Question

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
1. |α| < 1
2. |α| = 1
3. |α| > 1
4. |α| < 3/2

Answer 1

Correct Answer - Option 1 : |α| < 1

y[n] = α y[n - 1] + x [n]

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