Question

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

I have been asked this question in an interview.

Origin of the question is Design of FIR Differentiators in section Digital Filters Design of Digital Signal Processing

Answer 1

Correct answer is (d) Zero response at zero frequency

To explain I would say: 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.