Question

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

This question was addressed to me in my homework.

My question is based upon Design of FIR Differentiators in section Digital Filters Design of Digital Signal Processing

Answer 1

Right answer is (b) Anti-symmetric

Easy explanation: We know that the unit sample response of an ideal differentiator is given as

h(n)=\(\frac{cos⁡πn}{n}\)

So, we can state that the unit sample response of an ideal differentiator is anti-symmetric because cos⁡πn is also an anti-symmetric function.