Question

The general linear constant coefficient difference equation characterizing an LTI discrete time system is?

(a) y(n)=-\(\sum_{k=1}^N a_k y(n-k)+\sum_{k=0}^N b_k x(n-k)\)

(b) y(n)=-\(\sum_{k=0}^N a_k y(n-k)+\sum_{k=0}^N b_k x(n-k) \)

(c) y(n)=-\(\sum_{k=1}^N a_k y(n)+\sum_{k=0}^N b_k x(n) \)

(d) None of the mentioned

I had been asked this question during an internship interview.

I'm obligated to ask this question of Structures for Realization of Discrete Time Systems topic in portion Discrete Time Systems Implementation of Digital Signal Processing

Answer 1

Correct choice is (a) y(n)=-\(\sum_{k=1}^N a_k y(n-k)+\sum_{k=0}^N b_k x(n-k)\)

For explanation: We know that, the general linear constant coefficient difference equation characterizing an LTI discrete time system is given by the expression

y(n)=-\(\sum_{k=1}^N a_k y(n-k)+\sum_{k=0}^N b_k x(n-k)\)