# 44. The input-output relationship of a causal ...

44. The input-output relationship of a causal stable LTI system is given as $y[n]=\alpha y[n-1]+\beta x[n]$  If the impulse response h[n] of this system satisfies the condition $\Sigma^\infty_{n=0}h[n]=2$, the relationship between α and β is

(A) α = 1−β /2

(B) α = 1+β/2

(C) α = 2β

(D) α = −2β

Hint:
Explanation:

Discuss the solution.