Stability Condition of a Discrete-Time LTI System Thu,S< implies v[n]≤B,<∞ indicating that yn is also bounded To prove the converse, assume that yn]is bounded, i. e,y川l≤B Consider the input given by xm=/Sm1-m)ifh-nl≠0 K fh[-n」]=0 Copyright C 2001, S.K. MitraCopyright © 2001, S. K. Mitra 3 Stability Condition of a Discrete-Time LTI System • Thus, S < implies indicating that y[n] is also bounded • To prove the converse, assume that y[n] is bounded, i.e., • Consider the input given by  y[n]  By   n By y[ ]     − = − −  = 0 0 , if [ ] sgn( [ ]), if [ ] [ ] K h n h n h n x n