Stability Condition of a Discrete-Time LTI System where sgn(c)=+l ifc>0 and sgn(c)=-1 fc<0andK≤1 Note: Since xl叫]≤1,{x]} is obviously bounded For this input, yn] at n=0 is y0]=∑gn(]=S≤B,< k Therefore, y[n]<B, implies S< oo Copyright C 2001, S K MitraCopyright © 2001, S. K. Mitra 4 Stability Condition of a Discrete-Time LTI System where sgn(c) = +1 if c > 0 and sgn(c) = if c < 0 and • Note: Since , {x[n]} is obviously bounded • For this input, y[n] at n = 0 is • Therefore, implies S < −1 K 1 n By y[ ]   x[n] 1   =− = = k y[0] sgn(h[k])h[k] S  By  