The input 𝑥[𝑛] and output 𝑦[𝑛] of a discrete-time system are related as

Q. The input 𝑥[𝑛] and output 𝑦[𝑛] of a discrete-time system are related as 𝑦[𝑛] = 𝛼𝑦[𝑛 − 1] + 𝑥[𝑛]. The condition on 𝛼 for which the system is Bounded-Input Bounded-Output (BIBO) stable is

(A) |𝛼| < 1

(B) |𝛼| = 1

(C) |𝛼| > 1

(D) |𝛼| < 3/2

Ans: |𝛼| < 1

Sol:

y[n] = α y[n – 1] + x [n]

The given system is BIBO stable for |α| < 1