# Digital Filters Round Off Effects

This set of Digital Signal Processing Multiple Choice Questions & Answers (MCQs) focuses on “Round Off Effects in Digital Filters”.

1. The quantization inherent in the finite precision arithmetic operations render the system linear.
a) True
b) False

2. In recursive systems, which of the following is caused because of the nonlinearities due to the finite-precision arithmetic operations?
a) Periodic oscillations in the input
b) Non-Periodic oscillations in the input
c) Non-Periodic oscillations in the output
d) Periodic oscillations in the output

3. The oscillations in the output of the recursive system are called as ‘limit cycles’.
a) True
b) False

4. Limit cycles in the recursive are directly attributable to which of the following?
a) Round-off errors in multiplication
c) Both of the mentioned
d) None of the mentioned

5. What is the range of values called as to which the amplitudes of the output during a limit cycle ae confined to?
a) Stop band
b) Pass band
c) Live band
.

6. Zero input limit cycles occur from non-zero initial conditions with the input x(n)=0.
a) True
b) False

7. Which of the following is true when the response of the single pole filter is in the limit cycle?
a) Actual non-linear system acts as an equivalent non-linear system
b) Actual non-linear system acts as an equivalent linear system
c) Actual linear system acts as an equivalent non-linear system
d) Actual linear system acts as an equivalent linear system

8. Which of the following expressions define the dead band for a single-pole filter?
a) |v(n-1)| ≥ (1/2).2−b1+|a|
b) |v(n-1)| ≥ (1/2).2−b1−|a|
c) |v(n-1)| ≤ (1/2).2−b1−|a|
d) None of the mentioned

.

9. What is the dead band of a single pole filter with a pole at 1/2 and represented by 4 bits?
a) (-1/2,1/2)
b) (-1/4,1/4)
c) (-1/8,1/8)
d) (-1/16,1/16)

10. The limit cycle mode with zero input, which occurs as a result of rounding the multiplications, corresponds to an equivalent second order system with poles at z=±1.
a) True
b) False

11. What is the necessary and sufficient condition for a second order filter that no zero-input overflow limit cycles occur?
a) |a1|+|a2|=1
b) |a1|+|a2|>1
c) |a1|+|a2|<1
d) None of the mentioned

12. An effective remedy for curing the problem of overflow oscillations is to modify the adder characteristic.
a) True
b) False

13. What is the dead band of a single pole filter with a pole at 3/4 and represented by 4 bits?
a) (-1/2,1/2)
b) (-1/8,1/8)
c) (-1/4,1/4)
d) (-1/16,1/16)