Question

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

(a) \(\frac{cos⁡πn}{n}\)

(b) \(\frac{sin⁡πn}{n}\)

(c) n.sin πn

(d) n.cos⁡ πn

I had been asked this question during an online interview.

My enquiry is from Design of FIR Differentiators topic in chapter Digital Filters Design of Digital Signal Processing

Answer 1

Right answer is (a) \(\frac{cos⁡πn}{n}\)

For explanation I would say: 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)=\(\frac{cos⁡πn}{n}\).