More roc properties (3)Ifxn] is of finite duration, then the roc is the entire z-plane except possibly at z=0 and/or2=oo Why? X() ∑ rnz Examples COunterpart 6mn]←1 ROC all z|ot)←1 roC all s ROC2≠0|0t-T) e-e{s}≠ 6+1]←2ROC2≠0∞o6(+1)←cTe(}≠
More ROC Properties (3) If x[n] is of finite duration, then the ROC is the entire z-plane, except possibly at z = 0 and/or z = ∞. Why? Examples: CT counterpart
ROC Properties Continued (4 )Ifx[n] is a right-Sided sequence, and if ==ro is in the roC, then all finite values of z for which =>ro are also in the roc ●●鲁● ro 1 TTIITTTTTT. converges faster th n r1",r1>r0 ∑ml P99●99
ROC Properties Continued (4) If x[n] is a right-sided sequence, and if | z| = r o is in the ROC, then all finite values of z for which | z| > r o are also in the ROC