# FIR Differentiator Design

This set of Digital Signal Processing Multiple Choice Questions & Answers (MCQs) focuses on “Design of FIR Differentiators”.

1. How is the frequency response of an ideal differentiator related to the frequency?
a) Inversely proportional
b) Linearly proportional
d) None of the mentioned

2. Which of the following is the frequency response of an ideal differentiator, Hd(ω)?
a) -jω ; -π ≤ ω ≤ π
b) -jω ; 0 ≤ ω ≤ π
c) jω ; 0 ≤ ω ≤ π
d) jω ; -π ≤ ω ≤ π

3. What is the unit sample response corresponding to Hd(ω)?
a) cosπnn
b) sinπnn
c) n.sin πn
d) n.cos⁡ πn

4. The ideal differentiator ahs which of the following unit sample response?
a) Symmetric
b) Anti-symmetric
c) Cannot be explained
d) None of the mentioned

5. If hd(n) is the unit sample response of an ideal differentiator, then what is the value of hd(0)?
a) 1
b) -1
c) 0
d) 0.5

6. In this section, we confine our attention to FIR designs in which h(n)=-h(M-1-n).
a) True
b) False

7. Which of the following is the condition that an differentiator should satisfy?
a) Infinite response at zero frequency
b) Finite response at zero frequency
c) Negative response at zero frequency
d) Zero response at zero frequency

8. Full band differentiators can be achieved with an FIR filters having odd number of coefficients.
a) True
b) False

9. If fp is the bandwidth of the differentiator, then the desired frequency characteristic should be linear in the range of _____________
a) 0 ≤ ω ≤ 2π
b) 0 ≤ ω ≤ 2fp
c) 0 ≤ ω ≤ 2πfp
d) None of the mentioned

10. What is the desired response of the differentiator in the frequency range 2πfp ≤ ω ≤ π?
a) Left unconstrained
b) Constrained to be zero
c) Left unconstrained or Constrained to be zero
d) None of the mentioned

11. What is the weighting function used in the design of FIR differentiators based on the chebyshev approximation criterion?
a) 1/ω
b) ω
c) 1+ω
d) 1-ω

12. The absolute error between the desired response ω and the approximation Hr(ω) decreases as ω varies from 0 to 2πfp.
a) True
b) False

13. Which of the following is the important parameter in a differentiator?
a) Length
b) Bandwidth
c) Peak relative error
d) All of the mentioned

14. In this section, we confine our attention to FIR designs in which h(n)=h(M-1-n).
a) True
b) False

15. What is the maximum value of fp with which good designs are obtained for M odd?
a) 0.25
b) 0.45
c) 0.5
d) 0.75