![The input π₯[π] and output π¦[π] of a discrete-time system are related as](https://www.gkseries.com/blog/wp-content/uploads/2023/08/The-input-π₯π-and-output-π¦π-of-a-discrete-time-system-are-related-as-.jpg)
Q. The input π₯[π] and output π¦[π] of a discrete-time system are related as π¦[π] = πΌπ¦[π β 1] + π₯[π]. The condition on πΌ for which the system is Bounded-Input Bounded-Output (BIBO) stable is
(A) |πΌ| < 1
(B) |πΌ| = 1
(C) |πΌ| > 1
(D) |πΌ| < 3/2
Ans: |πΌ| < 1
Sol:
y[n] = Ξ± y[n β 1] + x [n]
The given system is BIBO stable for |Ξ±| < 1