Correct Option: A

The difference equation is

y[n] =	1	x[n] +	1	y[n - 1] -	1	y[n - 2]
	4		4		2

= 4y[n] – y [n – 1] + 2y [n – 2]
= x[n]
Eigen values are
4α² – α + 2 = 0,
⇒ α₁₂ = 0.125 ± j0. 696
Its magnitude are less than 1. Thus system is stable.

y[n] =	1	(x[n] + y[n – 1] + 2y [n – 2])
	4

Response at time, n, depends on the excitation at time n and the responses at previous time. It does not depend on any future values of the excitation.