1. 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

Answer: B

An ideal differentiator has a frequency response that is linearly proportional to the frequency.

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

Answer: D

An ideal differentiator is defined as one that has the frequency response
Hd(ω)= jω ; -π ≤ ω ≤ π.

3. What is the unit sample response corresponding to Hd(ω)?

A. cosπn/n
B. sinπn/n
C. n.sin πn
D. n.cos πn

Answer: A

We know that, for an ideal differentiator, the frequency response is given as
Hd(ω)= jω ; -π ≤ ω ≤ π
Thus, we get the unit sample response corresponding to the ideal differentiator is given as
h(n)=cosπn/n

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

Answer: B

We know that the unit sample response of an ideal differentiator is given as
cosπn/n
So, we can state that the unit sample response of an ideal differentiator is anti-symmetric because cosπn is also an anti-symmetric function.

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

Answer: C

Since we know that the unit sample response of an ideal differentiator is anti-symmetric,
=>hd(0)=0.

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

A. True
B. False

Answer: A

In view of the fact that the ideal differentiator has an anti-symmetric unit sample response, we shall confine our attention to FIR designs in which h(n)=-h(M-1-n).

7. Which of the following is the condition that a 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

Answer: D

For an FIR filter, when M is odd, the real-valued frequency response of the FIR filter Hr(ω) has the characteristic that Hr(0)=0. A zero response at zero frequency is just the condition that the differentiator should satisfy.

8. Full band differentiators can be achieved with an FIR filter having an odd number of coefficients.

A. True
B. False

Answer: B

Full band differentiators cannot be achieved with FIR filters having an odd number of coefficients, since Hr(π)=0 for M odd.

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

Answer: C

In most cases of practical interest, the desired frequency response characteristic need only be linear over the limited frequency range 0 ≤ ω ≤ 2πfp, where fp is the bandwidth of the differentiator.

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

Answer: C

In the frequency range 2πfp ≤ ω ≤ π, the desired response may be either left unconstrained or constrained to be zero.