Stability Condition of a Discrete-Time LTI System Proof: Assume hn] is a real sequence Since the input sequence x[n]is bounded we ave xl≤Bx<∞ Therefore y小=∑m-≤∑klnk1 k k ≤Bx∑k]=B k=-o Copyright C 2001, S.K. MitraCopyright © 2001, S. K. Mitra 2 Stability Condition of a Discrete-Time LTI System • Proof: Assume h[n] is a real sequence • Since the input sequence x[n] is bounded we have • Therefore x[n]  Bx   y[n] h[k]x[n k] h[k] x[n k] k k =  −   −  =−  =− x k  Bx  h k = B  =− [ ] S