{n}u(-n)