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

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

a) True

b) False

2. What is the desired response of the differentiator in the frequency range 2πf_{p} ≤ ω ≤ π?

a) Left unconstrained

b) Constrained to be zero

c) Left unconstrained or Constrained to be zero

d) None of the mentioned

3. 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

4. Which of the following is the important parameter in a differentiator?

a) Length

b) Bandwidth

c) Peak relative error

d) All of the mentioned

5. 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

6. If h_{d}(n) is the unit sample response of an ideal differentiator, then what is the value of h_{d}(0)?

a) 1

b) -1

c) 0

d) 0.5

7. How is the frequency response of an ideal differentiator related to the frequency?

a) Inversely proportional

b) Linearly proportional

c) Quadratic

d) None of the mentioned

8. Which of the following is the frequency response of an ideal differentiator, H_{d}(ω)?

a) -jω ; -π ≤ ω ≤ π

b) -jω ; 0 ≤ ω ≤ π

c) jω ; 0 ≤ ω ≤ π

d) jω ; -π ≤ ω ≤ π

9. Full band differentiators can be achieved with an FIR filters having odd number of coefficients.

a) True

b) False

10. In this section, we confine our attention to FIR designs in which h(n)=h(M-1-n).

a) True

b) False

11. What is the maximum value of f_{p} with which good designs are obtained for M odd?

a) 0.25

b) 0.45

c) 0.5

d) 0.75

12. If f_{p} 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 ≤ 2f_{p}

c) 0 ≤ ω ≤ 2πf_{p}

d) None of the mentioned

13. The absolute error between the desired response ω and the approximation H_{r}(ω) decreases as ω varies from 0 to 2πf_{p}.

a) True

b) False

14. What is the unit sample response corresponding to H_{d}(ω)?

a) cosπnn

b) sinπnn

c) n.sin πn

d) n.cos πn

15. 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