Question

What is the unit sample response of the m^th filter?

(a) hm(0)=0 and hm(k)=αm(k), k=1,2…m

(b) hm(k)=αm(k), k=0,1,2…m(αm(0)≠1)

(c) hm(0)=1 and hm(k)=αm(k), k=1,2…m

(d) none of the mentioned

I got this question in final exam.

The query is from Structures for FIR Systems topic in section Discrete Time Systems Implementation of Digital Signal Processing

Answer 1

Correct answer is (c) hm(0)=1 and hm(k)=αm(k), k=1,2…m

The best explanation: We know that Hm(z)=Am(z) and Am(z) is a polynomial whose equation is given as Am(z)=\(1+\sum_{k=1}^m α_m (k)z^{-k}\), m≤1 and A0(z)=1

A0(z)=1 => hm(0)=1 and Am(z)=\(\sum_{k=1}^m α_m (k)z^{-k}\)(m≤1)=> hm(k)=αm(k) for k=1,2…m.