# Rational Z Transform

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) anu(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)=anu(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)nu(n)
b) 2(0.5)nu(n)
c) 0.5(2)nu(-n)
d) 2(0.5)nu(-n)