Stability Condition of a Discrete-Time LT System Proof: Assume h[n] is a real sequence Since the input sequence xn is bounded we have x{]≤Bx< Therefore yn=∑m-≤∑k]xn-k k Bx∑Hk=BxS k 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