Correct Option: A

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