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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⁡ πnI 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»

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)=\(\frac{cos⁡πn}{n}\).



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